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-p°p°(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-p°p°(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-p°p°(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/c², 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 e² w2 1
¿¿ = ¿ Ú (1 ¿ ¿¿¿¿¿¿¿).wdw (1.5)
dl c² w& s'1. n(w)²b²
where n(w) denotes that the medium may be dispersive.
Substituting w=2pc/R above gives;
dW 1 dR
¿¿ = 4p²e² Ú(1 ¿ ¿¿¿¿) ¿¿
dl n²b² R³
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 ¿¿ sin²qc Ú Ï dEp
hc
Here L is the length of radiator in metres,
A is the fine structure constant
(= 1/137), Epis the photon energy, and Ï is the energy
dependent acceptance of the apparatus.
The factor Ï 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 = ¿¿¿ Ú Ï dEp (1.7)
hc
then in S.I. units, and per electron volt (eV), Np has the value;
Np = 37000 Ú Ï dEp
and the detected number of photons may be expressed as;
N = NpL sin²qc (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;
ìb/b = Ê {(ìn/n)² + tan²qc.ìqc²}
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 ìb/b of less than one part in 10³ is required.
Since b is related to g by;
g = 1 / Ê(1-b²)
this accuracy in b corresponds to one in g of;
ìg/g = b².g² ìb/b
Hence;
ìg
¿¿ = g²b²tanqc ìqc
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/ÊN
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;
ìg g²b³n
¿¿ = ¿¿¿¿¿ ìqc (1.9)
g ÊNpL
The angular spread, ìqc, 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 ìx
in the determination of an avalanche position at a hit wire
is given by;
ìx = s/Ê12
If the chamber is read out electronically every ìt seconds,
and the nominal electron drift velocity in the applied electric field
is bd,
then the computed drift length y
contains an error term;
ìyeec. = bd ìt
which holds if the pulse duration is short compared with ìt.
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 ìy due to diffusion is given by [13];
ìydff. = Ê(2Dy/mE)
where D is the diffusion constant, m is the mobility (m²s-±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 R² = x²+y²,
is determined to within ìR;
ìR = 1/R ((xìx) + (yìy))
ìx 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.
ìxtt. = s/Ê12 + Ê(2Dx/mE)
ìytt. = ìtbd + Ê(2Dy/mE) (1.10)
The error in qc is just ìR/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, Ï, of a dielectric medium, the
refractive index is defined to be;
n = Ê(m.Ï)
With the exception of ferromagnetic materials, and in the
vast majority of cases, m deviates from unity by a few parts
in 10´.
Ï defines the constant of proportionality between the electric
field in a medium, E, and the polarisation, P;
(Ï - Ï0).E = P
Ï0 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 Ï 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 n² may be expressed in terms of Ï, and hence in terms
of w, it is found [14];
Nmqe² fjFONT FACE=SYMBOL>
n(w)² = 1 + ¿¿¿¿.û ¿¿¿¿¿¿¿¿¿¿¿¿¿ (1.11)
Ï0me j (w0.²-w²+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
n²-1 @ 2(n-1)
holds. Then Equation 1.11 becomes;
Nme² fjFONT FACE=SYMBOL>
n-1 = ¿¿¿¿ û ¿¿¿¿¿¿¿¿¿¿¿ (1.12)
2Ï0m w0.²-w²-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, Ïc, 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 Ïc 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 b².
For BR, -dE/dx is given by;
dE
- ¿¿ = Na W Z² 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 ìqc, 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];
Ê<q²> = 1/Ê2b².(Es/E).Ê(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= mc².Ê(4p.137)
= 0.023 GeV
The radiation length, Xp is given by the expression;
1/X0 = 4A (N/A) Z² re² lne(183 1/³ÊZ)
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
<q²> = (Es/E)²
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);
ìqc = 2 (0.023/10)² = 10-µ radians
Thus the total contribution to ìqc 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)³ + (1/8).(d/f)².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;
ìqc(Airy) = 1.22 R/(b²n²d)
This takes a maximum value when the Cherenkov light is just
collected by the optical system, that is when qc = d/(2L).
Hence;
ìqc(Airy)mx. = 1.22 R/(2Lqc) (1.16)
which is of order 10-· m-±.
In conclusion, the total error ìqc on the Cherenkov angle
is given by the sum in quadrature of the individual errors
discussed above;
(ìqc)² = (ìqg)²+(ìqd)²+(ìqm.)²
+(ìqe)²+(ìR/f)²+(ìqa)² (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 200°C 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 4°C 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 4°C, 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 mm³.
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 ìti (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.ìti + 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 22°C.
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 sin²qc
where L was 2 m, and sin²qc is 6.8x10-´ for a 14 GeV/c
pion passing through argon at 22°C, 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 7.5®9 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:
ìqg = 2.10-³
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 7.5®9 eV, and
calculating the change in Cherenkov angle of a 10 GeV/c pion in this
range.
This yields an error:
ìqd = 2.10-³
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:
ìqo = 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:
ìqc = 3.10-³
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 ® wp°p, 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. = û ¿¿¿ . Vv
v
where mv is the mass of the meson and fv is a constant
appropriate to that meson.
The matrix element M(gA®B) is then given by:
M(gA®B) = û (e/2fv) M(VA®B)
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. M²
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. M² 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.(M²) is accompanied by
daughter trajectories with L = Lmx.(M²) - 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
pp®p+p-p+p-p°, and observed the w meson to be an
enhancement at 0.787 GeV/c².
At about the same time, the r meson was photoproduced at
Cornell and seen to have a mass of 0.72 GeV/c².
In 1962 the c meson was observed in the channels
K-p®î°K+K- and K-p®î°K°K° 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/c² 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 0.3±0.1.
(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/c² 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 0.4±0.1.
The analysis of Barber [20] et al. followed, which related to
data taken of the photoproduction reaction
gp ® p+p-p°p°p 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/c² 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 m².
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 mm³, 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 mm³, 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 ìE/E @ 10%/ÊE, 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 d²-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-p°p°(p)
6.1 Introduction
Photoproduction experiments have shown an enhancement in the
4p mass spectrum from the reaction gp ® p+p-p°p°
in the mass region of 1.2 GeV/c²,
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-p°p° [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-p°p°(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 (MM²)
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 MM² to be
in the range -2.1 to 3.9 GeV²/c´.
This gave a final event sample of 8100 events.
The MM² 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-p°p° 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
w®p°g) 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-p°p°(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/c², 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/c² 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
5.0±0.3 GeV-².
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 0.86±0.27 mb, with the parameter a = 0.6±0.2.
The cross-section quoted above has been corrected for
effects such as a) the tagging system efficiency, b) efficiency
of the program TRIDENT, c) w®ppp 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/c² 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)-² (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
ÿ = (q,c), ÿh = (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+Íp-|²
R = ¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿
3 [(M(3p)/3)² - M²(p)]²
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-p°p°p, (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.3®A.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/c².
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/c² 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 d², 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/c², a width of @0.230 GeV/c²,
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.3®A.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 û A-± H'
where c are normalisation constants.
The acceptance matrix was compiled by integrating the acceptance function
A(ÿ,ÿh) folded with the unbiassed moment sums H and H , over
the decay angles, defined below, which were used in the analysis,
A = ÚÚ A(ÿ,ÿh) H H dÿ dÿh (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, ÿ = (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 kÍz, k the direction
of the incoming photon), and x is given by yÍz.
The second set, ÿh = (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 zÍzh
and xh is given by yhÍzh.
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, d² 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 = 1®11) The coherence factors, see App. A.5
Fits were performed in 9 separate bins of 4p mass,
of width 0.10 GeV/c², from 0.9 GeV/c² to 1.8 GeV/c².
From the fitted quantity F1, a D/S ratio for the 1+ signal
was evaluated using the expressions:
Fq = S/Ê3 + D/Ê6 <
font FACE="SYMBOL">
S² + D² = 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, ëp 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 gp®Bp 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 ë 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 î 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 d² 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
ëi - 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 d².
For each of the nine mass bins, identical to those containing
the experimental moment sets, the following procedure was used
to calculate this d².
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, ë, 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/p²) . (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 Ês.
(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 d² 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 d²
from all 9 had been calculated.
After this procedure, the global value of d² was returned to
the MINUIT minimisation routines, and the variable parameters therein
adjusted.
The process continued until a minimum in d² 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 d² 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/c²
and width @230 MeV/c² 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/c² 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 (ÿ,ÿh).
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 sin²qh 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 d²- 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 d² 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/c².
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/c² and has a FWHH @200 MeV/c².
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/c².
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 : d² = 185 for 117 DOF
M(1+) = 1.21 , ë(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/c² for the state with spin-parity Jp, ë(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 : d² = 253 for 116 DOF
M(1-) = 1.21 , ë(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 d²)
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/c²), 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 d² for FIT3, the results of which are shown in
Figure 8.7, and below, for the 1- non-resonant case.
Results from FIT3 : d² = 298 for 208 DOF.
M(1+) = 1.212 , ë(1.212) = 0.231 , D/S = 0.234
M(1-) = 0.770 , ë(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 : d² = 300 for 206 DOF.
M(1+) = 1.214 , ë(1.214) = 0.231 , D/S = 0.233
M(1-) = 0.770 , ë(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 d² of all the fits described
(d²- probability @0.3%).
Results from FIT5 : d² = 296 for 203 DOF.
M(1+) = 1.213 , ë(1.213) = 0.234 , D/S = 0.234
M(1-) = 0.770 , ë(0.770) = 0.436 , (1- mass fixed)
M(0-) = 1.890 , ë(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 d², 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 .
d² = 296 for 208 DOF.
M(1+) 1.213 ± 0.007
ë(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)
ë(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
gp®wp°p can be summarised as follows:
(a) The inspection of the wp° decay angles in the chosen reference
frames indicates that the 1.2 GeV/c² 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 d²- probabilities, or with slightly better
d²- 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/c² 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/c²
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 w°p°') 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 e¶t, 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
d²- 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. ¾ 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 ¾ 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 (X®wp°, w®ppp)
are the experimental averages of the product of
two D-functions [1],
H(lmLM) = ÿ) . Dl (ÿh) >
Where (ÿ,ÿh) are the decay angles shown in Figure A.5.
They thus form an orthogonal set in each event:
Hi(lmLM) = D (ÿ) Dl(ÿh) ± (-1)+ D (ÿ) Dl(ÿh)
For systems X containing only spin parity states 1+ 1- 0- (wp°
cannot be in 0+), diagonal and interference contributions in the decay
angles (ÿ,ÿh) 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 &
nbsp;
H±(lmLM) = ¿ û ¿ àe [H±(lmLM)]
N 2
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. = û ri. î'LM|Jiî>
fi. = û 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., i¾j)
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 î'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:
ûûri. = 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/Ê2) cosqi exp(icp)
fq = (1/Ê2) sinqi cosei exp(icq)
fjq= (1/Ê2) sinqi sinei exp(icjq)
where p/2®qi®0, 2p>ci®0, p/2®ei®0.
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 î, 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/Ê1+q²R²
2 q²R²/Ê9+3q²R²+q´R´
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)