A Ring Imaging Cherenkov Detector
and
The Photoproduction Reaction gp wpp .
by
Julian James Bunn
September, 1983
A Thesis submitted for the degree of Ph.D. in the Faculty of Pure Science, The University of Sheffield.
TABLE OF CONTENTS
 
 
                                                                Page No.
 
Acknowledgements......................................................V

Abstract.............................................................VI

PART I : A RING IMAGING CHERENKOV DETECTOR
Chapter I    The Technique of Ring Imaging Cherenkov Detectors
         1.1 Introductory Background to Cherenkov Detectors...........1
         1.2 Ring Imaging : Some Theoretical Aspects..................3
         1.3 Sources of Error in the Determination of qc..............6
             a) Photon Localisation...................................8
             b) Dispersion...........................................10
             c) Energy Loss in the Medium............................12
             d) Multiple Coulomb Scattering..........................13
             e) Optical Aberrations..................................15
             f) Diffraction..........................................15
             References..............................................17

Chapter II   An Experimental Ring Imaging Detector
         2.1 Introduction............................................18
         2.2 The Test Beam C13.......................................18
         2.3 Experimental Layout.....................................19
             a) The Radiator Vessels and Mirror......................21
             b) Radiator and Photoionising Gas Systems...............21
         2.4 The Time Projection Chamber (TPC).......................23
         2.5 On-Line Data Acquisition................................25
             a) Trigger Logic........................................25
             b) Event Description....................................26
             c) On-Line Software.....................................27
             References..............................................29

Chapter III  An Analysis of the Experimental Data
         3.1 Introduction............................................30
         3.2 Straight Ionisation Tracks in the TPC...................31
         3.3 Efficiency Scan of the Drift Gap........................32
         3.4 Cherenkov Rings in the TPC..............................33
         3.5 Interpretation of Results...............................38
             References..............................................42
PART II : AN ANALYSIS OF THE PHOTOPRODUCTION REACTION
g p w p p
Chapter IV   Vector Meson Photoproduction
         4.1 Introduction............................................43
         4.2 Mesonic Currents from the Photon........................43
         4.3 Meson Spectroscopy and the Naive Quark Model............45
         4.4 The Vector Mesons.......................................47
         4.5 The wp State : Experimental Situation...................48
             References..............................................51

Chapter V    The Experimental Investigation of Vector Meson States
in Photoproduction
         5.1 Introduction............................................52
         5.2 The Photon Beam and Tagging System......................52
         5.3 The OMEGA Spectrometer and Associated Detectors.........55
             a) The Hydrogen Target..................................55
             b) The OMEGA MWPCs......................................56
c) The Cherenkov Counter and
                Scintillation Hodoscopes.............................57
 
             d) The Photon Detector..................................58
             e) The Electron Positron Pair Veto Counters.............59
         5.4 Formation of the Experimental Trigger...................61
         5.5 Offline Event Reconstruction and Simulation Software....63
             a) TRIDENT..............................................64
             b) JULIET...............................................65
             c) GEORGE...............................................66
             d) MAP..................................................66
             References..............................................68

Chapter VI   Observation of the State wp in p+p-pp(p)
         6.1 Introduction............................................69
         6.2 Selection of the Data...................................69
         6.3 Background Subtraction..................................70
         6.4 Overall Features of the Selected Data...................71
         6.5 Simulation of the Experimental Acceptance...............72
             References..............................................76

Chapter VII  A Spin-Parity Analysis of wp
         7.1 Introduction............................................77
         7.2 Acceptance Correction of the Experimental Data..........78
         7.3 Helicity Formalism and Decay Angular Distributions......79
         7.4 Model Independent Fits to the Data Moments..............81
         7.5 Model Dependent Fits to the Data Moments................82
             a) Details of the Fitting Method........................83
             References..............................................87

Chapter VIII Results and Overall Conclusions
         8.1 Introduction............................................88
         8.2 Spin Parity Analysis using Decay Angular Distributions..88
         8.3 Results from the Model Independent Fits.................89
         8.4 Results from the Model Dependent Fits...................92
         8.5 Summary and Conclusions.................................98
             References..............................................100

Appendix A.1 Simulation of a subset of the wp Data..................101
             a) Introduction.........................................101
             b) Software Framework...................................101
             c) Generation of the Events.............................102
             d) Particle Tracking through the Detectors..............103
             e) Simulation of the JULIET Software....................104
             f) Comparison of Real and Simulated Data................106
             References..............................................107

Appendix A.2 Software selection of the total wp data................108

Appendix A.3 Expressions for the Moments (1).........................109

Appendix A.4 Expressions for the Moments (2).........................110

Appendix A.5 Formalism used in the Model Dependent Fitting Program...111
ACKNOWLEDGEMENTS

I would like to thank the following people for helping me in one way or another over the last three years.

My supervisor, Professor W. Galbraith, for his good-humoured assistance and advice throughout my period of research at the University of Sheffield, and at C.E.R.N.

My parents, for their continuous warm support and encouragement.

My colleague, Dr. John V. Morris, for numerous discussions, and for remarkably clear explanations of the wp analysis.

Dr.Peter Sharp and Dr.Tom Ypsilantis, for instilling some of their own enthusiasm for the Ring Imaging technique in me.

Dr. Jean Richardson, for making the last months of my research particularly enjoyable.

Drs. Richard McClatchey and Colin Paterson, for conversations both on high energy physics, and largely off it, which I consistently found enjoyable.

The following members of the EGAMMA collaboration, who helped me in various ways: Drs. George Lafferty, Glenn Patrick, Martyn Davenport, John Lane and John A.G. Morris.

The S.E.R.C. for the provision of a research studentship, and C.E.R.N. for the use of its superb facilities.

ABSTRACT

The work described in this thesis covers two distinct aspects of high energy particle physics, and was undertaken mainly at the C.E.R.N. laboratory, Geneva, Switzerland.

In the first part of the thesis, an experimental investigation of the properties of a detector based on the emission of Cherenkov light in a gaseous radiating medium (argon) is described. A charged particle beam of selected momentum in the range 4-18 GeV/c was allowed to pass through the radiating medium. The Cherenkov light so produced was collected by a spherical mirror and brought to a focus as a ring image in the focal plane within the active area of a Time Projection Chamber. Electrons created in the photoionisation of a sensitive gas in this chamber drifted to a plane of 48 wires, the signals from which were decoded to reconstruct the ring image. The results clearly show the capability of the detector for distinguishing between different charged particle types in the beam.

The second part of the thesis is concerned with the study of the photoproduction of the so-called higher vector meson states using a plane-polarised photon beam, of well measured energies within the range 20-70 GeV, which interacted in a target of liquid hydrogen. This target was situated inside a region of magnetic field (1.8 Tesla) which was produced by the Omega magnet. Also within the magnetic field volume was a system of MultiWire Proportional Chambers, which afforded the reconstruction of the charged particle tracks produced in the interaction and the location of the interaction vertex within the target. Neutral pions were detected by identifying photons from the decay p gg in a large lead-glass array. An electronic trigger selected events of the type gp p+p-pp(p) where the symbol (p) signifies that the recoil proton was sometimes detected. Events of this type were recorded onto magnetic tape, and subsequently analysed offline. The analysis presented in the thesis refers to the specific channel gp wp(p) p+p-pp(p), where the w is seen in its p+p-p decay mode, the total cross-section for which is shown to be 0.86 0.27 mb. A determination is made of the spin-parity content of the wp state, using both a model dependent and also a model independent fit to the double moments of the sequential decay (X w + p, w p+p-p). The results indicate that an enhancement in the mass spectrum of wp events occurs at @1.21 GeV/c, and is shown to be due to the dominant presence of the Jp=1+ B(1.23) meson. The results also show that the data are consistent with the presence of a small contribution from a 1- signal, which may be interpreted either as the tail of the r(0.77), or as a resonance above wp threshold, or as the result of some other process, such as the Deck mechanism.

Chapter I The Technique of Ring Imaging Cherenkov Detectors

1.1 Introductory Background to Cherenkov Detectors

From a consideration of Maxwell's equations, Heaviside [1] predicted the possibility of observing a special form of radiation when a charged particle passed through matter. Nearly sixty years later, in 1934, Cherenkov and Vavilov [2] described such an effect, where the nature of the light seen depended on the gross structure of the medium and on the momentum of the incident particle. Tamm and Frank [3] developed the classical theory which accounts for this light, now referred to as Cherenkov radiation.

The time variation of the polarisation induced by the passage of a charged particle through matter leads in principle to a radiation field at some point distant from the particle's instantaneous position. For slowly moving particles, this field has global symmetry, and, as a result of interference between the various radiating elements of the medium, no net field is observed some distance away. However, for fast particles the polarisation is axially asymmetric, and at a threshold velocity where the particle velocity, b, exceeds that of light in the medium;

b = c / n         (1.1)
(n is the refractive index), coherence between the induced polarisation at different points along the particle trajectory is achieved. This gives rise to emission of light along the direction of coherence (Figure 1.1).

The radiation is emitted in a forward cone of half-angle qc given by;

cosqc = 1 / bn       (1.2)
where b is the ratio of the particle velocity in the medium to the speed of light in vacuo. Light is emitted from all points along the particle's path, the electric vector of the radiation being in a direction perpendicular to the surface of the Cherenkov cone.

The use of this effect in experimental high energy physics is in determining the velocity of a charged particle and, in some cases, its direction through a detector. Cherenkov detectors in general consist of some transparent medium (either gaseous, liquid or solid) in which the particles produce Cherenkov radiation, and some form of electronic detector which responds to this light. In most applications to date the electronic detector has been a photomultiplier.

From Equation 1.2 it is seen that no light is emitted unless

b > 1 / n       (1.3)
and this determines a lower limit on the particle velocity for detection in a given medium. Detectors which respond to light from particles with b above this threshold are termed 'threshold' Cherenkov detectors. Those which detect radiation over a small range of cone angles qc are called 'differential' Cherenkov detectors. Finally, the 'ring imaging' Cherenkov detector preserves the spatial information from the photons emitted around the light cone by detecting the spatial position of each photon in two dimensions.

For a long time it was impossible to detect Cherenkov rings from single particles. In 1963, Butslov[4] et al., photographed the first rings from single cosmic ray particles. However, the low quality of the images, which was due to distortions, prevented a reliable estimate of the ring size to be made. At Princeton in the same year, Poultney [5] et al. detected whole rings from a negative pion beam of momentum 820 MeV/c. The experiment used a system of lenses which focussed the radiation to a ring of radius approximately 90 mm, which was then detected by a photomultiplier. Three years later, in 1966, Iredale [6] et al., detected rings produced by radiation from protons of momentum 5.8 GeV/c in the NIMROD machine. In that experiment a least squares fit to at least ten detected photons around a ring was made to determine the ring radius. By this method the Cherenkov angle qc was determined to within 9 mrad.

The attraction of these experiments was that both the velocity and the direction of the particle were measured. Since then, much interest has been aroused in the possibility of extracting enough information from Cherenkov rings to make threshold Cherenkov counters obsolete, except for relatively crude particle identification.

A description of the construction and testing of a small ring imaging Cherenkov detector constitutes part of this thesis. The remainder of this chapter is concerned with the theoretical background of the technique.

1.2 Ring Imaging : Some theoretical aspects.

A ring imaging Cherenkov detector essentially measures the angles of emission of the photons around the Cherenkov light cone and the intersection at some plane of this cone. Figure 1.2 shows a simple ring imaging detector. Photons emitted by the charged particle while travelling through the radiator vessel are reflected at the spherical mirror to form a focussed ring at the plane of the detector D. From the photon positions a determination may be made of the particle direction; for single particles this requires at least three detected photons. Since the photon positions in general are affected by the experimental resolution, there is a pattern recognition problem in determining the size of the ring or other conic section detected. However, the quantity of information extracted for each detected particle is larger, for example, than that for a threshold Cherenkov detector.

The photons produced in the radiator vessel are emitted uniformly along the particle trajectory at the angle qc, Equation 1.2. These photons are focussed by the spherical mirror of focal length f to a ring image of radius R at the focal surface;

R = f tanqc       (1.4)
In the present example the focal surface is approximated to the detector plane D. The two-dimensional position of each photon on the ring must then be measured to determine the ring size and position to the best attainable accuracy. In practice this can be achieved by converting the photons to photoelectrons in some suitable gas mixture, then causing these electrons to drift in an electric field and enter a multiwire proportional chamber (MWPC). Within this chamber the avalanche at a wire, caused by an impinging photoelectron, determines the position of the initial photon in one dimension (this is simply the wire address). From the overall time taken for the photon to convert, the produced photoelectron to drift and the avalanche to cause a pulse on the hit wire, and a knowledge of the drift velocity in the gas, the other space co-ordinate of the Cherenkov photon can be determined.

The Tamm-Frank [3] expression for the Cherenkov radiation loss per unit length of radiator is;

dW     e w2                1                                
 =      (1  ).wdw        (1.5) 



dl     c w& s'1.         n(w)b 



where n(w) denotes that the medium may be dispersive. Substituting w=2pc/R above gives;
dW                                 1     dR            
 = 4pe (1  )              



dl                             nb    R            
and it is seen that the intensity of radiation is inversely proportional to the third power of the wavelength. Thus Cherenkov light is mainly concentrated in the short wavelength region of the spectrum. Since;
W = NphT         (1.6)
where Npis the number of photons emitted, h is Planck's constant and T the photon frequency, Npcan be determined for a given length of radiator. The proportion of these photons actually detected by the apparatus per unit energy range is given by;
             LA                                                
N = 2p  sinqc   dEp                    
             hc                                                
Here L is the length of radiator in metres, A is the fine structure constant (= 1/137), Epis the photon energy, and is the energy dependent acceptance of the apparatus. The factor might, for instance, comprise the quantum efficiency of the photoionising gas, the photon reflection efficiency of a mirror and the transmission factors of any windows in the detector: it is clearly wavelength dependent. The integral must be taken over the range of wavelengths to which the detector is sensitive. Defining Np per unit energy interval as;
         2pA                                                        
Np =    dEp                    (1.7)            
         hc                                                     



then in S.I. units, and per electron volt (eV), Np has the value;
Np = 37000   dEp
and the detected number of photons may be expressed as;
N = NpL sinqc   (1.8)
Np may usefully be thought of as a constant which characterises the efficiency of the detector.

1.3 Sources of error in the determination of qc

From the Cherenkov relation (Equation 1.2) it is deduced that the error in measuring b is related to the r.m.s. errors in qc and n by;

b/b =  {(n/n) + tanqc.qc}
In a particle beam of momentum 10 GeV/c for instance, the values of b for pions, kaons and protons are; b(proton) = 0.9966 b(kaon) = 0.99878 b(pion) = 0.999902 Thus to separate these three types of particle an accuracy b/b of less than one part in 10 is required.

Since b is related to g by;

g = 1 / (1-b)
this accuracy in b corresponds to one in g of;
g/g = b.g    b/b
Hence;
g                                                             



 = gbtanqc qc                         



g                                                                
This equation holds when there is no dispersion or when a measurement is made of g from a single photon. If N photons are detected, then this error is reduced to 1/N of its single photon value, given that the refractive index is constant over the energy range of the detected photons. N is derived from Equation 1.8 by integrating over the energy acceptance of the detector. For a detector with a characteristic Np, and with N photons detected;
g     gbn                                     



 =  qc                (1.9)                
 g     NpL                                                
The angular spread, qc, will comprise contributions from; {a} the accuracy in the localisation of the Cherenkov photons, {b} the dispersion of the radiator medium, {c} the energy loss in the medium, {d} the multiple scattering of the charged particle in the medium, {e} optical aberrations in mirrors, and {f} diffraction due to the finite length of the radiator.

It will be useful (for later purposes) to describe each of these contributions in a little more detail now.

1.3(a) Photon Localisation

Since the multiplicity of Cherenkov photons radiated per particle may be as low as one or two in a given detector, the efficient conversion and detection of such photons is essential. Depending on the event sampling rate required, several methods for detecting single photons in two dimensions exist. At low rates, for example, image-intensifiers may be used [7], as may a charge-coupled-device (CCD)[8] or Time-Projection-Chamber (TPC) [9]. Time Projection Chambers and Charge Coupled Devices are also able to operate at high sampling rates, although in the case of the CCD, the expense of making the device sufficiently large to detect whole rings, or sufficiently good optically to reduce the ring size, is often prohibitive. The TPC, on the other hand, is a well-proven single photon detector in the ring imaging context [10,11,12], and has the advantage of being relatively simple and easy to operate.

TPC operation is discussed in detail below (Chapter 2), and essentially involves the conversion of single photons to photoelectrons, which then drift under the influence of an electric field to enter a Multiwire Proportional Chamber (MWPC), where they are detected spatially (see Figure 1.3). The spatial accuracy and detection efficiency depend upon factors which include the quantum efficiency of the photo-ionising gas, the transmissivity of the windows, the MWPC wire spacing, the frequency at which the TPC is read out electronically, the diffusion constants of the photo-ionising gas and the localisation of the avalanches within the MWPC. The last four points relate to errors in the measured position of each photon.

For an MWPC with inter-wire separation s, the r.m.s. error x in the determination of an avalanche position at a hit wire is given by;

x = s/12
If the chamber is read out electronically every t seconds, and the nominal electron drift velocity in the applied electric field is bd, then the computed drift length y contains an error term;
yeec. = bd t
which holds if the pulse duration is short compared with t. The drift velocity itself contains an error due to electron diffusion. In general, the spatial resolution of drift chambers is mainly limited by density fluctuations in the primary ionisation, and the electron's transverse and longitudinal diffusion over the drift length y. Variations in the characteristics of the avalanches, and in their formation rate, will occur around the MWPC anode wires. Delta rays (see below), together with the gas pressure and ambient temperature can also affect the TPC performance. The r.m.s. displacement y due to diffusion is given by [13];
ydff. = (2Dy/mE)
where D is the diffusion constant, m is the mobility (ms-V-)and E is the applied drift field (Vm-). The quantity D/m is approximately equal to the average vibrational energy of the gas electrons.

The radius of the Cherenkov (detected) ring, given by R = x+y, is determined to within R;

R = 1/R ((xx) + (yy))
x contains the term in s above, and also a term due to the transverse diffusion of the photoelectron in the drift region. To a good approximation the transverse and longitudinal errors due to diffusion may be set equal.
xtt. = s/12 + (2Dx/mE)

ytt. = tbd  + (2Dy/mE)     (1.10)
The error in qc is just R/f, where f is the focal length of the optical system.

1.3(b) Dispersion

In terms of the relative permeability, m, and the relative permittivity, , of a dielectric medium, the refractive index is defined to be;

n = (m.)
With the exception of ferromagnetic materials, and in the vast majority of cases, m deviates from unity by a few parts in 10. defines the constant of proportionality between the electric field in a medium, E, and the polarisation, P;
( - 0).E = P
0 is the permittivity of the vacuum. If an electromagnetic wave of frequency w is incident on the dielectric, then the molecules within the medium undergo forced oscillations. For large values of w the molecules are unable to follow the forcing vibrations, and their contributions to the polarisation field will decrease. The polarisation field P is thus weaker, and is smaller.

By a classical treatment, the polarisation field is considered as being the product of the number of contributing electrons per unit volume and the dipole moments of each. The sizes of the dipole moments vary with the forcing electromagnetic wave. Since n may be expressed in terms of , and hence in terms of w, it is found [14];

                        Nmqe                fjFONT FACE=SYMBOL> 



n(w) = 1 + .      (1.11)
                     0me j (w0.-w+ig jw)
where qeis the electronic charge, Nm is the number of molecules per unit volume, and meis the mass of the electron. The sum is taken over the number of different oscillators j with natural frequencies w0., in the medium. The number of summations and the w0 will change from medium to medium. &jare the damping coefficients, and the fjlabel the oscillator strengths.

Colourless transparent gases have their w0 outside the visible region of the spectrum; this is the reason for such gases being colourless. When w << w0 the refractive index is constant. The refractive index will slowly rise as w approaches one of the regions of resonance, w0.. This is the so-called 'normal' dispersion condition.

The regions in the spectrum around w0 are called the absorption bands of the material. In these areas, dn/dw is negative and the dispersion is termed 'anomalous'.

For many gases at low pressure, and when w is far from w0., n-1 is small, and the approximation

n-1 @ 2(n-1)
holds. Then Equation 1.11 becomes;
            Nme            fjFONT FACE=SYMBOL>                                    
n-1 =        (1.12)             



            20m     w0.-w-igjw        
Nm is proportional to the density of the gas. Figure 1.4 shows the variation of the quantity n-1 for argon at NTP for photon energies in the range 7.5 to 9 eV, this range being the one of interest in the present work.

1.3(c) Energy loss in the medium

The main process by which charged particles lose energy when passing through matter is through Coulomb interactions with atomic electrons. (The loss of energy to nuclei in this way is small by comparison.) The direct removal of electrons from neutral atoms by the incident particle is termed 'primary' ionisation. The knocked-out electrons, if of sufficient energy, may then cause 'secondary' ionisation, such electrons being called 'delta-rays'. Ionisation loss has a minimum at relativistic energies, and to a good approximation is the same for particles of equal charge and velocity.

In addition to ionisation loss, the close encounters between fast charged particles and nuclei result in decelerations with the emission of radiation, and this process, 'bremsstrahlung' (BR), is an important process by which electrons lose energy in matter. The critical energy, c, is usefully defined as the energy at which, in unit length of material, the particle loses the same energy by ionising atoms as it does by radiating. The radiation length, X0, is then defined for energies much larger than c to be the thickness of material which causes a reduction by 1/e of the particle's incident energy. It is found that, for the ionisation part, -dE/dx (the rate of kinetic energy loss in the medium) is independent of particle rest mass, and inversely proportional to b. For BR, -dE/dx is given by;

    dE                                                             



-  = Na W Z f(Z,E)                (1.13) 



    dx                                                             



where W is the total energy of the particle, Na is the number of atoms per unit volume and Z is the charge on the nuclei in the medium. The bremsstrahlung radiation is emitted into a cone of semi-angle q, given by;
         m                                                     



q =                                                      



        m+E                                                     



where m is the particle rest mass. From a knowledge of the rate of energy loss undergone by the particle in traversing the length of the radiator, a determination may be made of the change in Cherenkov angle qc, since b is energy dependent.

1.3(d) Multiple Coulomb Scattering (MCS)

As a charged particle moves through a medium it interacts in the Coulomb field of each nucleus passed. This results in some deviation from the particle's initial direction. Each deviation may be considered as a small angular shift, and several such interactions result in lateral scattering of the particle. In practice, the largest and smallest scattering angles likely to occur are limited by the finite size of the nucleus and the effects of nuclear screening, respectively. Nuclear screening is the reduction of the nuclear Coulomb field at large distances by the presence of the atomic orbital electrons. By treating the scattering process statistically (making the assumption that all deviations are small), the root mean square scattering angle may be expressed as [15];

<q> = 1/2b.(Es/E).(X/Xp)   (1.14)
where X is the length of the medium traversed, Xp the radiation length in the medium, E the total energy of the particle, and Es is given by;
Es= mc.(4p.137)

   = 0.023 GeV

The radiation length, Xp is given by the expression;

1/X0 = 4A (N/A) Z re lne(183 1/Z)
where N is Avogadro's number, A is the atomic mass of the medium, Z is its charge number and re is the classical electron radius. Approximately, the mean square scattering angle per unit radiation length is
<q> = (Es/E)
The contribution to the error in qc is simply twice this value, being, as an example, for a particle of momentum 10 GeV/c (the principal beam momentum used in the detector tests Chapter 2);
qc = 2 (0.023/10) = 10- radians
Thus the total contribution to qc is small when gases at low pressure are used, since linear radiation lengths are considerable in such cases.

1.3(e) Optical Aberrations

In differential and ring imaging Cherenkov detectors the preferred mirrors are spherical. Such mirrors have smaller aberrations and are more easily manufactured than parabolic mirrors. If the radius of the formed image at the focal plane of the detector mirror is R (Equation 1.4), then the radial spread on R due to spherical and coma aberrations, is given by [16];

DR/R = -(1/8).(d/f) + (1/8).(d/f).qc   (1.15)
where d is the diameter of the mirror, and f its focal length. The contribution to the error in qc from the optical aberrations is thus simply DR/f.

1.3(f) Diffraction

Since the observed light in the detector originates from a finite length of radiator, account must be taken of the incoherence of photons from different points along the particle trajectory. The image of a point source of light when focussed by an optical system takes the form of an Airy disc, when viewed through a circular aperture. Often, unless the mirror is of very high quality, the aberrations will mask observation of this disc. However, the width, w, of the central fringe in the Airy disc (where the majority of light is concentrated) can be expressed in terms of the aperture, and the focal length of the system [17];

w = 1.22 R.f/d
where d is the aperture, f the focal length, and R the wavelength of the light. This is manifest as an error in the radius of the focussed ring, R, and may thus be translated to an error in qc;
qc(Airy) = 1.22 R/(bnd)
This takes a maximum value when the Cherenkov light is just collected by the optical system, that is when qc = d/(2L). Hence;
qc(Airy)mx. = 1.22 R/(2Lqc)  (1.16)
which is of order 10- m-.

In conclusion, the total error qc on the Cherenkov angle is given by the sum in quadrature of the individual errors discussed above;

(qc) = (qg)+(qd)+(qm.)

       

        +(qe)+(R/f)+(qa)           (1.17)
Some other sources of error, which depend on details of the detector used, will be discussed where appropriate below.

Having outlined the physical principles underlying a Cherenkov Ring Imaging detector, the next chapter describes a prototype of such a device, which was constructed and used successfully in a particle beam of principal momentum 10 GeV/c to locate Cherenkov rings and prove the technique as viable. The final chapter in the first part of this thesis presents results obtained with this device, and an analysis of the particular errors arising in the technique.


 
REFERENCES
[1] O.Heaviside, see T.Kaiser, Nature 247(1974)400
[2] P.A.Cherenkov, Doklady 2(1934)451
[3] I.E.Tamm and I.M.Frank, Doklady 14(1937)107
[4] A.Butslov et al., N.I.M. 33(1962)574
[5] S.K.Poultney et al., Rev.Sci.Ins. 20(1963)267
[6] A.Iredale et al., IEEE Trans.Nucl.Sci. 13(1966)339
[7] B.Robinson, Phys.Scripta 23(1981)716
[8] R.S.Gilmore et al., N.I.M. 206(1983)189
[9] T.Ekelof et al., Phys.Scripta 23(1981)718
[10] T.Ypsilantis et al., N.I.M. 173(1980)283
[11] R.S.Gilmore et al., N.I.M. 157(1978)507
[12] M.Davenport et al., IEEE Trans.Nucl.Sci. 30(1983)35
[13] W.Farr et al., N.I.M. 154(1978)175
[14] J.V.Jelley., 'Cherenkov radiation and its applications.'
     (Pergamon Press,1958)
[15] B.Leontic, CERN 14(Yellow Report,1959)
[16] E.Hecht and A.Zajak, 'Optics' (Addison-Wheley,1974)
[17] W.A.Fincham and M.H.Freeman, 'Optics' (Butterworths,1974)

Chapter II An Experimental Ring Imaging Detector

2.1 Introduction

This chapter describes the experimental details and arrangement of a small ring imaging Cherenkov detector. The detector as a whole was assembled and operated during the period June to December 1982 in the C13 test beam, derived from the CERN Proton Synchrotron (PS) machine. High energy pions passed through a length of argon radiator. Cherenkov light produced in the radiator was collected by a spherical mirror and brought to a focus within the active area of a TPC. The component parts of the ring imaging detector had previously been constructed and partially tested at the Rutherford Appleton Laboratory.

2.2 The Test Beam , C13

This was a secondary beam located in the East Hall of the PS machine and derived from the extracted proton beam striking a secondary target. The target itself could be changed, but was usually a 5 mm diameter rod of aluminium of length 250mm This target gave the highest electron flux in the beam (about 7% of the total particles). The normal intensity incident upon the target was 2.10 protons per pulse. At 10 GeV/c there were approximately 5.10 pions per 10 protons incident on the target. The momentum of the particles could be adjusted between the limits 4 and 20 GeV/c, by varying the strength of the field in a momentum-selecting magnet.

The experimental area where the ring imaging detector was set up was approximately 16 m. in length, and the final focus of the beam could be moved along this length by adjusting collimators and steering magnets. In front of the area available to users were situated two scintillation counters, two gas threshold Cherenkov counters, and one MWPC. A second MWPC was installed at the rear of the area. Each Cherenkov counter was 3 m. in length, could withstand 3 bar of overpressure, and both were normally filled with helium.

2.3 Experimental layout

The apparatus used in the prototype ring imaging detector is shown in Figure 2.1. This consisted of two large radiator vessels each of length 2m and of diameter 30 cm. The first of these could be bolted to the second to obtain a radiator medium of length 4m. The second vessel had a side arm to which the Time Projection Chamber (TPC) could be attached. Within the second radiator, provision was made for mounting a mirror whose axis could be moved to point at an angle to the radiator's long axis. In this way Cherenkov light from the beam particles could be reflected along the side arm to the TPC for detection. Upstream of the first radiator sat four MWPCs, two of a type which measured positions of tracks in one dimension, and two which measured tracks orthogonally. For convenience these were labelled either 'x-chambers' or 'y-chambers'. Downstream of the second radiator vessel sat a similar group of four MWPCs. At each end of this equipment were positioned a group of scintillation counters, three counters upstream and two counters downstream.

Each scintillation counter was constructed using discs of plastic scintillator coupled to phototubes. One counter of the upstream group, and one of the downstream group, used discs of diameter 1 cm. The remaining counters contained discs of diameter 5 cm. In this arrangement S1, S2 and S5 were of the larger diameter and S3, S4 the smaller. By defining a hardware trigger T5 as being the coincidence between signals from all five counters viz.,

T5 = S1.S2.S3.S4.S5    (2.1)
one could restrict the size of the beam 'seen' by the rest of the apparatus to a small angular width (Figure 2.2). Conversely, by defining, for example, the hardware trigger T4 as being;
T4 = S1.S2.S4.S5           (2.2)
the effective size of the beam so defined was larger in area than that selected by the trigger T5 (Figure 2.3). Given the hardware trigger from the scintillation counters, the eight MWPCs yielded the spatial information to determine the track of the charged particle.

The MWPCs were of two types, as already mentioned. The 'x-chambers' consisted of wires which ran vertically and hence provided a measurement in x; the 'y-chambers', on the other hand, measured y. Each wire plane was separated from the adjacent plane by 1 cm, each wire was of diameter 100 mm, and the inter wire separation was 1 mm. (The number of wires in each chamber varied between 24 and 64 depending on its position and type.)

With this arrangement a charged particle entering the apparatus, and satisfying the angular requirements of the hardware trigger, could, in principle, deposit energy in one or more of the MWPCs. For at least two digitisings from each end of the system of MWPCs, and from like chambers, a determination could be made of the particle direction in at least one of the two dimensions.

2.3(a) The Radiator Vessels and Mirror

Each radiator vessel was constructed from stainless steel piping of large bore with flanges welded onto the pipe at both ends for connection to other apparatus. Each pipe was baked at 200C before use in the experiment, to remove occluded surface impurities. This was done to minimise out-gassing at low gas pressures. The downstream vessel, as well as having a side arm to which the TPC might be attached, also had a port to which the pumping system was bolted (Figure 2.1). For some tests, it was desired to reduce the length of radiator gas through which the beam particles passed, in order to investigate the reduction in N for the detector (Equation 1.8). This was achieved by detaching the upstream vessel (Figure 2.1). and then sealing off the downstream vessel with the stainless steel flange (marked F in Figure 2.1).

The mirror had a focal length of 80 cm, a diameter of @30 cm. and it was coated with a layer of magnesium fluoride deposited on the reflective surface of aluminium. The coatings were of such a thickness that optimal reflectivity in the wavelength region of interest was achieved. The mirror was so positioned within the rear radiator vessel that its focal axis bisected the angle between the side arm axis and the beam axis, i.e. the mirror was rotated about the vertical so that its focal axis was at an angle of approximately 15 degrees to the beam axis.

2.3(b) Radiator and Photoionising Gas Systems

The gas system may be divided into two parts, one which regulated the flow of radiator gas to the radiator vessels, and the other which provided the TPC with the photoionising gas mixture.

The radiator gas system is shown schematically in Figure 2.4. To remove all traces of oxygen (which has a short absorbtion length for photons in the wavelength region of interest), the radiator vessels were initially evacuated to a pressure of 10- Torr using a rotary and a diffusion pump. The vessels were then filled to just above atmospheric pressure with argon, which was passed through Messer Griesheim GMBH 'OXYSORB' filters, and the oxygen concentration metered (Meter type BOC Z-OX). The meter could be coupled either to the input or return gas lines (Figure 2.4). The purified gas flowed into the radiator vessel(s) at the upstream end, and out at the downstream end. With this system, the oxygen concentration in the radiator gas flowing to the vessels was measured to be < 1 p.p.m., and remained at this level throughout the tests.

The substance TEA (Tri-Ethyl-Amine) was used as a photoionising gas because of its low ionisation potential (7.52 eV) for conversion of photons to photoelectrons. It exists as a liquid at 4C with a partial vapour pressure of 20 Torr. The quantum efficiency for conversion of photons in TEA is shown versus photon energy in Figure 2.5, together with the transmission of the CaF2 windows used in the detector. An admixture of TEA and methane (CH4) was created using the mixing system shown in Figure 2.6. The relative amount of TEA in the final mixture fed in to the TPC determined the conversion length for photons, A, within the drift volume. For 10% of the CH4 flowing through the TEA 'bubbler' (Figure 2.6), with the TEA at a temperature of 4C, the resulting conversion length A, was 6 mm.

2.4 The Time Projection Chamber (TPC)

A TPC essentially comprises two regions; the first region is a drift volume in which ions drift towards the second region, an MWPC, in which the ions are detected (Figure 1.3). The information received from the associated electronics gives the drift times of the ions in the first region, hence the term 'time projection'. The device thus measures the two dimensional position of any ion in the drift region by converting the time of drift to a linear displacement;

yin. = bdift..t               (2.3)
where bdift is the drift velocity of the photoelectrons in the gas.

The TPC used in the present investigations was constructed at the Rutherford Appleton Laboratory , and details of its construction exist elsewhere [1]. Figure 2.7 shows both a plan view and a side elevation of the device.

Referring to this figure, field shaping wires of diameter 100 mm surround a cage of dielectric material of dimensions 100x100x40 mm. These wires were wound as separated wire loops, each at a distance of 2 mm from the adjacent loop: the windings ran along the interior and exterior sides of the cage. The electric potential between each successive loop was constant and graded by a resistor chain. Two circular holes in opposite sides of the cage contained windows through which the Cherenkov photons passed to be converted in the photoionising gas within the chamber. One of these windows was made from calcium fluoride, the other from fused silica (quartz). Both had a thickness of 3 mm. The drift field wires lay flat against, and on both sides of, each window. A variable resistor was connected between the field shaping wire nearest the MWPC plane and earth, in order that the drift field could be varied to optimise conditions. The furthermost field shaping wire was held at a high negative potential (usually 10 KV). Thus any photoelectrons (or other negatively charged particles) within the conversion gap (the space between the two windows) were constrained to drift towards the MWPC plane. This MWPC consisted of 48 wires each of 20 mm diameter, and spaced by 2 mm. These wires lay between two cathode wire planes at earth potential and separated from each other by 10 mm. Each of these wires was coupled to a 0.2 mA threshold amplifier attached directly to the exterior frame of the TPC.

The drift region and MWPC were housed in a fibre-glass box through which the photoionising gas flowed. A second calcium fluoride window pressed against the one fitted in the drift cage (with the cage orientated as shown) and existed to isolate the photoionising gas from the exterior. In the case where the TPC was clamped to a radiator vessel under vacuum, the stainless-steel support seen in Figure 2.7 ensured that this second calcium fluoride window did not break. The support was held at earth potential and consequently some small distortion of the electric field at the entrance windows occured. The loss of collection efficiency due to this effect was measured to be @10%.

2.5 On-Line Data Acquisition

2.5(a) Trigger Logic

Figure 2.8 shows a logic diagram of the electronic circuitry used in the acquisition of the data. Two types of experimental trigger were implemented, the first being a 'real' event trigger derived from the detection of a charged particle in the detector, and the second being a 'random' event trigger derived from a pulse generator. The 'random' trigger generated background events for analysis, and for comparison with real events.

Signals from the five scintillation counters Si were fed to AND gates, where a coincidence was demanded between some combination to define the trigger, T (see above). The desired coincidence was scaled, and fed to an OR gate together with the random trigger (Trn.). The output signal (an 'event trigger', EV,) from this OR gate was fanned-out for use by a variety of elements;

EV = T4(T5).OR.Trn.     (2.4)

The beam-line MWPCs were strobed in on reception of EV, and the detected signals fed to CAMAC. The Time-to-Digital-Converters (TDCs) for the TPC were started by a delayed EV signal. Each TDC channel (1 - 48) was then stopped when a pulse was detected from the appropriate wire. Whilst the signals were being accumulated by CAMAC the reception of other events by the acquisition system was inhibited. As soon as the event had been read in, this veto was removed, so that the next event could be received.

A start-of-burst (SOB) signal was fed directly to the on-line computer together with an end-of-burst (EOB) signal.

2.5(b) Event Description

Event records as provided by the on-line software were characterised by one or more digitisings in the beam-line MWPCs, together with information from the TDCs associated with the TPC. In addition to this information, several scalers were incremented at each event, and added to the data record. The type of event ('real' or 'random') could be determined by examining two such TDC values on the event record.

Each of the 48 TDC channels associated with the TPC was present on the record as an integer number running from 0 to 1024. The numbers were proportional to the time which had elapsed since the common start signal from EV via CAMAC, and as such gave a description of the drift time spectrum over all wires. There was no capability for storing more than one digitising on any given wire per event . Each TDC channel thus contained either an in-range time (0 - 1023) or a 'run-out' (1024) corresponding to no hit on the wire.

Calibration of the TDCs associatd with the TPC was accomplished in the following way (Figure 2.9). A pulse-train of frequency 100 MHz was produced using a gate-generator. One of the pulses from this train was used to form a coincidence with a pseudo-random 1 KHz signal from a pulse generator. The coincidence was fanned out and used as a common TDC start signal. Another pulse from the 1 MHz train was then fanned out and used as a common TDC stop signal. In this way the difference between start and stop signals was an integral number of 10 ns time bites. Thus in each of the 48 TDC channels examined off-line there was a series of spikes, separated in TDC channels by the equivalent of 10 ns. A fit in each TDC channel to the inter-spike separation yielded the calibration constants ti (nanoseconds per TDC channel), and to (the dead time in nanoseconds for channel i).

Thus for a given digitising Ni read by CAMAC at wire number i, the equivalent time which had elapsed since the common start signal was given by;

t = Ni.ti + to     (2.5)

From a survey of the beam-line MWPC positions, and a knowledge of the wire configuration in each MWPC, a determination of the particle position could be made at each MWPC plane, given a digitising in the corresponding ordinate. Multiple hits (>1) in each MWPC were discriminated against in the on-line and off-line software. Straight line fits to digitised information of the single hit variety enabled a rather accurate determination of the particle trajectory through the detector to be made.

At normal intensities about 2000 particles per burst were read by CAMAC with T defined as in Equation 2.2. With T defined as in Equation 2.1, about 200 particles per burst were recorded.

2.5(c) On-Line Software

The purpose of the on-line software was to provide enough information during the running periods to enable qualitative decisions to be made on the performance of the detector. A determination of the efficiency of the detector could be made but the statistical accuracy was poor. Depending on the section of the detector being evaluated, such as the TPC, the beam-line MWPCs or the trigger, several different analysis programs could be invoked to provide the relevant distributions of interest and corresponding statistics. An important feature of the capability of the computer (Digital Equipment Corp. type PDP-11/34), on which these programs were stored, was the possibility of sharing the data between several programs all accumulating data simultaneously. The events were 'shared out' depending on the specific priority of each program, the higher the priority of the program, the more events per unit time being passed for analysis to that program. In addition to the programs used for on-line evaluation of the detector, it was possible to send experimental data via a cable link, to one of the CERN mainframe computers. Here the data were initially stored on disc, then copied to tape (6250 b.p.i.) by an automatic process. In this way more sophisticated software could be used to analyse the experimental data.

Thus the on-line software, coupled with the tape-writing facility, enabled a rather complete check to be made on the operation of the detector, and on the state of the particle beam itself.


 
REFERENCES
[1] Omega Photon Collaboration, CERN SPSC/P140 Add.3(1982)

Chapter III An Analysis of the Experimental Data

3.1 Introduction

In this chapter the analysis of the data obtained using the detector described in Chapter 2 is presented. Topics of particular concern will be the efficiency of the device for the detection of the ring images, and the accuracy with which the photoelectrons were detected spatially. The device was used in two distinct modes. First, the TPC was positioned such that the particle beam directly passed through the drift region, and tests were carried out to determine the charge collection efficiency of the chamber, the drift velocity of the ions in the drift region for different gas mixtures, and the spatial accuracy in the localisation of ionisation due to beam particles in this region. Secondly, with the TPC positioned on the side arm of the downstream radiator vessel (Figure 2.1), Cherenkov ring images were observed for various concentrations of the photoionising gas (TEA), and for various particle momenta. Measurements were made of the observed ring images in terms of their radius and sharpness in definition, as a function of these variables.

The results of the tests enabled a calculation to be made for Np (Equation 1.8), together with an assessment of the effectiveness of the device in distinguishing between two types of particle present in the beam.

3.2 Straight Ionisation Tracks in the TPC

The apparatus was initially set up with the TPC positioned at A in Figure 2.1. A traversing table allowed the TPC to be moved a known distance either in the up-down or left-right directions by remote control. The scintillators S1 -S5 were timed in, together with the eight beam line MWPCs. Adjustment of the time delay in the TDC signals associated with the TPC ensured that the electronic acquisition system strobed all 48 wires after the correct time had elapsed since reception of the event signal EV (Section 2.5a).

In this arrangement, the beam particles travelled through the TPC drift region parallel to the plane containing the TPC sense wires, and at right-angles to the wires themselves (Figure 2.7).

Figure 3.1 shows the wake of ionisation left by a beam particle which traversed the TPC drift region. After calibration corrections had been made (Equation 2.5), straight line fits to such events were made to determine the spatial position of each track in the following way. First, events with signals from less than 5 of the 48 MWPC wires were rejected. The digitisings from the remaining good events were fitted to straight lines. In the fitting procedure, if the sum of the residuals of each track point to the fitted track point was too large, then the track point with the largest residual was removed, and the fit repeated. This procedure was used a maximum of ten times, or until the number of track points was reduced to five. Finally, the errors on the fitted tracks were used to determine the accuracy to which their positions could be located within the TPC. Figure 3.2 shows a plot of the RMS error on the fitted times to all wires, after the fitting procedure. The peak at @7 ns corresponds to a time resolution of an ionisation point within the drift region of the TPC. The rise seen up to the cut-off point at @25 ns is due to extra tracks within the TPC which did not satisfy the trigger requirements. To interpret this time resolution in terms of a spatial resolution required a knowledge of the drift velocity of ionisation in the drift volume.

Measurements of the beam particle directions from the beam line MWPCs were used to determine the gradients of these directions in the y plane. The gradients, together with the measured position of the TPC, were used to derive the positions of intersection of the beam particles with the TPC. Each derived position was plotted against the fitted drift times for the resulting ionisation in the TPC. Figure 3.3 shows such a plot, where the drift field was 0.7 kV/cm. The inverse of the gradient of the straight line in Figure 3.3 is the drift velocity of ionisation in the chosen gas mixture, at the chosen drift field. By measuring the gradients of the lines in such plots, the drift velocity was determined for various values of the drift field Ed. Figure 3.4 shows the results of this analysis, and indicates a spatial error of 0.6 mm at a drift velocity of 90 mm/ms.

3.3 Efficiency Scan of the Drift Gap

To measure the charge collection efficiency of the TPC as a function of the point of ionisation in the drift region, the TPC was positioned in the beam so that the beam particles were perpendicular to the MWPC sense wires, but did not pass through either entrance window (see Figure 3.5). By moving the TPC in the left-right or up-down directions, and measuring the charge collected on a particular wire (chosen centrally in the chamber), the efficiency scan was performed. The wire numbered 25 had been previously measured to have an efficiency of 75%, and was arbitrarily selected to be the test wire. The TPC was initially positioned so that the centre of the beam was 20 mm nearer the MWPC wire plane than the centre of the drift region (see Figure 3.5, position marked 'A'). The TPC was then moved from a position where the beam centre was just below the CaF2 windows (see Figure 2.7) to a position where it was just above the quartz window. This move was completed in several steps, and the charge collected on wire #25 measured at each step. Subsequently, the TPC was moved so that the beam centre was positioned at the centre-line of the drift volume (Figure 3.5, position marked 'B'), and the scan performed again. The results are shown in Figure 3.6, where the entrance window regions are shown shaded. The chamber is seen to be more efficient for ionisation points closer to the MWPC wires than to the centre of the TPC.

3.4 Cherenkov Rings in the TPC

To operate the detector in its ring-imaging mode, the TPC was attached to the side-arm of radiator vessel 2, such that the area of drift volume just behind the entrance windows was in the focal plane of the spherical mirror (Figure 2.1). Some distortion of the reconstructed rings was expected with this configuration, and a Monte Carlo simulation of this effect [1] gave an indication of its extent. Cherenkov photons from those beam particles with velocities above the threshold, were collected and reflected by the mirror to the TPC. Within the TPC, the photons converted in the TEA/CH4 mixture at some point behind the entrance windows. The probability of conversion was governed by the mean free path of the photons, A, in the mixture, and this was short (<6 mm) compared with the length of the conversion space (@32 mm). After conversion, the resulting photoelectrons drifted through the gas mixture in a field determined by the voltage applied to wire #50 of the drift field cage. Upon reaching the edge of the drift region, the photoelectrons were accelerated over the remaining centimetre to the MWPC wire plane by the potential difference between wire #50 and the cathode plane of the MWPC. (The anode wires in the MWPC were at earth potential). This transfer of photoelectrons between the drift region and the MWPC region could be inhibited by applying negative bias across the gap. In practice, of course, the optimum transfer efficiency was required. This was achieved by measuring the number of photoelectrons collected at the MWPC as a function of both the drift field, Ed, and of the transfer gap bias field, Eb. Figure 3.7 shows a plot of the mean number of photoelectrons collected, np., versus Ed, for a setting of Eb= 30 Volts/mm. This plot reveals a clear plateau for values of Ed above 55 Volts/mm, and in accordance Ed was fixed at this value while other effects were investigated. The optimum value of Eb was arrived at by a similar procedure.

The photoelectron collection efficiency having been optimised, the properties of the observed ring-images were then examined. Figure 3.8 shows a plot of measured time versus wire number for several thousand events in the TPC, where the beam particle momentum was 10 GeV/c. At this momentum, the majority (@95%) of the beam particles were pions, the remaining few percent being electrons (above Cherenkov velocity threshold), muons (above threshold) and kaons (below threshold). The observed width of the ring image is large, partly due to the divergence of the beam; the particle directions were not coincident. Other effects which increased the observed ring width are discussed below. An inactive wire is seen at position 36; no times were recorded at this value of x.

To correct for the effect of the beam divergence, the gradient of the fitted beam track, dx/dz, (from the beam line MWPC information) was plotted versus the time digitisings on the TPC wires. Figure 3.9 shows two such plots (for wires #21 and #28), where the two regions of high density in each plot correspond to digitisings from opposite sides of the Cherenkov ring. The straight lines shown, demonstrate the variation of the position of the ring image as a function of the beam divergence. Vertical lines, in these plots, would indicate co-incident beam particles in the apparatus from event to event. To impose zero divergence in the software, the time digitisings on all the TPC wires were corrected using the slope of the best lines through each of the two regions.

Figure 3.10 thus shows the corrected time spectra on wires #28 and #21 for beam momenta of 4 and 7 GeV/c. Although the statistics are poor at 4 GeV/c, the two spikes clearly indicate the presence of a ring. At this momentum, (see Table 3.1), only electrons and muons are above threshold, so this is likely to be a b=1 electron ring. At 7 GeV/c the ring projection on both wires is clearly seen, with improved statistics. At this momentum, electrons, muons and pions are all above threshold (Table 3.1), and the beam particles were predominantly pions.

TABLE 3.1 : Radii of Ring Images at the Selected Beam Momenta
P(GeV/c)                        R(e-)                        R(m-)                        R(p-)                        R(K-)                        mm. 
                                                                                                                                                                                                                      &
nbsp;                        
                        4                                     22.2                         6.90                         below                        below                         
                        7                                     22.2                         18.7                         15.5                         below                         
                       10                                     22.2                         20.6                         19.2                         below                        
             14                                     22.2                         21.4                         20.7                         below                         
                       16                                     22.2                         21.6                         21.1                         below                        
             18                                     22.2                         21.7                         21.3                         below                        
This table assumes a refractive index for argon of n=1.000368 at the peak of the TEA quantum efficiency curve, and at a temperature of 22C. Indicated in Figure 3.10 are the two smaller spikes corresponding to the electron ring at 7 GeV/c (which has the same radius as that at 4 GeV/c). With higher electron statistics, these would be better defined, but notwithstanding, demonstrate the capability of the device for discriminating between electrons and pions at this momentum.

To observe the behaviour of the device as a function of particle momentum, several thousand events were recorded at beam momenta of 4,7,10,14,16 and 18 GeV/c. In Figure 3.11 are plotted the accumulated rings at each momentum setting. At 4 GeV/c the statistics are poor; only electrons and muons produce light in the radiator vessel. The shadow of the 'Mercedes Benz' support (see Section 2.4) is seen as a depletion of events at three points around the ring, accounting for a loss of @10% of the incident Cherenkov photons. Here again, wire #36 was inactive, and this is seen as an absence of events at x=7.0 cm. At 7 GeV/c, the electron ring is discernible as a faint background surrounding the more intense pion ring. At 10 GeV/c and above, the electron rings are absorbed into the pion rings, which gradually have increased in diameter with increasing momentum. (The apparent variation in the observed widths of the accumulated images is accounted for by different total numbers of particles for which data were accumulated at the various momenta.)

To investigate the ring sizes at these momenta settings, single events with three or more observed photoelectrons were fitted to circles (the assumption being that the reconstructed spatial positions of the photons lay on a circle), and the computed value of the radius plotted. Figure 3.12 shows the results, which are tabulated in Table 3.2, to be compared with Table 3.1.

TABLE 3.2 : Fitted Radii of Ring Images at the Selected
Beam Momenta
P(GeV/c)                      R(e-)                      R(m-)                      R(p-)                      R(K-)                      mm. 
                                                                                                                                                                                                               
;            
            4                                            19.0                                                                             below                                  
                     7                                            19.0                                                                             14.0                                  
           10                                            19.0                                                                             17.0                                  
           14                                            19.0                                                                             18.0                                  
           16                                            19.0                                                                             18.0                                  
           18                                            19.0                                                                             18.5                                  
In particular, the plot of fitted radii at 7 GeV/c shows evidence for an accumulation at @19 mm. as well as one at @14 mm. Events with a high multiplicity of detected photoelectrons were rare (see later), however, several events with greater than 7 digitised points on the ring image are plotted in Figure 3.13 to clarify the operation of the detector.

The observed number of photoelectrons (n) is expected to follow a Poisson distribution, with a mean m, such that

 
                
 
                
 
                
 
                
 mne-m
 
                
 
                
 
                
 
                
 
                
 
                
 
                
 
                
 
                
 
                
 
                
 
P(n)                 =                                                                                                                                                                                                             
                                                                                     n!                                                                                                                                                                                            
The probability of observing zero photoelectrons is then given by:
P(0)  =  e-m
Thus the number of events with no photoelectrons detected was divided by the total number of events recorded to give P(0), and hence m, for each value of the beam momentum. At 14 GeV/c, m was measured to be 0.8. This is not the only method of calculating m, but is relatively unbiassed by effects such as photon cross-talk between the MWPC wires, and noise in the chamber itself. Since detection efficiences existed, the observed value of P(0) was in fact higher than for perfectly efficient detection. From these values of m, the 'figure of merit', Np, may be calculated for the device.
m  =  Np L sinqc
where L was 2 m, and sinqc is 6.8x10- for a 14 GeV/c pion passing through argon at 22C, emitting Cherenkov light at a wavelength of 150 nm. (the peak response of TEA). This gives a value:
Np = 600 m-
which while low, is not inconsistent with other examples of Cherenkov detectors [2].

The reason why Np is low may be attributed to collection inefficiences, and also to other details of the Cherenkov photon detection method. In particular, account must be taken of the following factors:

Detection Efficiences
1) Transmission of Argon (impurities < 3 ppm)                                    99% 































































































































2) Reflectivity of mirror at 150 nm                                                                                 70%
3) Transmission of two CaF2 windows                                                               65%x65%
4) Transmission of drift field wires                                                                         80% 































































































































5) Transmission of 'Mercedes Benz' support                                              90% 































































































































6) Quantum efficiency of TEA/CH4 in range 7.59 eV          30% 































































































































7) Trigger efficiency of the detection system                                    80%         
8) Probability photon converts in Drift Gap                                             83% 































































































































9) Efficiency of Drift Gap for inefficient first mm. 97% 































































































































10)Kaons present in beam give no Cherenkov light                   95% 































































































































Total Efficiency for single Cherenkov Photon         =                            4%

3.5 Interpretation of Results

The capability of the ring-image detector to locate the spatial positions of ionisation caused either by charged particles or far-UV photons has been demonstrated. The localisation of straight ionisation tracks within the TPC drift region was accomplished with a spatial accuracy of 0.6 mm. The charge collection efficiency of the fiducial TPC volume was determined by measuring ionisation drifts from a defined region to the TPC MWPC wire plane. As expected, the collection efficiency fell off at the edges of the fiducial volume, close to the entrance windows and drift field-shaping wires. The detector was sensitive to single photons. However, detection efficiency was found to be impaired not only by the type of entrance windows and photoionising gas mixture, but by such details of the design as the entrance window support and the drift field cage wires.

Ring images were observed at beam particle momenta of 4,7,10,14,16 and 18 GeV/c, and the twin rings due to pions and electrons resolved at 7 GeV/c. The ring images were rather broad, and were distorted due to the position of the TPC off the focal axis of the mirror. The fitted ring radii were smaller than those expected from a calculation using the refractive index of the gas at NTP, the particle mass and kinetic energy, and the focal length of the mirror. This is probably partly explained by conditions different from NTP prevailing at the time of the tests (e.g. a higher temperature in the experimental area), and partly by the failure of the ring fitting procedure on an eccentric ring. Unfortunately, the temperature of the radiator gas was not monitored during these tests; room temperature was assumed.

In general, the error on the fitted radii of the ring images at every momentum setting (Figure 3.12) was approximately 1 mm. This error can be compared with a theoretical calculation, from the approximations discussed in Chapter 1.

Firstly, the geometrical error on reconstructing the Cherenkov angle qc (Equation 1.10) has contributions from the intrinsic TPC wire spacing, s=2 mm, and the accuracy of measuring drift times in the TPC. The drift time accuracy is determined by such factors as the homogeneity of the drift field, and the time binning in the TDCs associated with the TPC, and has been measured to be 0.6 mm. Inserting these figures in Equation 1.10, and neglecting dispersion, obtains the geometrical error on qc:

qg  =  2.10-

Secondly, the angular spread due to dispersion in the radiator gas may be evaluated by inspecting the refractive indices of argon as a function of wavelength, as given by Bideau-Mehu [3] et al., for the photon energy range 7.59 eV, and calculating the change in Cherenkov angle of a 10 GeV/c pion in this range. This yields an error:

qd  =  2.10-

Thirdly, the chromatic and spherical aberrations of the optical system are evaluated using Equation 1.15. This equation will not hold exactly in this case, since the optical configuration of the device meant that the TPC active area was not precisely in the focal plane of the mirror. However, inserting the mirror diameter and focal length into Equation 1.15 yields an error on qc of:

qo  =  0.1/80

Finally, the errors due to energy loss, MCS of particles traversing the radiator gas volume at the energies involved and the error due to diffraction (Equation 1.16), are negligible.

Adding the three errors obtained above in quadrature, a final ring image error is obtained:

qc  =  3.10-
which implies an error on the ring radii of @2.5mm. This is in reasonable agreement with the experimental observations discussed above.

With further refinements in the TPC and optical systems, the device can accurately reconstruct the ring images from pions and electrons in the energy range 4 18 GeV/c. The muon intensity in the mixed beam was too low to determine whether these particles could also be resolved from ring images. In conclusion, the ring imaging Cherenkov detector has been demonstrated to be a viable device.


 
REFERENCES
[1] J.A.G.Morris, Private Communication
[2] J.Seguinot et al., N.I.M. 173(1980)283
[3] A.Bideau-Mehu et al., J.Quant.Spectrosc.Radiat.Transf. 25(1981)395

Chapter IV Vector Meson Photoproduction

4.1 Introduction

In this chapter, the theoretical ideas which underlie a photoproduction experiment such as that under discussion (WA57) are outlined. In particular, previous experimental results on photoproduction of vector mesons are discussed, and related to simple model predictions. The outcome of such a discussion leads to an interest in the particular reaction gp wpp, as a preparation for the treatment of the results from the WA57 experiment in the subsequent chapters.

4.2 Mesonic Currents from the Photon

It has long been recognised that photon-hadron interactions exhibit similar characteristics to hadron-hadron interactions. Examples of this are seen in the shapes of the gp and p+-p hadronic total cross-sections, which show proportionality (Figure 4.1) [1]. Following this observation, it is noted that the photon is in a state of mixed isospin with Jp. = 1--, and in this way is similar to the vector mesons, which have the same Jp.. This fact led to the idea of Vector Meson Dominance (VMD), whereby a free photon continually makes transitions to vector meson states in a virtual way. Using this idea, the matrix element for the process gA B is given by adding the diagrams appropriate to the process VA B, where V is a vector meson, including the couplings for the transitions g V (Figure 4.2). In the simplest VMD case, the three diagrams which contain respectively r, w and c dominate over all others. Generalised VMD (GVMD) overcomes some of the shortcomings of simple VMD by including the sum over higher vector mesons.

The coupling of a given vector meson V to the photon is thought of in terms of its contribution to the electromagnetic current ge.. Thus the total electromagnetic current is given by the sum over mesonic currents:

                                                                    mv                                                                                                                                                                                            































ge. =   . Vv                                                                                                                                                                                            































                                                   v                                                                                                                                                                                            































where mv is the mass of the meson and fv is a constant appropriate to that meson. The matrix element M(gAB) is then given by:
M(gAB) =  (e/2fv) M(VAB)
since a given meson V will couple to the photon with constant (emv)/(2fv).

With the understanding of strong decays (via the theory of Quantum Chromodynamics, QCD), models of hadron-hadron interactions have been proposed. Two such models relate to the so-called Pomeron, first introduced in considering OPE models [2], and also discussed in the next section. More recently, the Low-Nussinov model [3] discusses Pomeron behaviour by considering the exchange of two coloured gluons between the colliding hadrons. In the model due to Brodsky and Gunion [4] the Pomeron behaviour is described by the exchange of quarks. Etim and Masso [5] obtained the vector-meson/proton cross-section ratios by factorising X(gp) to terms in X(gg) and X(pp), which are measured, to obtain the following result:

X(rp) : X(wp) : X(cp) : X(J/ep) = 7.4 : 7.4 : 4 : 1
which is in good agreement with experiment [6]:
8 : 8 : 4-5 : 1
These experimental ratios indicate a strong violation of the naive postulate X(Vp) A 1/mv, when going from the trio of light mesons (r,w,c) to the heavier set (J/e,U ....). The ideas of QCD alone cannot explain all of the features of photoproduction cross-sections. This can be understood in terms of large contributions, which must be taken into account, from the region of so-called 'soft' physics, not calculable in perturbative QCD. Combining QCD with hadronic phenomenology leads to GVDM, which provides a smooth transition between the otherwise incompatible results from low mass and high mass vector meson production experiments.

4.3 Meson Spectroscopy and the Naive Quark Model

Spectroscopy of mesonic states began in 1947 with the discovery of the pion (p), which was followed by a succession of discoveries yielding higher states such as the r, w, G and K* resonances. Latterly, the discovery of the J/e in 1974 has renewed interest in meson spectroscopy.

The symmetries in the hadron spectrum viewed in terms of isospin multiplets: SU(2) and SU(3), are explained by describing them as combinations of the fundamental quarks. The early quark model of Gell-Mann and Zweig proposed that hadrons contain three quarks, and mesons a quark-antiquark pair. The quarks exist in a triplet representation of SU(3), posses 1/3 integral baryon number, and 1/3 or 2/3 integral charge (where the fundamental unit is the charge on the proton). Free quarks are never observed, and this is explained by a super strong binding force which causes 'quark confinement' and accounts for the large masses of the hadrons. The binding force is believed to be mediated by the exchange of vector glouns, particles that carry the colour charge of QCD.

The simplest description of hadronic states is achieved by thinking of the constituent quarks as moving non-relativistically in a harmonic oscillator potential. This is the so-called 'naive' quark model. The sequence of levels predicted by such a model depends on the intrinsic spin, S and orbital angular momentum, L of the constituent quarks:

J = L + S  ,  P = (-1)l+  ,  C = (-1)l+

When the observed mesons are plotted on a J vs. M or Chew-Frautschi plot (Figure 4.3), they cluster into the SU(3) nonets which are distributed in bands of rising spin and alternating parity. The nonets subdivide into octets and singlets (3x3 = 8+1) with possible mixing between the I=Y=0 members (Figure 4.4). States with the same S lie on approximately straight lines in the J vs. M plot (Figure 4.3). The Regge Theory [7] describes these lines as 'trajectories'; particles of a given type (with respect to internal quantum numbers) comprise each cluster. A simple harmonic oscillator potential in conjunction with some relativistic wave equation provides the similar spacing between bands of orbital angular momentum L, and produces a sequence of levels with alternating parity. The leading Regge Trajectory, L = Lmx.(M) is accompanied by daughter trajectories with L = Lmx.(M) - 2n, where n runs from unity upwards.

Experimentally, vector meson photoproduction in particular is seen to be diffractive: there are sharp forward peaks in the angular distributions, the cross-sections (both total and differential) are roughly constant with energy, there is often exchange of the vacuum quantum numbers in the t channel, and helicity is often conserved in the s channel. The exchange of the vacuum quantum numbers in this way has been associated with the exchange of the imaginary particle called the Pomeron. If the Pomeron trajectory is written as Ap(t), then the Regge Theory predicts a differential cross-section for the exchange:

dX                                  2(Ap(t)-1)                                                                                                                                                                                                   
;                           















 @ s                                                                                                                                                                                                                                                                                
dt                                                                                                                                                                                                                                                                                                                   















where s is the centre of mass energy. If Ap(t) is unity, then the cross-section is energy independent. Other Regge trajectories other than the Pomeron may be exchanged, in which case the behaviour of the cross-section is no longer necessarily energy independent.

4.4 The Vector Mesons

In 1961, Erwin[8] et al. used a pion beam to observe the r meson in a bubble chamber at Brookhaven. Maglic [9] et al. inspected the mass spectra from the neutral three pion combinations in the proton-antiproton reaction ppp+p-p+p-p, and observed the w meson to be an enhancement at 0.787 GeV/c. At about the same time, the r meson was photoproduced at Cornell and seen to have a mass of 0.72 GeV/c. In 1962 the c meson was observed in the channels K-pK+K- and K-pKK when the KK invariant mass spectra were plotted [10]. Much later, in 1972, a further vector meson was tentatively announced from e+e- annihilation data [11], this was what is known as the r'(1.6) meson, the first radial recurrence of the r(0.77). The existence of the r' was confirmed in photoproduction of four charged pions at SLAC [12]. In that experiment, a photon beam with energies in the range 4.5-18 GeV was used, and streamer chambers were used to measure the reaction products. The r' was again confirmed by Bingham [13] et al., using a polarised photon beam of energy 9.3 GeV. To complete the set of bona-fide vector mesons known to date, the J/e was discovered simultaneously in 1974 in e+e- data [14], and in pp collision data [15].

4.5 The wp State : Experimental Situation

Production of wp has been studied in hadron-hadron and photon-hadron interactions. In general, an ambiguity between spin-parity assignments of 1+ and 1- has existed for the resonant state at a mass of @1.2 GeV/c in the wp mass spectrum. The assignment of this resonance would determine whether it was the 1+ B(1.23) axial vector meson, or the first radial recurrence of the r(0.77), the 1- r(1.25), predicted by Veneziano [16].

The B meson was first observed by Abolins [17] et al. in 1963. Its existence was confirmed by Baltay [18] et al. in 1967, but the spin-parity assignment of 1+ remained uncertain until the analysis of Chaloupka [19] at al. in 1974. The r'(1.25) is much less well documented than the B meson. The only good evidence comes from the analysis of NINA data taken by Barber [20] et al., and from e+e- data compiled by Conversi [21] et al.

Chronologically, the investigation of resonances decaying to wp has proceeded as follows. In 1968, Ascoli [22] et al. observed the B- in

p-p  wp-p                           4.10
and assigned it to one of 1+,2+,3-,4+.... , with polarisation information preferring the 1+ solution. Six years later, in 1974, Chaloupka arrived at a unique 1+ assignment for the B- in the same reaction, and measured the D/S ratio as being 0.30.1. (The D/S ratio indicates the relative amounts of l=2 to l=0 waves in the B- decay products.) In that experiment natural parity exchange was observed. In the same year, Ballam [23] et al. saw a 1.24 GeV/c enhancement in the photoproduction reaction
gp  pp+p- + neutrals               4.11
but were unable to assign a spin-parity due to lack of angular information on the neutral particles. However, in the following year, Chung [24] et al. performed an elegant spin-parity analysis on data obtained for the reaction
p+p  wp+p                          4.12
at 7.1 GeV/c, and settled on a firm 1+ assignment for the wp+ enhancement. The spin-parity analysis described in this thesis follows the analysis of Chung in that experiment.

Later, in 1977, Gessaroli [25] et al. took data from reaction 4.10 using a p- beam of momentum 11.2 GeV/c. The produced B- meson was assigned Jp= 1+ with a D/S ratio of 0.40.1. The analysis of Barber [20] et al. followed, which related to data taken of the photoproduction reaction

gp  p+p-ppp                  4.13
at energies between 2.8 and 4.8 GeV. Their results indicated that the enhancement in the wp mass spectrum at 1.2 GeV/c was from the decay of a 1- state. The conclusion, however, was arrived at by fitting the results with the assumption of s-channel helicity conservation (SCHC). This result was confirmed by Aston [26] et al. in 1980, when events in reaction 4.13 were used to identify a 1- state decaying to wp. But here again, to arrive at a firm conclusion, the assumption of SCHC was made.

Latterly, and in a preliminary analysis of a subset of the data discussed in this thesis, Atkinson [27] et al. found two solutions for the spin-parity of the wp enhancement. The experiment was very similar to those of Aston et al. (loc.cit.) and Barber et al. (loc.cit.), but was of greater statistical accuracy. The two solutions found were: a) a dominant 1- signal when SCHC was imposed, and b) a dominant 1+ signal when SCHC was not imposed. The characteristics of the 1+ signal were consistent with it being the B meson, as measured in the other experiments described.

The present thesis presents the analysis of the total sample from the experiment of Atkinson et al. (loc.cit.). The results of the analysis help to resolve the B(1.23) and r'(1.25) ambiguity in wp, and a detailed account of this is given in Chapter 8.


 
REFERENCES
[1] Particle Data Group, Rev.Particle Properties, Phys.Lett. 111B(1982)
[2] G.A.Winbrow, DNPL-R30(1973) and ref.'s therein
[3] S.Nussinov, Phys.Rev.Lett. 34(1975)1286
[4] S.J.Brodsky and J.F.Gunion, Phys.Rev.Lett. 37(1976)402
[5] E.Etim and E.Masso, CERN TH-3557(1983)
[6] A.Chodos et al., Phys.Rev. D10(1974)2599
[7] T.Regge, Nouvo Cimento 14(1959)951
[8] A.R.Erwin, Phys.Rev.Lett. 11(1961)628
[9] B.C.Maglic et al., Phys.Rev.Lett. 7(1961)628
[10] L.Bertanza et al., Phys.Rev.Lett. 9(1962)180
[11] J.Laysacc and F.Renard, Nouvo Cim.Lett. 1(1971)5
[12] G.Barbarino et al., Nuovo Cim.Lett. 3(1972)689
[13] H.H.Bingham et al., Phys.Lett. 41B(1972)635
[14] J.E.Augustin et al., Phys.Rev.Lett. 33(1974)1406
[15] J.J.Aubert et al., Phys.Rev.Lett. 33(1974)1404
[16] H.J.Schnitzer, Phys.Rev. 18(1978)3482
[17] M.Abolins et al., Phys.Rev.Lett. 11(1963)381
[18] C.Baltay et al., Phys.Rev.Lett. 18(1967)93
[19] V.Chaloupka et al., Phys.Lett. 51B(1974)407
[20] D.P.Barber et al., Z.Phys. C4(1980)169
[21] M.Conversi et al., Phys.Lett. 52B(1974)375
[22] G.Ascoli et al., Phys.Rev.Lett. 20(1968)1411
[23] J.Ballam et al., Nucl.Phys. B76(1974)375
[24] S.U.Chung et al., Phys.Rev. D11(1975)2426
[25] R.Gessaroli et al., Nucl.Phys. B126(1977)382
[26] D.Aston et al., Phys.Lett. 92B(1980)211
[27] M.Atkinson et al., CERN EP-81/113(1981)

Chapter V The experimental investigation of vector meson states in Protoproduction.

5.1 Introduction

The investigation of vector meson states in photoproduction was the main purpose of the WA57 experiment, carried out at CERN between 1979 and 1980 using the SPS machine. Briefly, (more details are given below), a photon beam of accurately known momentum was incident on a target of liquid hydrogen. The reaction products were detected in the OMEGA spectrometer, a large superconducting magnet, producing a vertical field, which deflected the charged particles from the interactions through a system of MWPCs. Neutral pions, after decaying into photon pairs, were located spatially, and their energy determined, by a photon detector comprising a combination of three separate detectors. A gas-filled Cherenkov detector was also present to discriminate between charged particles from target interactions. A track multiplicity of between 2 and 5 demanded in an experimental trigger was intended to provide a large sample of photoproduced vector mesons. Event reconstruction offline allowed selections to be made for particular types of event.

5.2 The Photon Beam and Tagging System

The method used to derive a beam of high energy photons from protons of momentum 240 GeV/c, circulating in the CERN SPS machine was intended to provide an accurate momentum measurement of each photon incident on the hydrogen target (Section 5.3a). To achieve this the protons were extracted from the SPS ring and directed towards the West Experimental Area, where the WA57 equipment was situated. Septum magnets in the West Area then split the extracted proton beam into three separate beams, one of which impinged on a beryllium target. The resulting proton-nucleon interactions produced (amongst other particles) neutral pions, which promptly decayed, mainly via the channel;

p                                                                    gg                                  (99%)                                   (5.1)
The resulting high energy photons, emitted at small angles with respect to the direction of flight of the neutral pions, were incident on a lead converter, and thus produced electron-positron pairs. Electrons from these pairs, of momentum 80 GeV/c (2%), were then selected to strike the 'tagging' target, a silicon crystal having its crystal planes orientated precisely with respect to the incident electron beam direction. Bremsstrahlung radiation (BR) was then emitted in a direction close to that of the incident electron beam. By determining the electron momentum accurately before and after BR, the photon momentum was determined. Figure (5.1) shows a diagram of the equipment used to achieve the required accuracy in momentum.

Sixteen planes of MWPCs, in each of regions At and Bt, were arranged in four groups; a) with vertical wires, b) with horizontal wires, c) with wires inclined at 45o to the vertical (u-planes), and d) with wires inclined at -45o to the vertical (v-planes). Scintillation hodoscopes in these two regions were included to permit rejection of background and to identify double electron ambiguities [1]. Magnets M3 and M4 (Figure 5.1) were placed to sweep electrons to region Ct after interaction in the tagging target, and to sweep those electrons not interacting in the target to the Beam Dump. Region Ct consisted of MWPCs, scintillation hodoscopes and a lead glass detector array. The passage of scattered electrons through the lead glass resulted in the emission of Cherenkov radiation, and this was collected as visible light by photomultiplier tubes.

Using this arrangement, and under normal conditions, the post-BR electrons had measured momenta between 10 and 60 GeV/c, which yielded an energy range of 'tagged' photons from 20 to 70 GeV (given the incident electron beam of momentum 80 GeV/c).

The geometry of this arrangement, and the energies involved, gave rise to inaccuracies in the derived photon momenta unless account was taken of a) a beam-halo, resulting from over-correction of dispersion for electrons radiating in or before region At, b) charged particles entering the OMEGA region, c) BR other than that from the tagging target, and d) electromagnetic radiation from photons converting downstream of the tagging target. Such corrections were achieved by the inclusion of (respectively) a) 'holey-veto' counters (HOV1 and HOV2), which vetoed off-axis photons, and were placed as shown in Figure 5.1, b) a scintillation counter CV, c) radiation veto counters (RV1, RV2 and RV3), and d) veto counters (PV1 and PV2) for e+e- pairs.

In particular, a significant proportion (20%) of the electrons interacting in the tagging target radiated more than once (double bremsstrahlung). Such events were identified by the 'beam-veto' counter (BV), situated at the downstream end of the entire apparatus, where one (or more) photons was detected some time after a primary photon interaction in the hydrogen target.

5.3 The OMEGA Spectrometer and Associated Detectors

The centre-piece of the OMEGA Spectrometer is a large superconducting magnet capable of sustaining a 1.8 Tesla magnetic field between two cylindrical coils of diameter 2 m, placed one above the other on a common vertical axis, and separated by 1.5 m. Four support columns separated the two pole pieces, and withstood the compressive force of 4000 tonnes due to the magnetic field, together with the weight of the iron itself. The OMEGA co-ordinate system was defined as (looking downstream and along the length of the hydrogen target), OMEGA z-axis vertical, OMEGA y-axis positive to the left, OMEGA x-axis in the forward direction. The magnetic field vector pointed along the z direction.

Apart from the magnet, the other spectrometer components used in WA57 consisted of a hydrogen target and several sets of MWPCs for the determination of charged particle trajectories through the apparatus (see Figure 5.2). Further downstream were situated the large volume gas Cherenkov detector operating at atmospheric pressure, several scintillator hodoscopes, and the photon detector already mentioned.

5.3(a) The Hydrogen Target

The liquid hydrogen target was contained in a tube of stainless steel of diameter 25 mm and length 600 mm. It was situated within OMEGA so that its long axis was at an angle of 45 mrad, with respect to the direction of the incoming 'tagged' photon beam. Just upstream, two scintillation counters (S4 and C4) (Figure 5.2) were placed so as to veto electromagnetic pairs from photon conversions between CV (section 5.2) and the target. The Barrel Counter (BC) surrounded the target and was a circularly symmetric set of 24 scintillator slats. Slightly downstream of the hydrogen target lay the End-Cap scintillator (EC), comprising a disc of plastic scintillator connected to a long light-guide. Photon interactions in the hydrogen target were accompanied by the emission of high energy charged particles in a downstream direction, and often by a recoil proton.

5.3(b) The OMEGA MWPCs

Charged particles originating from the hydrogen target were detected by an arrangement of MWPCs designed to give optimal information for track reconstruction offline. This arrangement comprised three regions: Region C with MWPCs immediately surrounding the hydrogen target, Region B with MWPCs just downstream from the EC, and Region A containing MWPCs well downstream of the target, but still located within the OMEGA magnetic field.

Region C chambers (ten on each side of the target) mainly provided track digitisings for large angle, low momentum particles such as recoil protons (the target 'fragmentation' region). The chambers consisted of planes of 256 wires, the inter-wire separation being 2 mm. Only sixteen (eight on each side of the target) of these chambers were used, the detection efficiency in Region C being rather low (approximately 30%), and the geometry insensitive to other than low momentum, large angle particles. A High Precision (wire) Chamber (HPC1) was positioned just downstream of the EC, and within Region C. The track digitisings in this chamber, a plane of 150 wires with inter-wire separation 0.5 mm, improved the offline reconstruction of events.

The majority of charged particles were of high momentum, and were usefully recorded as digitisings in Region A, further downstream of Region B. Region B was primarily used to identify low momentum particles from target interactions, and contained 6 chambers each of 768 wires (inter-wire separation 2 mm). Wires in these chambers were orientated either in the u or v planes (Section 5.2), and each wire plane was separated from an adjacent plane by a distance of 16 mm.

The MWPCs of Region A detected the fast forward particles, utilising more than one wire plane per chamber to avoid track confusion due to high spatial density of particles. Each wire plane in Region A had the same specification as a plane in Region B. The 'Beusch Chamber' occupied the position shown in Figure 5.2, and contained four wire planes with wires oriented along the directions u,v,y,z.

Two drift chamber modules (DC1 and DC2) were placed in the vertical plane, downstream and outside of the region of magnetic field in the OMEGA Spectrometer. At these planes the charged particle trajectories were essentially straight lines, and digitisings from the DC's aided in offline track reconstruction.

5.3(c) The Cherenkov Counter and Scintillation Hodoscopes

The Cherenkov counter used was a threshold device providing crude identification of particles with momenta above @ 5.6 GeV/c. The counter comprised thirty two light cells, each containing a pair of mirrors for collection of the Cherenkov light, and was filled with carbon dioxide (CO2) at atmospheric pressure. Light was thus collected for charged pions with momenta > 5.6 GeV/c, charged kaons with momenta > 17 GeV/c and protons/anti-protons with momenta > 32 GeV/c. The active aperture of the device was approximately 2.5 m.

Just upstream of the Cherenkov vessel were placed 18 vertical scintillator slats, the so-called Bonn Hodoscope (BH). In front of this hodoscope sat another one, H1, with vertical scintillator slats orientated to cover the edges of two slats in BH immediately downstream Attached to the downstream end of the Cherenkov counter was a further vertical hodoscope array (BACKH). All three scintillator hodoscopes existed to facilitate and clarify the operation of the Cherenkov triggers, together with the so-called 'K - Matrix', a matrix of electronic signals set up specifically to select charged kaons.

5.3(d) The Photon Detector

One of the most important detectors used in the present experiment was that enabling the accurate reconstruction of neutral pions which originated in the target interactions. Since the main decay mode of neutral pions is into two photons which are isotropically distributed in the pion rest frame, the photon detector was designed to measure the positions and energies of such photons at a plane approximately 11 m downstream of the hydrogen target. There was the added possibility of distinguishing between electromagnetic pairs (background) and incident photons (Section 5.3(e)).

The photon detector comprised three separate elements (Figure 5.2). In order downstream, and the first of these elements, SAMPLER, existed to initiate electromagnetic showers. It comprised two horizontal arrays of 21 lead glass blocks. Each block had dimensions 140x100x1450 mm, the 100 mm dimension being in the sense of the OMEGA x-axis. One of the pair of median-plane SAMPLER blocks was pulled out to allow non-interacting beam photons to pass through (the median-plane is defined in Section 5.3e).

Downstream from the SAMPLER sat PENELOPE, an array of 768 scintillators, each of dimensions 10x15x1400 mm. These scintillators were orientated in four groups of 192 elements; two groups had the scintillators pointing vertically, and two horizontally. This produced a system with crossed areas (15x15 mm.) of scintillator in each of the four quadrants, as viewed along the OMEGA x-axis. The purpose of PENELOPE was to determine the positions of showers initiated in the SAMPLER.

Finally, immediately downstream of PENELOPE , and completing the photon detector, was OLGA (Omega Lead Glass Array). Over three hundred lead glass blocks , each of dimensions 140x140x500 mm, were arranged such that the incident faces of all blocks lay in the vertical plane, and such that the whole array presented an approximately circular cross-section as seen from the hydrogen target. The central block in this array was removed to permit photons which had not interacted to pass through to the counter BV downstream (Section 5.2). The effect of OLGA was to present about twenty radiation lengths of material to impinging photons, which caused total absorption of the energy in most cases. Photomultiplier tubes attached to the rear of each OLGA block collected the showered energy in the form of Cherenkov light, and provided the means of determining the incident photon energy with a resolution E/E @ 10%/E, and with some spatial accuracy (7 mm.).

5.3(e) The Electron-Positron Pair Veto Counters

At the photon beam energies used in the experiment the cross-section for electromagnetic pair production was two orders of magnitude higher than that for hadroproduction. Because of this, it was necessary very effectively to veto electron-positron pairs originating in the hydrogen target. Since electromagnetic pairs were in general emitted along the photon beam direction, the effect of the OMEGA magnetic field was to bend their trajectories in the horizontal plane, the so-called 'median-plane'. The 'median-plane' was loosely defined at any downstream detector as being that region extending from z = -7 mm to z = 7 mm in the OMEGA co-ordinate system.

Two scintillators, placed horizontally, and separated by 140 mm to allow the passage of non-interacting beam photons, covered the 'median-plane' at the rear of BH (Section 5.3(c)). These 'OLAP' counters overlapped the 'median-plane' region of the SAMPLER, and were intended to detect charged particles in this area.

Electron Veto Arrays (EVA's) were placed on either side of, and just downstream of, OLGA. Electromagnetic particles missing detection in the OLAP and OLGA-PENELOPE-SAMPLER (O-P-S) detectors were likely to enter and trigger one of the EVA's. Detection of such particles was achieved by a combination of lead scintillator sandwich type and ordinary scintillation counters, which afforded the possibility of distinguishing between showers initiated by hadrons, and electromagnetic events.

Using the OLAP's, EVA's and the O-P-S detectors, electromagnetic background events were successfully discriminated against, so that the contribution to the rate of final triggers was approximately the same as the hadronic event rate.

5.4 Formation of the Experimental Trigger

In this section the formation of the trigger chosen to provide an event sample of the type;

g p                                  p+ p- p p (p)      5.2
is described. This trigger, named the 'Pizero Trigger', aimed to select events with at least one photon of a defined minimum energy impinging on the face of the photon detector. Other triggers, included in the logic diagram shown in Figure 5.3 for completeness, and not relevant to the subject matter of this thesis, are described elsewhere [1].

The basis for the trigger system was the identification of a photon interaction in the hydrogen target. Such an interaction had to be accompanied by a signal from the photon tagging system (Section 5.2). This basic trigger, or 'loose trigger', LT, activated the acquisition system to record the event information to follow. As the information from the rest of the tagging system, the OMEGA MWPCs and the downstream detectors became available, the trigger condition became more specific. The result was to prejudice the data acquisition towards event topologies of particular interest, and in the case of the Pizero Trigger, to prejudice it against EM events in the median plane region as well.

The loose trigger, LT, was formed when the following conditions were met: (a) the tagging system indicated the presence of an electron in HC1 and HC2 (Figure 5.2), (b) a signal from EC was received, (c) no signal from either S4, V4 or PV was received (Section 5.2). Ideally, these conditions ensured that a 'clean' photon was incident on the hydrogen target, and that particles from the resulting interaction passed through the EC.

LT prompted the acquisition system to accept information from the photon detector, the Cherenkov counter, and the Bonn and Back hodoscopes via CAMAC. An 'intermediate loose trigger', ILT, which demanded that no signal from the Beam Veto counter was received, existed to prompt strobing in of information from the tagging system MWPCs. At this stage enough time had elapsed for the tagging lead glass array to respond, together with the various scintillation counters in this region. Signals from these devices were used to form the 'Strobe 3' level trigger, S3, which embodied the minimum requirements for all triggers used in the experiment. From now on, the discussion refers only to the subsequent formation of the Pizero Trigger.

The photoproduced four pion state described by Equation 5.2 was expected to have at least two forward-going charged particles in OMEGA. The Strobe 4 level trigger, S4, thus demanded between 2 and 5 signals from an OMEGA A-chamber wire plane, in fact the y-plane of chamber A1 (Figure 5.2). Rejection of electromagnetic background was achieved at the next trigger level, S5, by defining an EMVETO signal;

EMVETO = (OLAPl.OLGAl).OR.(OLAPr.OLGAr).OR.EVAl.OR.EVAr
where the terminology is as described in Section 5.2, and the subscripts l (r) refer to a signal from the left (right) hand median plane region of the appropriate detector. S5 was defined as S4 in anti-coincidence with this EMVETO signal;
                                                                                                                                                                                                                           &
nbsp;                  
S5 = S4.EMVETO                                                                                                                                                                                                            
In this way, charged particles entering either of the EVA's, or either side of the OLGA median plane, inhibited the Pizero Trigger.

The next step in the formation of the final trigger was to determine the presence of at least one photon interaction in OLGA. This was complicated by the possibility of hadrons showering in the lead glass, and by the fact that electromagnetic showers from photons were not always confined to a single OLGA block. To overcome these difficulties, the upper and lower halves of OLGA were split into 'column pairs' for electronics purposes; the signal from a vertical column of OLGA blocks was fanned in with that from the column to its left, and, separately, with that from the column to its right. The fanned in 'half column pair' (HCP) signals were thus the analogue sums of signals from pairs of adjacent columns, both above and below the median plane region.

The HCP energy threshold was set at 2 GeV to define the minimum shower energy below which noise and background signals became intolerable [1]. The completion of the Pizero Trigger at Strobe 6, thus required coincidence between S5 and at least 2 GeV in one or more OLGA HCP's, denoted by HPCn:

S6 = S5.HCPn > 2 GeV

On reception of this trigger, or any of the other final triggers which are not directly the concern of this thesis, the data acquisition system read in the detector information available via CAMAC.

5.5 Offline Event Reconstruction and Simulation Software

Data from the experiment, stored on 6250 b.p.i. magnetic tape, was passed through the software chain shown in Figure 5.4. The program TRIDENT existed to reconstruct charged tracks from chamber digitisings and a knowledge of detector geometries. To do this, a method of pattern recognition was used. The program JULIET placed TRIDENT information in the context of particle types; it combined this information with that from the tagging system and downstream detectors to identify the particles present and also to compute their momenta and energies. A further program, GEORGE, was then used to process the JULIET information in the framework of a particular event type requirement; it was within GEORGE that 'cuts' to isolate a specific sample of events were imposed.

The program MAP was used to calculate the acceptance of the whole detector in the physics channel of interest. MAP, coupled with OMGEANT [2], TRIDENT, JULIET and GEORGE, provided the most complete tool available for an accurate simulation of the detector and software biasses. However, it was sometimes sufficient to use MAP by itself; in this case particles generated by a separate Monte Carlo program (such as SAGE), were tracked through the detector elements, and the desired trigger requirements applied. Appendix A.1 describes such an exercise.

5.5(a) TRIDENT

Event reconstruction in TRIDENT consisted of three stages, a) track recognition, b) track momentum evaluation, c) vertex reconstruction. For track recognition, digitisings from the two drift chambers DC1 and DC2 were used with the hydrogen target centre as a constraint point. Track finding in Regions A, B and C (Figure 5.2) was accomplished by recognising a collection of digitisings as being likely to signify a track. Candidate tracks were extrapolated backwards and forwards to check matching with other chamber digitisings until all the chambers had been investigated. Track momenta were determined by quintic spline fits to a track model. Vertex reconstruction enabled primary and secondary vertices to be identified by approximating the charged tracks to helices (circles when viewed in the OMEGA magnet's bending plane) and computing the intersection points of these helices. Candidate vertices were rejected if a fit to the distance of closest approach to the defined main vertex was poor. Once the main vertex had been defined, together with any secondary vertices present, the track properties were recomputed at these points. The resulting banks of information were then written to MAXIDST's (MAXI Data Summary Tapes) for processing by JULIET.

5.5(b) JULIET

The program JULIET (a) deduced the tagged momentum of the photon in each event from Region At, Bt and Ct information, (b) reconstructed neutral pions from selected pairs of photons detected in OLGA/PENELOPE/SAMPLER, (c) determined the type of particle corresponding to each track found by TRIDENT, and (d) attempted to assign one charged particle as the recoil proton if this was kinematically sensible.

Digitisings from Regions At and Bt were examined by JULIET, and tracks fitted by pairing up the digitisings so that extrapolation through the regions caused intersections at points corresponding to other digitisings. Tracks extrapolated from At were required to meet those from Bt in between the two regions, and if they did, an electron momentum was calculated for the whole matched track. Region Ct tracks were projected backwards to the tagging target, where the intersection point was required to be the same as that from the matched track projected from Regions At and Bt. From the fitted track parameters, the photon momentum was calculated. A JULIET 'Region Ct Rescue' occured when no track in Regions At and Bt could be found to correspond with the one found in Ct; in this case the lost track was assumed to be of momentum 80 GeV/c.

Photon detector information was used by JULIET to match photon pairs to the pizero mass hypothesis. To do this, showers characteristic of a hadron impact in OLGA were first ignored. The remaining showers were frequently close together, and in such cases an attempt was made to discriminate between them on the basis of the OLGA block energy distributions and PENELOPE information. After these processes, the measured shower energies from assigned single photons were taken in pairs, and a fit made to the p mass. Pairs with d-probability for the fit of less than 3% were rejected, and better pairs sought. Photons remaining unpaired at the end of this analysis were assumed to be cases where the absent photon had missed the detector, or had been the victim of some other acceptance bias.

5.5(c) GEORGE

The program GEORGE translated the data banks from JULIET into a 'user - friendly' format. It facilitated processing of events in terms of specific physics channels, and it was in GEORGE that most users placed software criteria to define a 'clean' sample of the required events.

5.5(d) MAP

The program MAP (Manchester Acceptance Program) [3] was the general simulation program used for calculating experimental acceptance for specific physics channels. It contained data on detector positions, distortions and efficiences. The user specified a set of separately calculated Monte Carlo events, the detectors through which the particles were to be tracked, and the trigger requirement to define the accepted events. MAP thus tracked the event particles through the detector elements, one at a time.

In later versions of MAP, the treatment of photons was improved over the earlier version by linking MAP with the JULIET software used to identify p's in the data stream, and was justified by the inclusion of a full electromagnetic shower simulation for the lead glass in the photon detector. By doing this, problems with successfully simulating the biasses introduced by the rather complex JULIET software (see Appendix A.1), were avoided.


 
REFERENCES
[1] R.H.McClatchey, Ph.D.Thesis, Univ. of Sheffield(1981) Unpub. [2] F.Carena and J.C.Lassalle, OMGEANT Users Guide (1982) Unpub. [3] A.P.Waite, P.J.Flynn, D.Barberis, MAP User Guide(1982) Unpub.

Chapter VI Observation of the state wp in p+p-pp(p)

6.1 Introduction

Photoproduction experiments have shown an enhancement in the 4p mass spectrum from the reaction gp p+p-pp in the mass region of 1.2 GeV/c, when events were specifically selected to contain an w meson [1,2,3,4]. Interpretation of this enhancement as a resonance has been uncertain due to the possibility of there existing either a diffractively produced Deck-type [5] background, or the tail of the r(0.77) meson above wp threshold (i.e. the coupling r wp ), or some combination of both background effects. Leaving aside these possiblities, there are two meson resonances such that the enhancement could be related to the production reactions

g p  B(1.23) p               (6.1)
or
g p  r'(1.25) p              (6.2)
Here the vector meson state B(1.23), Jp=1+, is the well-established axial vector meson first observed by Abolins [6] et al., and r'(1.25), Jp=1-, is the comparatively dubious first radial excitation of the r(0.77), hinted at in data obtained in the reaction e+e-p+p-pp [7].

6.2 Selection of the data.

Events containing two to five prongs were selected in order to be consistent with the event production hypothesis gp p+p-pp(p). In addition, at least one photon was required to have been detected in the O-P-S system (Section (5.3d)). The effect of the EM background was reduced by the action of the median plane veto (ibid.). Offline, the additional condition, that four well-measured photons were present in O-P-S, was imposed. Figure 6.1 shows the 4p invariant mass distribution for the resulting sample. The distribution of missing mass squared (MM) between the 4p system and the gp system shows a broad peak at the square of the mass of the proton, together with a tail corresponding to other missing particles (Figure 6.2). Final selection of the events,

g p  wp (p)                 (6.3)
was achieved by requiring MM to be in the range -2.1 to 3.9 GeV/c. This gave a final event sample of 8100 events. The MM spectrum (Figure 6.2) indicates the presence of approximately 20% background under events of the type (6.3). Appendix A.2 shows the full list of cuts applied in the program GEORGE in order to select the required p+p-pp events, before a 'peak-minus-wings' selection of an w meson is made (see next section).

6.3 Background subtraction

Figure 6.3 shows the invariant mass of the two possible p+p-p combinations in the final sample of events. The w meson is seen to sit on top of a non-negligible background, which must be subtracted to ensure the presence of an w.

To achieve this subtraction, weights were assigned to the two possible 3p combinations in reaction (6.3) in the following way;

-3
Peak Minus Wings Subtraction Bands
w peak 0.733 < M(p+p-p) < 0.833 weight = +1 w wings 0.683 < M(p+p-p) < 0.733 weight = -1 0.833 < M(p+p-p) < 0.883 weight = -1 elsewhere weight = 0
This method produced a sample of 2304 weighted wp events. In the distributions below, the weights described have been applied to each event, and this will subtract the background successfully if it is a linear function of mass in the region of the w. Backgrounds due to the other decay modes of the w (such as wpg) faking the 3p mode, were estimated to be negligible.

6.4 Overall features of the selected data

In this section, the overall features of the data selected to be wp in p+p-pp(p) are discussed. The 3p spectrum shown in Figure 6.3 exhibits a clean w signal of FWHM @40 MeV, sitting above the background (of level @20%). The 4p spectrum before and after subtraction of w-background events (Figure 6.1) shows an enhancement at a mass of @1.21 GeV/c, and this signal (the shaded area in the Figure), is essentially unchanged by the w selection procedure. The enhancement at a mass of @1.6 GeV/c observed before subtraction of the w-background is attributed to the four pion decay mode of the r'(1.6) vector meson [8].

The t-spectrum (where t is the square of the momentum transfer to the 4p system) shown in Figure 6.4 is consistent with a peripheral production mechanism, and thus with the hypothesis of diffractive photoproduction of the wp state. The slope of this distribution shows that the differential cross-section, dX/dt, varies with t as @ eb., where the slope parameter, b has the value 5.00.3 GeV-.

Figure 6.5 shows the incident photon energy spectrum for all events. The energy dependence of the cross-section was fitted using the form:

X(Eg) = X(g>) (g>/Eg)a
over the energy region 20-70 GeV, where g> was the mean incident photon energy (39 GeV). This fit showed that the cross-section at the mean photon energy of 39 GeV was 0.860.27 mb, with the parameter a = 0.60.2. The cross-section quoted above has been corrected for effects such as a) the tagging system efficiency, b) efficiency of the program TRIDENT, c) wppp branching ratio, and d) the conversions of charged pions in the spectrometer material. In Figure 6.6 the result is extrapolated to lower energies to compare with the results from other photoproduction experiments.

In summary, both the energy and t-dependence of the wp differential cross-section indicate that the production is diffractive. The w-selection procedure used on the 4p data provides evidence that the 1.21 GeV/c enhancement comprises mainly wp events.

6.5 Simulation of the experimental acceptance

Before discussing the decay angular distributions observed in the present data, the nature of biasses which the finite acceptance of the apparatus imposes on the raw data must be considered. Such biasses were caused by geometry and inefficiences of the detector elements used in the experiment. The software used to reconstruct pizeros from photons in the reaction products also produced effects which changed these distributions from their true shapes. To analyse these effects, the program MAP (Section 5.5d), and the Monte Carlo program SAGE [9], were used.

Events were generated using SAGE in each of 10 bins of the 4p system, and these were then passed through the MAP software. The distributions of certain variables in the experimental data were used to weight events in the Monte Carlo generation. The generated incident photon energy spectrum was thus reproduced by weighting the Monte Carlo events according to the experimental spectrum obtained when a trigger on just e+e- pairs was used (the so-called 'un-biassed pairs trigger'). The differential cross-section, as a function of t, was imposed as an exponential of slope 5 (GeV)- (see above). All angular distributions in the simulation were generated isotropically.

Thus for each event generated in a particular bin of 4p mass, the decay angles = (q,c), h = (qh,ch) (see Section 7.3), were evaluated and stored. Each event then passed through MAP, and if accepted was stored in MINIDST format (Appendix A.1 and Section 5.5a). After this process, the MINIDSTs were treated identically to those containing the experimental data; the same GEORGE program was used to analyse both types (Section (5.5c) and Appendix A.2). Finally, the acceptance function relating the input event distribution to the accepted event distribution was calculated.

The distributions of various interesting quantities for both the experimental data and the simulated data are now discussed, in order to show their good agreement.

Figure 6.7 shows the four pion mass spectrum for simulated events (solid line), overlaid on the corresponding spectrum obtained with the experimental data (dashed lines). The agreement between the two spectra is artificially good, since the simulated events were weighted to reproduce the experimental distribution. Figure 6.8 shows the absolute value of t, |t|, in the overall centre of mass (gp - system). Again, the agreement is forced to be good (see above), but there is some discrepancy at low values of t, corresponding to fast-forward going events in the gp - system. This discrepancy is possibly caused by the absence of a full simulation of TRIDENT (Section (5.5a)). Figure 6.9 shows the w-decay Dalitz factor, R, given by,

                                                                                     4 |p+p-|                                                                                                      
R                 =                                                                                                       
                                   3 [(M(3p)/3) - M(p)]                                                                                                      
in the peak-region, and in the wings regions, where p+ p- are the momentum vectors of the charged pions in the 3p centre of mass, M(3p) is the invariant mass of the three pion system, and M(p) is the mass of the charged pion. R is predicted to be flat for a 3p system isotropically distributed in the centre of mass, and to be rising linearly for the decay of the 1- w-meson. The experimental data (dashed lines) indicate that the w-meson is well selected from the background beneath its peak by using the background subtraction method described (Section (6.3)). Since there was no simulation of background events all events were of the type containing an w-meson in the simulated data. The R-distribution for simulated events thus shows a smaller level of background than in the experimental data. In the simulated data, the background is accounted for by resolution effects.

To check the rather critical simulation of the p detector acceptance, three distributions were chosen as indicators. The first of these, the distribution of photon energies detected in the O-P-S system (Section (5.3d)), is shown in Figure 6.10, where the simulation is again overlaid on the data. The second (Figure 6.11) is the radial separation between all pairs of detected photons on the face of OLGA (6 entries per event containing 4 photons). The last of these (Figure 6.12) is that of the minimum inter-photon separation at the face of OLGA, i.e. the smallest separation of all 6 possible per event. This distribution effectively maps the edges of the photon acceptance aperture.

It is seen from these distributions that the agreement between the simulated data and the experimental data is good, and this conclusion is a prerequisite one in order that a confident acceptance correction be made to the angular distributions in the real data stream.


 
REFERENCES
[1] D.P.Barber et al., Z.Phys. C4(1980)169 [2] V.Chaloupka et al., Phys.Lett. 51B(1974)407 [3] D.Aston et al., Phys.Lett. 92B(1980)211 [4] M.Atkinson et al., CERN-EP81/113(1981) [5] R.T.Deck, Phys.Rev.Lett. 13(1964)169 [6] M.Abolins et al., Phys.Rev.Lett. 11(1963)381 [7] M.Conversi et al., Phys.Lett. 52B(1974)493 [8] M.Atkinson et al., Phys.Lett. 108B(1982)55 [9] J.Friedman, SAGE Ref. Manual, SLAC Comp. Group Tech. Memo 145(1972) [10] J.Ballam et al., Nucl.Phys. B76(1974)375

Chapter VII A Spin-Parity analysis of wp

7.1 Introduction

Following the formalism outlined by Chung [1], a spin-parity analysis of the photoproduced four pion state,

g p  p+p-ppp,             (7.1)
in which events were weighted to select those p+p-p combinations lying in the w peak region, is presented. The analysis made use of the double moments H(lmLM) which describe the sequential decay of the wp state, and which may be expressed in terms of the production and decay amplitudes for each contributing spin-parity. Details of the formalism used are to be found in Appendices A.3A.5.

A spin-parity analysis of the wp state, (given sufficient statistics and the application of appropriate corrections for effects of experimental acceptance), would allow a determination of the relative contributions from channels (6.1) and (6.2). In the past, such an analysis[1] has shown the enhancement to be dominated by the decay of the B meson, which is produced by natural parity exchange, e.g. the exchange of an w meson in the t-channel. Aston [2] et al. found a dominant 1- solution when their statistics forced the assumption of s-channel helicity conservation (SCHC). Atkinson [3] et al., in a preliminary analysis of the data described in this thesis, found two solutions: one in which the B decay was prominent when SCHC was not imposed, and one in which the decay of a 1- state dominated given SCHC.

The moment contributions from spin-parities Jp = 1+, 1-, and 0- in the wp state were evaluated across the mass interval from threshold to 1.8 GeV/c. Fits to a complete set of symmetric and anti-symmetric moments, arising from interference between different spin and different parity states, were made in nine bins of 4p mass (of 100 MeV/c each). In addition, the measured moments were fitted simultaneously in these bins to a model in which the decaying state was parameterised as a mixture of up to 3 pure spin-parity states. This involved specifying the spin density matrix for the photoproduced state, and calculating the matrix element for the decay in terms of relativistic Breit-Wigner amplitudes or a background function. The double moments so derived from each contributing Jp state were then summed in each 4p mass bin, and compared with the measured moments in that bin to calculate an overall value of d, which was then minimised by varying the parameters of the model.

The analysis of the wp channel from data obtained in the WA57 experiment is considered, with emphasis on the results of the model fits to the double moments in these data. Model independent fits to the data are also described. It will be shown that the data are well described by a B meson and a relatively small amount of 1- background decaying to the final state particles. The results from the model dependent fits show the B meson to have a mass of @1.21 GeV/c, a width of @0.230 GeV/c, a D/S ratio (see Section (7.5)) of @0.25 and a spin density matrix element rpp @0.4, figures which are in agreement with other experiments [1,2,3,4,5], and with the results from the model independent fits.

7.2 Acceptance correction of the experimental data.

The spin-parity content of the wp state was analysed in terms of so-called 'double' moments H(lmLM) (see Section (7.3) and Appendices A.3A.5), which were calculated on an event by event basis from the decay angular distributions, and then summed over the whole event sample. The moments calculated from the experimental data were thus biassed by the acceptance. To correct for these biasses, a linear algebra technique [6] was used.

The method required the inversion of an acceptance matrix A , where A signifies the set (lmLM), and b the set (l'm'L'M'), which effectively translated the measured moment sums H' into the corresponding set of corrected moment sums H . Thus,

H                 = c                  A-                  H' 



































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































where c are normalisation constants. The acceptance matrix was compiled by integrating the acceptance function A(,h) folded with the unbiassed moment sums H and H , over the decay angles, defined below, which were used in the analysis,
A  =  A(,h) H                 H                 d dh   (7.2)

7.3 Helicity formalism and decay angular distributions

Two sets of angles are defined which describe the sequential decay (X wp , w p+p-p) (see Figure A.5). The first set, = (cosq,c), are the w meson directions referred to the axes xyz, where z is the direction of X (gp system), y is the normal to the production plane (given by evaluating kz, k the direction of the incoming photon), and x is given by yz. The second set, h = (cosqh,ch), the helicity angles, are the directions of the w decay plane normal (w frame) referred to the axes xhyhzh where zh is the direction of the w meson (X frame), yh A zzh and xh is given by yhzh. Both sets of axis are right-handed.

Figure 7.1 shows each of these angles plotted for the experimental data, the superimposed curves show the shape of the acceptance. The angle q is heavily biassed by the acceptance at the edges of the plot. The angle c, and the two helicity angles are relatively unaffected by acceptance effects, and some conclusions on the spin-parity content of the system X may be drawn by examining their distribution (see Chapter 8).

The principle of the spin-parity analysis to be discussed lies in the determination of a set of 25 moments from a set of expressions in the experimental angular distributions of the final state pions (see Appendix A.3). The moments may also be expressed in terms of the production density matrix and helicity decay amplitudes for each contributing spin-parity state (see Appendix A.4). The set of moments were thus evaluated in the experimental data, corrected for acceptance effects, and then analysed to yield the spin-parity content of the photoproduced wp system.

To check that the 25 moment set was sufficient to describe the spin parity content of the observed angular distributions, the generated simulation events were weighted using the corrected moments set, and the resulting acceptance angular distributions compared with those seen in the experimental data. The smooth lines shown in Figure 7.2 show the results of this check, and it is seen that the simulation accurately reproduces the distribution of the data (also shown, with error bars) within the errors.

7.4 Model Independent Fits to the Data Moments

In this section, d minimisation fits to the set of 25 double moments derived from the experimental data are described. The principle involved was to take the expressions for the moment sums given in Appendix A.4 in terms of the density matrix and helicity decay amplitudes, and by assigning and then varying numbers for each of these quantities, minimise the difference between the observed sums and the sums calculated using the expressions. The variable parameters were thus the following:

Model Independent Fit Parameters
N+ - The amount of 1+ signal N- - The amount of 1- signal N - The amount of 0- signal Fq - The helicity 1 amplitude for 1+ rpp - The density matrix element for 1+ rpp - The density matrix element for 1- Ai - (i = 111) The coherence factors, see App. A.5

Fits were performed in 9 separate bins of 4p mass, of width 0.10 GeV/c, from 0.9 GeV/c to 1.8 GeV/c. From the fitted quantity F1, a D/S ratio for the 1+ signal was evaluated using the expressions:

Fq = S/3                 +                 D/6                                                                                                                                                                                           <
font FACE="SYMBOL"> 































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































S                 +                 D                 =                 1                                                                                                                                                                 &nbs
p;                          































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































SCHC (see below) was imposed, if required, by fixing the value of rpp to be zero for that spin parity. Three types of fit were chosen; one in which the amount of 0- signal was allowed to be non-zero, one in which it was constrained to be zero, and one in which it was constrained to be zero, and the 1- signal was forced to be SCHC. The reasons for these choices will be discussed later in Chapter 8.

7.5 Model Dependent Fits to the Data Moments

For each resonant state decaying into wp the matrix element describing the process can be divided into two parts; that which describes the production mechanism for the state, and that which describes its subsequent decay [1] (Appendix A.5).

From previous analyses [1,2,3,4,5], the data were expected to contain contributions from the decay of at least two spin-parity states in wp. The moment distributions as a function of 4p mass were anomalous with the hypothesis of a single spin-parity state saturating the wp channel (see Chapter 8). Model fits to these moments were thus performed for various admixtures of spin-parities, by explicitly calculating the moment contributions of each state to the set of moments chosen for the analysis. This was achieved by parameterising each state as a relativistic Breit-Wigner, produced in helicity states defined by a density matrix, which satisfied the constraints described in Appendix A.5. This Appendix contains the theoretical details of the procedure used in the fitting program.

The Breit-Wigner amplitudes used in the fitting program


where mp is the resonance mass, p is the width and m is the 4p mass at which the expression is evaluated, contained mass dependent widths. These were justified in the case of the B-meson by considering the behaviour of the cross-section for gpBp at wp threshold; since wp is the only observed decay mode of the B, the width of the resonance must be zero at this point. The mass dependence of was given by:

There was provision for using either mass dependent or mass independent widths, depending on the expected nature of the contribution to the wp cross section.

Non-resonant parameterisations of the decay amplitudes were also tried as replacements for the Breit-Wigner functions. In particular, the Weibull function [7]:

W(x) = (x/X)(x/X)a-exp(-(x/X)a)
where x = M(4p)-Mtreshold., and X,a are fit parameters, usefully described an incoherent background of zero phase, and was very flexible in shape.

The parameterisation of the density matrix outlined in Appendix A.5, allows the imposition of, for instance, SCHC. This is achieved by noting that rpp= 0.0 and rqq= 0.5 for such a mechanism, which is satisfied when q=p/2 and e takes any value. Thus for SCHC the only variable parameter (when e is chosen to be p/2) determining the density matrix for state i is cjq.

Specifying the density matrix using the method described introduces 5 fit parameters per spin-parity state (1 fit parameter in the case of spin-parity 0-). Imposing SCHC further reduces the number of fit parameters. The density matrix is mass independent, and the angles ci may loosely be thought of as the production phases for helicities in state i.

7.5(a) Details of the Fitting Method

The program used to fit the experimental data moments to the required resonance model will now be described. Several different versions of this program were used to investigate the effects of altering model parameters and specification.

Twenty five measured moments together with their full covariance matrix (25x25) for each of 9 mass bins had previously been calculated for the experimental data, and stored on disc. This information was read in for calculating d for the model moments. A maximum of 5 resonant (or background non-resonant) spin-parity states were allowed, although in practice, to avoid complication, only one, two or three were used to describe the data. For each desired spin-parity state the possible values of l, the orbital angular momentum between the p and w in the 4p centre of mass, were specified. The fit parameters for each state were then set up:

Model Dependent Fit Parameters
Mi - The resonance mass i - The resonance width at half-height Gi - The normalisation Ri - The interaction radius qi - 1st. density matrix angle ei - 2nd. density matrix angle ci - Helicity +1 phase angle ci - Helicity 0 phase angle ci - Helicity -1 phase angle D/S - The l=2 to l=0 amplitude at 1+ resonance
and these were then the variables used by MINUIT [8], which controlled the minimisation of d.

For each of the nine mass bins, identical to those containing the experimental moment sets, the following procedure was used to calculate this d. The above angles were used as described in Appendix A.5 to form the complete density matrix for all contributing states. The w-p centre of mass momentum, computed at the centre of the 4p mass bin under consideration, together with the interaction radius and l-wave, enabled the calculation of the helicity decay amplitudes to be made for each state. These amplitudes were then folded with the relativistic Breit-Wigner amplitudes calculated using M, , G, and R for all states. A program which calculated the full set of complex non-zero double moments [9] arising from the specified spin-parity state mixture, was then used to evaluate the 25 moment set corresponding to the experimental data set. The real parts of these complex sums were then used to calculate the quantities that would be measured experimentally. Each moment sum Hk was subsequently folded with a factor corresponding to phase space and the observed t-dependence in the experimental data [10]:

Hk' = Hk . (q/p) . (1/s) . ((exp(btmn.) - exp(btmx.))/b)
where b is the slope of the t-distribution, q is the centre of mass momentum of w-p in the 4p centre of mass and p is the centre of mass momentum of the 4p system in the overall centre of mass, energy s. (The normalisation constants, omitted in the above equation, were absorbed into the fitted values of Gi in the fitting program.)

The resulting 25 moment sums were then compared with the experimental data set in that mass bin. Using the full covariance matrix, a d was formed in the bin, and this was added to a global sum over all 4p mass bins. The next mass bin was then considered, and so on until the d from all 9 had been calculated.

After this procedure, the global value of d was returned to the MINUIT minimisation routines, and the variable parameters therein adjusted. The process continued until a minimum in d was reached. In a typical fit, where two resonant states (1+ and 1-) were fitted to the data, there existed 18 free variable parameters for MINUIT (one phase for the 1+ state was always fixed in the fits described, see Appendix A.5). These 18 parameters determined a set of 25x9 = 225 moment sums. This gave 207 degrees of freedom, and a typical value of minimum d in a fit of this type was 290.

The model dependent fits to the data using the program described above were carried out after extensive checks had been made to remove errors in the code. Several methods of checking the program were used, mainly involving hand calculation of the moment contributions from the explicit expressions described in Appendix A.5, and comparing these with the values derived by the program itself. Another method used a faked set of data moments, the spin-parity content and normalisation of which were known. In this case the fitting program converged on the input data, within errors, and afforded good confidence in the fitting program.


 
REFERENCES
[1] S.U.Chung et al., Phys.Rev. D11(1975)2426 [2] D.Aston et al., Phys.Lett. 92B(1980)211 [3] M.Atkinson et al., CERN-EP81/113(1981) [4] R.Gessaroli et al., Nucl.Phys. B126(1977)382 [5] V.Chaloupka et al., Phys.Lett. 51B(1974)407 [6] G.Grayer et al., Nucl.Phys. B75(1974)189 [7] W.T.Eadie et al., 'Statistical Methods in Experimental Physics', (North Holland,1971) [8] F.James and M.Roos, MINUIT, CERN-D506(1977) [9] D.McFadzean, 'WA48 Sequential Decay Double Moments Routines' (1981) Unpub. [10] J.V.Morris, Private Communication

Chapter VIII Results and Overall Conclusions

8.1 Introduction

In this chapter the results of the model dependent and independent fits to the data moments are presented, together with conclusions drawn from the decay angular distributions of the wp state. It will be shown that the data are consistent with the photoproduction of a resonant 1+ signal, of mass 1.21 GeV/c and width @230 MeV/c which dominates over a small S-channel helicity conserving 1- signal. The 1+ signal is identified as the B(1.23) meson in the decay mode expected, and the properties of this meson, such as the D/S ratio at resonance and the density matrix element rpp, are in agreement with the accepted values.

For completeness, the possibility of including some 0- state is also discussed but, in practice, its presence is inadmissible on the grounds that such a component cannot be diffractively produced.

8.2 Spin Parity Analysis using Decay Angular Distributions

The enhancement at @1.2 GeV/c in the wp mass spectrum (Figure 6.1) may be attributed to a single broad resonance. In this case a unique spin and parity may be assigned to it, and deductions made about these quantum numbers from the observed decay angular distributions (,h).

As already mentioned (Section 7.3), the acceptance biasses introduced into the angle q (Figure 8.1) cause a large uncertainty in the interpretation when this angle is used. Thus, to analyse the enhancement, the remaining three angles (c, qh and ch) are used. Only contributions from Jp= 1+, 1-, 0- are considered, since these appear to be a complete set for the adequate description of the data.

Turning first to cosqh, this angular distribution is consistent with a sinqh behaviour (Figure 8.1). The angle refers to the w-decay, and shows that helicity 1 is preferred over helicity 0. The wp enhancement is thus not Jp= 0-. Conservation of angular momentum requires that dominant wp Jp= 1- produces w-helicities 1, which satisfies the observed behaviour in cosqh. Another possibility is the production of a Jp= 1+ wp state with a non-zero D/S ratio (Section 7.4).

Looking now at the distribution of ch in Figure 8.1, a strong cos2ch behaviour is seen. A state with Jp= 1- and SCHC would reproduce this effect, as also would a non-SCHC Jp= 1+ state. For the 1+ state to be dominant, a density matrix element rpp> 0.3 would be required.

The distributions in the helicity angles thus show that the wp enhancement is a) not 0-, and can be either b) dominant 1- with SCHC, or c) dominant 1+ with non-SCHC where (rpp> 0.3).

Turning to the angle c (Figure 8.1), this shows a sinc distribution which can be caused only by interference between helicity 1 and helicity 0 for the wp state. Since spin zero has been ruled out above, a non-SCHC mechanism in the production of the enhancement is concluded.

8.3 Results from the Model Independent Fits

In this section the results of fits to the 25 moment set varying the amounts of Jp= 1+, 1-, and 0- states, and the corresponding density matrix elements are presented. (The fitting method has already been described in Section 7.4.)

Three distinct fits were made, the first being one wherein all the fitting parameters were allowed to vary. The results from this fit (FIT1) are shown in Figure 8.2. This figure shows fits made separately over all nine bins in 4p mass. The d- probability fluctuated between the different mass bins, but was always acceptably high (> 3%).

The amount (N) of Jp= 0- is seen to be small and, within errors, globally consistent with zero. This bears out the conclusions drawn in the previous section. The amounts of Jp= 1+ and 1- are roughly equal, although the MINOS [1] errors plotted suggest some dominance of the 1+ signal. MINOS errors are those errors on the parameter values which cause a change in the d of unity.

In accordance with the observation of a consistently small 0- component, for the subsequent fits to be described, N was forced to be zero in all mass bins.

The results of the next fit (FIT2) are shown in Figure 8.3, where the difference between this and FIT1 is the suppression of the 0- signal. It is seen that the amount of 1+ signal exceeds that of the 1- signal in the peak region at @1.2 GeV/c. The 1- signal is produced by SCHC (rpp= 0.0) within errors, which is consistent in terms of previous experimental results discussed in Chapter 4.

Thus to constrain the 4p system even further, a third fit (FIT3) was performed, in which the 1- signal was forced to conserve s-channel helicity, and the suppression of the 0- state was retained. The results of this fit are shown in Figure 8.4, and are interpreted as the most significant of the three fits described. Here the 1+ signal is large compared with the 1- signal, and this leads to further examination of the properties of the 1+ state in order to identify it. The 1+ intensity peaks at @1.2 GeV/c and has a FWHH @200 MeV/c. The D/S ratio in the peak region is @0.25 when calculated from the fitted value of Fq, and the density matrix element rpp@0.4 across the mass range. Apart from the resonance width, these values are consistent with the interpretation of the enhancement as the B(1.23) Jp=1+ axial vector meson, as described in the Particle Data Group Tables [2]. The width of the peak may be attributed partly to experimental resolution, and partly to the possible presence of S-wave 1+ background. Such a background could originate from a Deck type process [3], and would explain the slightly lower value for D/S than expected for the B meson (0.25 compared with the normally accepted value 0.29). The resonance does not conserve s-channel helicity on production.

The conclusion from this analysis is that the enhancement observed in the wp mass spectrum is due largely to non-SCHC production of the B(1.23) axial vector meson. Beneath the peak due to this meson, and at a level of @25% at most, exists a 1- broad background produced by SCHC. This background is consistent with being the tail of the r(0.77), or with being a resonance with a mass in the region of 1.2 GeV/c. It should be added that there is some evidence for a small amount of spin-parity 0-, but the level is insignificant, and inclusion of this in the fits causes some degree of ambiguity in the interpretation of the other spin-parity contributions.

8.4 Results from the Model Dependent Fits

To progress further in the spin-parity analysis, and make more quantitative statements, it is necessary to impose the constraint of continuity across the 4p mass range for all the fitted parameters, and to use the information contained in the phase difference between the production amplitudes for each contributing spin-parity state. In these model dependent fits (See Section 7.5 for the fitting method used) to the data moments the continuity of the contributing spin-parity intensities was imposed across the nine mass bins used, and the information on the phases of the production implicit to the anti-symmetric moment expressions were extracted.

A total of six fits is discussed, and where the results of a fit differ significantly from the previous fit, the later fit is plotted as a smooth curve on the experimental moments. In FIT1, the set of 14 symmetric moments (see Appendices 3 and 4) which contain no terms due to interference between un-like states of spin and parity, were fitted to the hypothesis of a single Jp= 1+ resonance decaying to wp. The results of this fit are shown in Figure 8.5, where the data appear with error bars, and the model predictions as a smooth dashed curve. The extracted fit parameters (see Section 7.5a) are given below:

Results from FIT1 : d = 185 for 117 DOF
M(1+) = 1.21 , (1.21) = 0.270 , D/S = 0.29 (fixed) rpp = 0.442 , rqq = 0.28 , rqp = -0.07 , rqjq = 0.05 R = 17F.
Errors on these fitted parameters are generally small, but exact values will only be quoted for the best fit, to be described below. Here, and in the following fit tables, M(Jp) refers to the resonance mass in GeV/c for the state with spin-parity Jp, (M) refers to the full width at half height of the resonance at the resonance mass M, D/S (Section 7.4) is calculated at the resonance mass, M, and R is the fitted 'radius of interaction' in the Blatt-Weisskopf barrier penetration factors (Appendix A.5), and is expressed in units of Fermis. The above results, for FIT1, show that whilst the symmetric moments are, in general, poorly described by the single 1+ hypothesis, many of the overall features in the data are reproduced. The behaviour of the data moments close to wp threshold show a sharp rise. Such a rise is poorly reproduced by a threshold factor varying as ql, where l is the orbital angular momentum between the w and the p in the 4p centre of mass, and q is the momentum of each of these mesons in this system. Hence the need for the inclusion of the barrier penetration factors (Appendix A.5) where the value of the parameter R determines the slope of the rise in intensity above wp threshold, a large value of R producing a sharp rise close to threshold. Moreover, the intensity is constrained by the phase space factors (Section 7.5a) to be zero at and below the threshold. The width of the resonance is expected to be strongly mass-dependent close to wp threshold if this decay mode is the only one observed for that resonance. However, either retaining this mass dependence, or removing it, made little difference to the fits.

In contrast to FIT1, FIT2 used a single 1- resonance to describe the 14 symmetric moment sums from the data, with the following results (see also Figure 8.6);

Results from FIT2 : d = 253 for 116 DOF
M(1-) = 1.21 , (1.21) = 0.278 rpp = 0.22 , rqq = 0.39 , rqp = 0.03 , rqjq = -0.03 R = 20 F. (maximum)
It can be seen (from the value of d) that this description of the data is poorer than that obtained with FIT1. The symmetric moments H+(2120), H+(2122), and in particular H+(2121) seen in Figure 8.6, show significant deviations from zero as a function of 4p mass, and this can only happen if Jp= 1+ is present (See Appendix A.4). A single 1- state does not account for the behaviour of the above moments. In addition, of course, all the non-zero anti-symmetric moments indicate the presence of interference between more than one spin-parity state. Thus the subsequent fit, FIT3, was made comprising an admixture of 1+ and 1- states.

For FIT3, the full set of 25 moments was used. This then accounted for the interference effects due to the presence of resonant or non-resonant terms in the moment intensities. From the results of the model independent fits (Section 8.2), it was expected that the data would be well described by the B(1.23) meson interfering with some 1- background. In seeking such a background, its form was parameterised by using either resonant or non-resonant amplitudes (corresponding to a "r'(1.25)" or the tail of the r(0.77), respectively). A non-resonant, slowly varying amplitude was achieved by placing a 'resonance' below wp threshold (in fact at 0.77 GeV/c), and then altering the amplitude of this state to affect the height of the resonance tail above threshold. Using either resonant or non-resonant 1- amplitudes made very little difference to the d for FIT3, the results of which are shown in Figure 8.7, and below, for the 1- non-resonant case.

Results from FIT3 : d = 298 for 208 DOF.
M(1+) = 1.212 , (1.212) = 0.231 , D/S = 0.234 M(1-) = 0.770 , (0.770) = 0.449 , (1- mass fixed) rpp = 0.434 , rqq = 0.283 , rqp = -0.09 , rqjq = 0.10 rpp = 0.032 , rqq = 0.484 , rqp = -0.08 , rqjq = 0.00 R(1+) = 7 F. R(1-) = 17 F. 1+ : 1- = 20 : 1
The fitted parameters for the 1+ state confirm the presence of the expected B meson, and are close to those obtained using the model independent fits. The 1- fitted parameters, on the other hand, indicate that a broad, featureless signal is required across the 4p mass region, and that this signal is SCHC (rqq@ 0.5). The smooth curves shown in Figure 8.7 show that this mixed 1+/1- model successfully predicts the overall features of the data moments, with some disagreement in the higher mass bins. The errors on the data disallow a firm statement to be made on the question of the resonant or non-resonant nature of the 1- signal. In the fit shown, the interpretation of the 1- state as being due to the tail of the r(0.77) is somewhat doubtful due to too large a value for the fitted width.

In an attempt to resolve the resonant/non-resonant ambiguity, the model fit was repeated with 1+ and 1- states as in FIT3, but with the 1- state forced to be SCHC. The results of this fit, FIT4, are summarised in the following table, but are essentially the same as those for FIT3. This was also the case with a resonant parameterisation of the 1- signal

Results from FIT4 : d = 300 for 206 DOF.
M(1+) = 1.214 , (1.214) = 0.231 , D/S = 0.233 M(1-) = 0.770 , (0.770) = 0.406 , (1- mass fixed) rpp = 0.437 , rqq = 0.281 , rqp = -0.08 , rqjq = 0.09 rpp = 0.000 , rqq = 0.500 R(1+) = 10 F. R(1-) = 19 F. 1+ : 1- = 17 : 1

As seen from the previous plots of moments versus 4p mass, some of the moments, such as H+(2111), show deviations from zero which suggest a contribution from 0- (see Appendix A.4). Hence FIT5 was performed using the 1+/1- parameters obtained in FIT3 as starting values, with the addition of a 0- state which was either resonant or non-resonant. This fit returned the best value of d of all the fits described (d- probability @0.3%).

Results from FIT5 : d = 296 for 203 DOF.
M(1+) = 1.213 , (1.213) = 0.234 , D/S = 0.234 M(1-) = 0.770 , (0.770) = 0.436 , (1- mass fixed) M(0-) = 1.890 , (1.890) = 0.205 rpp = 0.434 , rqq = 0.283 , rqp = -0.10 , rqjq = 0.10 rpp = 0.030 , rqq = 0.480 , rqp = -0.09 , rqjq = -0.05 rpp = 1.000 R(1+) = 6.7 F. R(1-) = 12 F. R(0-) = 1.1 F. 1+ : 1- : 0- = 17 : 1 : 0
The amount of 0- required by the fit was small, in agreement with the model independent fit results. The fitted parameters of the spin-1 states were essentially unchanged, when either resonant or non-resonant modes of the 0- state were used. From this result, it was concluded that the suppression of 0- in the second stage of the model independent fits was justifiable in terms of the subsequent assessment of the 1+/1- properties.

Finally, one of the above fits (FIT3), was repeated with a more flexible parameterisation of the 1- signal namely by a Weibull function described in Section 7.5. In line with the other fits, this made no significant improvement to d, and did not change the interpretation of the 1+ state as being the B meson.

Summarised below are the results of the model dependent fits, were the errors quoted are calculated from the variations of the parameters between each fit, and from the MINOS [1] errors.

Results from best fit : FIT3 .
d = 296 for 208 DOF.
M(1+) 1.213 0.007 (1+) 0.231 0.022 D/S 0.235 0.019 rpp 0.434 0.031 rqjq 0.095 0.091 Re rqp -0.090 0.071 M(1-) 0.770 (fixed) (1-) 0.401 0.030 rpp 0.031 0.064 rqjq 0.000 0.160 Re rqp -0.083 0.078 Re rqq 0.085 0.145 Im rqq 0.333 0.076 Re rqjq 0.100 0.055 Im rqjq -0.094 0.076 Re rqp 0.026 0.067 Im rqp -0.072 0.060 Re rpq 0.141 0.100 Im rpq -0.292 0.065 R(1+) 7.000 5.000 R(1-) 17.00 10.00

8.5 Summary and Conclusions

The results of the spin-parity analysis of the reaction gpwpp can be summarised as follows:

(a) The inspection of the wp decay angles in the chosen reference frames indicates that the 1.2 GeV/c enhancement in the mass spectrum can be explained by either an SCHC 1- signal, or a non-SCHC 1+ signal with non-zero D/S ratio, together with suitable backgrounds.

b) Model independent fits to the set of 25 double moments arising from spin parities 1-, 1+ and 0- in the wp decay angles then rules out the dominant 1- SCHC explanation. The presence of a 1+ non-SCHC dominant signal suggests the B(1.23) meson, and this is seen to ride on top of a 1- background of no more than @25% the height of the B peak. The 1- background conserves SCHC.

c) Any inclusion of 0- in such fits confuses the above interpretation, causing strong correlations between the fitted parameters, and hence large error bars. However, its presence is inconsistent with the proposed diffractive production mechanism, (and its amplitude, in any case, is small and is generally consistent with zero).

d) The technique used to fit the same set of 25 moments to a model provides more precise results. The model describes each spin-parity state in terms of relativistic Breit-Wigner amplitudes above or below wp threshold, and uses the full density matrix to calculate the moment contributions. Several different models are investigated to arrive at the most simple and consistent explanation of the appearance of the data. This is that the decay of the B(1.23) Jp= 1+ axial vector meson dominates over a background of SCHC Jp= 1-. Other models produce results consistent with this hypothesis, but either with worse d- probabilities, or with slightly better d- probabilities achieved at the expense of increased complication in interpretation. The results of the model dependent fits (in agreement with those of the model independent fits) show that the the enhancement at 1.2 GeV/c observed in the wp mass spectrum is best explained by photoproduction of the B(1.23) meson with at most 25% 1- SCHC background.

e) The possibility that this enhancement is the first radial recurrence of the r(0.77) is not ruled out, since both types of fit were unable to distinguish between resonant or non-resonant behaviour in the 1- background.

In conclusion, the work has utilised, for the first time, a complete set of moments in the analysis of a higher vector meson system. The analysis techniques are complex, and an attempt has been made in this thesis to extract the maximum amount of information, and expose unambiguously the roles of the different spin-parity states involved. The results have removed the ambiguity between a Jp=1+ and Jp=1- interpretation of the wp enhancement at @1.2 GeV/c in favour of the 1+ B(1.23) vector meson.


 
REFERENCES
[1] F.James and M.Roos, MINUIT, CERN-D506(1977) [2] Particle Data Group, Rev.Particle Properties, Phys.Lett. 111B(1982) [3] R.T.Deck, Phys.Rev.Lett. 33(1964)169
APPENDICES

Appendix A.1 Simulation of a subset of wp data

A.1(a) Introduction

For a preliminary analysis of the experimental data from WA57, the exclusive channel;

g p                                  w p (p)       (A.1)
was chosen. Events satisfying certain criteria (to be discussed below), were 'stripped' off MINIDSTs produced by JULIET (Section 5.4), and by MAXMIN (a program which condensed the MAXIDST's to a more manageable size) and processed to provide the interesting physics distributions and associated statistics. These data (called the 'Stripped sample of wp') were thus a subset of the data discussed in Chapters 6, 7 and 8.

The method of neutral pion detection and the detector positions used in the experiment, dictated that the acceptance for channel A.1 was low, and that experimental biasses were introduced into the angular distributions of the decaying particles. To remove these effects, and thus to clarify the physics processes involved, a Monte Carlo simulation of the experimental acceptance in this channel was performed.

A.1(b) Software Framework

The simulation program relied heavily on MAP [1](Section 5.5d). The program MAP interfaced with a particle generation program (see section A.1c), and then tracked the particles so generated through the apparatus, making decisions on their ultimate acceptance. Implicit in MAP were detector positions, apertures, distortions and other relevant parameters. Users of MAP were invited to impose a trigger requirement on the accepted particles and to specify the the detectors in which particle detection was to be simulated.

A.1(c) Generation of the events

The Monte Carlo generation of events was by the program SAGE [2]. Final state particles were defined to be;

p+ p- g g g g p
where the g's resulted from neutral pion (p) decay. The total process was described by (in order);
g p                                  X p                                                                                                                                                                                                                             
X                                                   w p                                                                                                                                                                        
                                    
w                                   p+ p- p                                                                                                                                                                    &nb
sp;     
p                                   g g                                                                                                                                                                                    &nb
sp;                                        
where both p's decayed by the 2g mode. Masses and widths of each particle were standard [3], except in the case of X, which was tentatively given a mass of 1250 MeV and width 300 MeV, (corresponding to the expected B(1230) 1+ meson in this channel).

The incident photon was described by the normal 1/k bremsstrahlung spectrum over the energy range 25 - 70 GeV, and by a linear rise in the region 20 - 25 GeV. The momentum transfer squared, -t, to the four-pion system in the overall centre of mass was parameterised by et, as expected for a diffractive process (see Chapter 4) and as observed in the data. All angles in the decay processes were generated isotropically at first, but the facility existed for weighting them with the observed experimental shapes as an acceptance check (see Section 7.3).

A.1(d) Particle tracking through the detectors

From the four-vectors generated in SAGE, and using the full OMEGA magnetic field map, the charged particles were tracked through the detector elements. Between 2 and 3 electronic signals from such tracks were demanded in the MWPC plane A1Y (Section 5.3). An inefficiency in this detector plane was modelled by a fit to an inverted gaussian distribution. A single hit in the EC counter was also required. The charged particles from events satisfying these requirements were smeared in position and momentum to simulate the resolution of the detector. Following this the EM veto (Section 5.3) was simulated by rejecting events if either charged track entered the median plane region at the photon detector.

The photons were treated entirely separately from the charged tracks in the event, and more complicated procedures were invoked to decide whether the event was accepted or not.

First, all four photons were required to enter the aperture of OLGA. This aperture excluded the missing block at the centre of OLGA, known as the 'Beam Hole'. This geometrical requirement alone reduced the number of accepted events to the level of 10%, before any other checks. Next, the successful photons were smeared in energy according to the observed experimental energy resolution function, and allowed to shower in SAMPLER (Section 5.3). Approximately 20% of incident photons passed through the SAMPLER without interacting; the remainder were made to deposit a fraction between zero and one half of their initial energy. Following this, each photon position on entry at OLGA was determined. Depending on this position with respect to the surrounding OLGA block boundaries, the photon energy was shared between blocks. This sharing involved implementing a complex algorithm in the software which essentially simulated the effects of the energy dependent EM shower profile in the OLGA lead glass blocks. In this procedure, use was made of an examination of the energy deposited in OLGA blocks as a function of photon impact position and photon energy from experimental data [4]. Finally, once each photon had been treated in this way a decision was made for trigger purposes on the basis of block energies and HCP's (Section 5.4). Events satisfying this trigger were then referred to the detector PENELOPE, where photon positions were smeared according to the observed experimental distributions.

A.1(e) Simulation of the JULIET software.

Biasses introduced by the program JULIET (Section 5.5) mainly involved the sub-program SNARK, which was used to identify photons from block energies and distributions in OLGA, together with PENELOPE and SAMPLER information, and to reconstruct neutral pions from the photons. A 1-C fit to the p mass was made given the information from each pair of identified photons. Examples of unwanted background to the successful (wanted) process of identifying the correct photon pairs and constructing the corresponding p four-vectors were: a) choosing the wrong photon pairs, b) failure to correlate hits in PENELOPE and OLGA, and c) incomplete information at the detector edges. It was required to simulate these background generating effects well, since often they affected the angular distributions in a significant way.

Groups of adjacent blocks containing energy from electromagnetic showers were termed 'clusters'. Cluster topologies in OLGA, in general, consisted of up to 5 blocks, and were mainly of the 1 and 2 block variety. Clusters of greater than 5 blocks usually indicated the presence of two photons in close proximity, or the large spray of energy expected to be made by a hadron impact. The program SNARK attempted to discriminate between hadronic showers and the more useful showers initiated by photons in OLGA. In the case of two photon showers close together (such as those resulting from the decay of a fast p), SNARK made decisions on the energy of each incident photon from an examination of the individual block energies.

The complexity of the SNARK software made accurate simulation of the effects of this program difficult. Effort was mainly spent in reproducing the block mutiplicities per OLGA cluster seen in the experimental data. It was decided that this was more critical for accuracy than was the simulation of energy distribution within a cluster. Once a cluster of blocks had been determined in position and energy content, the perimeter edges were compared with those of other clusters. Pairs of clusters sharing a common block edge were labelled as unresolved, and such an event was rejected.

Initially, the 1-C fit to the p mass was made by taking all 6 photon pair combinations and rejecting those with d- probability for the fit of less than 3%. In distinction from the real data stream, it was known in the simulation which photon pair combinations were the correct ones,and this enabled an evaluation of the effectiveness of the fitting process to be made. Finally, it was only necessary to fit the correct pairs of photons; fitting the wrong combinations only produced a negligible background.

A.1(f) Comparison of real and simulated data

Distributions sensitive to the experimetal acceptance in the channel A.1 were chosen to highlight possible defects in the simulation. The photon acceptance and A1Y inefficiency were thus particularly well investigated in order to optimise the program. In the end, all the chosen simulation distributions agreed within errors with those of the experimental data.

Figure A.1 shows the photon beam energy distribution plotted for real and for simulated data. In all the distributions to be discussed, real data are shown as points with solid error bars, and the simulated as a dashed line.

Figure A.2 shows the separation between identified photons on OLGA face (6 entries per event). The leading edge of this distribution is especially sensitive to the procedure used to discriminate between adjacent showers in the photon detector. It can be seen that the simulation follows the behaviour of the data in this region faithfully, indicating that the SNARK biasses were correctly reproduced.

Figure A.3 shows the p energy spectrum for real data and its simulation. A poor simulation of the 1-C fitting procedure would be apparent as a mismatch between these two distributions.

Finally, Figure A.4 shows the azimuthal 'dip' (dy/dx), of charged tracks in the median plane region. The absence of events in the region -7 mrad. to +7 mrad., demonstrates the effect of the EMVETO (Chapter 5). The depletion of events around +15 mrad., is due, in the data, to an instrumental inefficiency in the trigger plane A1Y, and, in the simulation, to the inverted gaussian used to reproduce the effect.


 
REFERENCES
[1] A.P.Waite, MAP Users Guide, Version I, Unpublished, 1981. [2] J.Friedman, SAGE Ref. Manual, SLAC Comp. Group Tech. Memo 145(1972) [3] Particle Data Group, Rev.Particle Properties, Phys.Lett. 111B(1982) [4] T.Brodbeck, Energy Distributions in OLGA Blocks, 1980 ,Private Comm.
Appendix A.2 'GEORGE' parameter selections to define wp sample.
(1) NVX = 1 : One main vertex only (2) -172. 4 : No Region Ct rescues (4) NGT = 0 : No un-paired 'first-class' photons (5) NPI0 = 2 : Two reconstructed p's (6) NNEG = 1 : One negative particle at main vertex (7) 0 0. : Exclude events with zero polarisation (9) NG = 4 : Four reconstructed photons (10) 20. g <70. : Beam momentum range in GeV/c (11) LBB(16,8)="0" if Eg<25 : Well measured photons for Eg<25 GeV/c (12) P(p) <10. or if not DIP(p) > 7 mrad. : No charged tracks in the EMVETO (13) Eg(OPS) > 0.25 : All OPS photons have energy >0.25 GeV (14) Eg(OPS)mx. > 1.5 : Photon with most energy has > 1.5 GeV (15) Eg(OPS)mx. <17. : Photon with most energy has < 17 GeV

Appendix A.5 Formalism used in the Model Dependent Fitting Program

The formalism outlined in this appendix is largely derived from that of Chung [1]. The double moments of the sequential decay (Xwp, wppp) are the experimental averages of the product of two D-functions [1],

H(lmLM) = ) . Dl (h) >
Where (,h) are the decay angles shown in Figure A.5. They thus form an orthogonal set in each event:
Hi(lmLM) = D () Dl(h)  (-1)+ D () Dl(h)
For systems X containing only spin parity states 1+ 1- 0- (wp cannot be in 0+), diagonal and interference contributions in the decay angles (,h) are completely described by a set of 25 such moments (Appendix A.3). These explicit expressions may be calculated for each event, and the moment sums evaluated:
                                                                                      1                  1                                                                                                                                &
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where only the real parts of the moments are measured in the experimental angular distributions.

The photoproduction of a meson system may be defined in terms of the spin density matrix which determines the spin sub-states in which the meson is found, and a set of helicity decay amplitudes which determine the amplitude for the decay of the meson from its different possible helicity states. The complex moment sums H[lmLM] can be related to the production density matrix ri., and the helicity decay amplitudes Fi[1],

Hi.(lmLM) = ti. fi. <10l0|10>
where
ti. =                                                                                                  ri. 'LM|Ji>

fi. =  Fi Fj R'Lm|JiR><1R'lm|1R>
Appendix A.4 shows the expressions relating the 25 moments to the density matrix elements r, and the helicity decay amplitudes F. In this table N+, N- and N refer to the amplitudes of spin-parity states 1+, 1- and 0- respectively. For the interference density matrix elements (ri., ij) it is worth noting that only the real part of the expression
ri. exp(i[ci-cj])
is measured, where ci-cj is the phase difference between the decay amplitudes Fi and Fj.

The density matrix must satisfy constraints such as parity invariance:

ri. = GiGj (-1)    (-1)                                 rj j
where 's label the helicities, G's the parities, J's the spins of the states i and j. The diagonal terms in the matrix thus satisfy:
ri. = (-1)                                                 ri.
The overall normalisation must be satisfied:
ri. = 1
For pure spin-parity states the condition [1]:
ri. = rj.
should hold.

A minimal parameterisation of the density matrix is obtained by considering the following expressions:

Equations generating the density matrix
fp = (1/2) cosqi exp(icp) fq = (1/2) sinqi cosei exp(icq) fjq= (1/2) sinqi sinei exp(icjq)
where p/2qi0, 2p>ci0, p/2ei0. The unpolarised density matrix may then be parameterised by combining these three equations in the following way:
ri. = fifj  + GiGj (-1)ij. (-1)   fifj
which satisfies the constraints described above. The 5 angles q, e, cjq, cp, cq, for each state i are assumed to be independent of mass; the density matrix is thus mass-independent. For states with spin 0, helicities -1 and +1 are forbidden, and the density matrix is completely specified by the angle cp.

Interference density matrix elements between states i and j satisfy:

|ri.| = Ai. ( |ri.| |rj.| )
where the Ai. are real coherence factors. Since the density matrix is unchanged by the replacement ci ci + D, where D is an arbitrary phase shift, the formalism contains a single redundant phase, c, which may be fixed at any value. All other phases are then measured in relation to this one, and the choice is made of cp for the 1+ state in the fitting program.

The helicity decay amplitude for a state of spin-parity Jp in helicity , is given by:


In this summation, l are the possible values of the orbital angular momentum between the decay products (in this case an w meson and a neutral pion). Cl are the amplitudes corresponding to these orbital angular momenta. Thus for a 1+ state decaying to wp, l may take the values 0 or 2 (S- and D-wave respectively), for 1- and 0- only l=1 is possible. At threshold, the amplitude for a 1+ D-wave decay must vanish, and we see that in general the ratio D/S is mass dependent. To account for this possibility, the amplitudes Cl were calculated using Blatt-Weisskopf barrier penetration factors [2].
Blatt and Weisskopf Barrier Penetration Factors.
l Bl(q) 0 1 1 qR/1+qR 2 qR/9+3qR+qR q in MeV/c , R in Fermis , 1 Fermi @ 197 MeV/c
The factors Bl(m) were evaluated from the above expressions, where q is the centre of mass momentum of w or p and Ri is a characteristic 'radius of interaction' describing the shape of the potential well from which the mesons emerge. Bl(mp) is the normalisation factor at the resonance mass mp, and Cl was derived from the D/S ratio at the resonance mass.

The specification of the decay amplitudes was completed in the fitting program by folding F with either the complex relativistic Breit-Wigner function or a background function appropriate to the state i.


 
REFERENCES
[1] S.U.Chung, Spin Formalisms, CERN-71/8(Yellow Report,1971) and
 S.U.Chung et al., Phys.Rev. D11(1975)2426
[2] J.M.Blatt and V.F.Weisskopf, Theor.Nucl.Phys. (John Wiley,1963)