3 >

LAMBDA PRODUCTION IN e+e" ANNIHILATIONS AT HIGH ENERGIES

Julia Karen Sedgbeer Imperial College, London

A thesis submitted for the degree of Doctor of Philosophy

at the University of London

September 1983

1

... ma per trattar del ben ahri vi trova'i3

ddro dell' altre cose, ahfio v'ho soorte.

Dante, Inferno, 1:3

LAMBDA PRODUCTION IN e+e" ANNIHILATIONS AT HIGH ENERGIES

Julia Karen Sedgbeer, Imperial College, London

ABSTRACT

The production of Lambdas in e+e“ annihilations has been measured using the TASSO detector at the storage ring PETRA. The detector is described briefly. The determination of the space-drift time relation in the central drift chamber is described in detail.

Inclusive Lambda production at centre of mass energies, W, between 14 and 36.7 GeV has been studied. Differential and scaling cross sections are presented for momenta up to 10 GeV/c at the highest energies. The value of R^ was found to be 0.52 ± 0.12 (stat.) ± 0.07 (syst.),0.89 ± 0.17 ± 0!ll, and 1.25 ± 0.09 ± 0.14 at W = 14, 22 and 34 GeV.

Comparisons have been made between the production of Lambdas and other baryons and mesons. The data have also been compared to models for baryon production in e+e” annihilations.

Lambda production in 3-jet events has been studied. An enhancement of the yield, consistent with a three-fold increase in the yield from gluon jets, was found.

in

CONTENTSPage

CHAPTER 1 INTRODUCTION 11.1 Introduction 11.2 Baryon Production 5

CHAPTER 2 EXPERIMENT AND DATA ACQUISITION 62.1 Introduction 62.2 PETRA 62.3 TASSO 82.4 Data Taking 142.5 Data Processing 15

CHAPTER 3 DRIFT CHAMBER CALIBRATION 213.1 Introduction 213.2 Drift Chamber 213.3 Space Drift-Time Relation 283.4 Results 36

CHAPTER 4 BARYON PRODUCTION IN e+e“ ANNIHILATION 404.1 Introduction 404.2 Quark-Parton Model 404.3 Q.C.D. 414.4 Fragmentation 424.5 Complete Monte-Carlo Models 464.6 Baryon Production in Fragmentation Models 49

CHAPTER 5 A(A) FINDING TECHNIQUES AND EFFICIENCIES 535.1 A(A) Finding 535.2 Efficiency Determination 66

CHAPTER 6 RESULTS ON A,A PRODUCTION 816.1 Introduction 816.2 Differential and Scaling Cross-sections 816.3 R^ ^ and A,A Yields 876.4 Transverse Momentum Distribution 936.5 Polarisation 102

CHAPTER 7 A PRODUCTION IN JETS 1047.1 Introduction 1047.2 3-Jet Analysis 1057.3 A Production in 3-Jet Events 1077.4 Study of Systematic Bias 115

APPENDIX: 1 Track Parameters 120APPENDIX: 2 Vertex Fitting Program 122REFERENCES 126ACKNOWLEDGEMENTS 129

iv

- 1 -

CHAPTER 1

INTRODUCTION

1.1

Electron-positron storage rings have provided many exciting experi

mental results1•1). The original motivation for these experiments was

to study Quantum Electro-Dynamics (QED) at high energies. However,

hadron production via e+e” annihilations has also become of great in­

terest. The intermediate state in e+e” annihilations to hadrons has

well defined quantum numbers, which is not so for hadron-hadron

collisions.

At the storage ring PETRA QED has been tested in leptonic reac­

tions e+e” -»• Z+Z~ (Z = e, y, t) to momentum transfers up to 'v- 1300 GeV2

The agreement with QED indicates that fundamental leptons are point­

like to ^ 10”16 cm. Recent results show that the data are in agree­

ment with the standard electro-weak model of Glashow, Salam and

Weinberg1•2).

The annihilation cross-section to hadrons can be explained in

terms of pair production of point-like, spin \ constituents of matter

(quarks) which couple to the intermediate state photon. Unlike pair

produced leptons the quarks are not observed as final state particles.

They fragment into hadrons through strong interaction processes not

well understood theoretically. The hadrons appear in well collimated

groups with low transverse momentum wrt each other, jets. First evi­

dence for jets was found at SPEAR1 *3). At PETRA energies the jets of

- 2 -

Fig. 1.1

a) Two jet event and b) three-jet event observed in the TASSO detector at 35 GeV cm energy.

- 3 -

hadrons are clearly visible (see Fig. 1.1) and this gives strong sup­

port that the underlying process is quark pair production. The angular

distribution of the jet axis wrt the beam direction is consistent with

a 1 + cos2 0 distribution expected for spin \ particles. The ratio, R,

between the hadronic cross-section, cr(e+e~ -*■ hadrons), and the y pair

cross-section a .+ - = 4ira/3s is predicted to bey y

R = 3 Z e2 [l + 0(ds)] +

where e^ is the quark charge and ag is the coupling constant of the

currently favoured strong interaction theory QCD. This is in good

agreement with the data1*4) (see Fig. 1.2). Data on long range charge

correlations between jets indicate that the quarks are charged1,5).

The field quanta of QCD are gluons which are also expected to fragment

into hadrons. Hard gluon bremsstrahlung will lead to events with a 3-

jet structure. Such events have been observed at PETRA1,6).

The precise way in which partons evolve into jets of hadrons is

not understood and is not calculable in perturbative QCD therefore

models to describe the fragmentation process have been formulated.

These models have been incorporated into Monte Carlo programs which can

then be used to compare the data with QCD predictions and to try to

understand the fragmentation process. The production of A’s in this

fragmentation process and comparison with the models is the main topic

of this thesis.

The data used in this thesis were taken at the TASSO detector at

PETRA. The detector, described briefly in Chapter 2, is well suited

t To first order in a .s

had

t -------1-------1-------1------- 1-------1-------1-------1------ 1— i-------1------- 1-------1-------1-------1-------1-------1-------1-------1-------1------- 1-------1-------1-------1------- 1------- 1-------1------- 1-------1-------1-------1------- 1 | i i i r

nr tV

n3.O

DIIcr t t

• ORSAY □ CELLO■ FRASCATI X JADE

O NOVOSIBIRSK + MARK J

x SLAC-LBL v PLUTOo DASP

* CLEO

a DHHM

▼ LENA

i--- 1---1— i— I--- 1----1--- 1---1— I___ i____I___ i___u. 1 i i i i

a TASSO

x MKD

OMAC

J------1___ I___ I___ I___ I___ l___ |___ I___ l___ |___ |___ L

10 15 20

W (GeV)

25 30 35 40

3 4 8 7 2

i-p>

i

Fig. 1.2

The ratio R of the total cross-section for e+e- annihilations to hadrons to the y pair cross-section, Oyy = 4lTa2/3s.

to the study of e+e“’ annihilations to hadrons as it includes a large

central detector, with good tracking and resolution, and facilities for

particle identification. The calibration procedure for the central

drift chamber is described in detail in Chapter 3.

Some fragmentation models are discussed in Chapter 4.

1.2 Baryon Production

First evidence on baryon production in e+e“ annihilation has come

from an investigation of p and p production using the time-of-flight

counters for relatively low energy protons. This study was necessarily

limited to protons with momenta below 2 GeV/c, however it showed that

baryon production was significantly greater than had been expected.

Chapter 5 describes the methods used to find A’s in the hadronic events

and the results are presented in Chapter 6. Using the excellent track­

ing and resolution of the TASSO central detector has enabled baryon

production to be investigated over a much greater momentum range.

In Chapter 7 an analysis is made to see if there is any evidence

for differences between A production in quark and gluon jets by study­

ing the relative A yields in 2 and 3 jet events. Recent evidence from

T decay, believed to proceed via three gluons, indicates a major en­

hancement in the A yield over that in the two quark continuum back^;

ground1' .

- 6 -

CHAPTER 2

EXPERIMENTAL SET-UP AND DATA ACQUISITION

2.1 Introduction

A brief description of the TASSO detector and the PETRA accelerator

is given here together with some details of the data taking procedures

and subsequent data processing. Only those parts of the experimental

set-up and data acquisition which are relevant to the work presented in

later chapters are described. Further details may be found in the

references.

2.2 PETRA

The PETRA e+e- storage ring accelerator2*1 is situated at the

DeutschesElektron Synchrotron (DESY), Hamburg (see Fig. 2.1). It pro-,

vides e+e” colliding beams at four interaction regions at centre-of-mass

(cm) energies, W, up to 36.7 GeV*. Two bunches of electrons and two of

positrons circulate in opposite directions and are stored for about

4-6 hours. The maximum luminosity up to the summer of 1982 was

1.7 x 1031 cm 2 s~\ giving an integrated luminosity of ^ 400-600 nb-1

per day as measured at the TASSO experiment. Prior to the installation

of mini-beta quadrupoles * ' the luminosity had been about one third of

this.

The data used in this thesis were taken between July 1979 and August

1982.

* Maximum energy up to the summer of 1982.

N

H08m-»-

3ADE NW «

access tunnelsw

MARK 1 SW

V NE PLUTO/CELLO

^ SE TASSO

Fig. 2.1 Petra.

- 8 -

2.3 TASSO

The TASSO (Twin Arm Spectrometer SOlenoid) detector2,3 is situated

in the SE interaction region at PETRA. It consists of a large cylindri­

cal solenoidal magnet producing a uniform field of 0.5 T along the beam

direction. Inside the solenoid are charged particle tracking chambers

(the central detector) which cover ^ 87% of 411 ster. Outside the coil

are liquid argon shower counters for the detection of photons and elec­

trons, Cerenkov and time-of-flight counters for the identification of

charged particles and muon detectors. The detector is shown in

Figs. 2.2-2.3, and the TASSO coordinate system ir Fig. 2.4.

The analysis presented in Chapters 5-7 uses only data obtained from

the central detector. This is described below.

2.3.1 Central Deteetor

The beam pipe is made of 4 mm thick aluminium and is situated at a

radius of 13 cm. Surrounding the beam pipe are four scintillation coun­

ters, 5 mm thick, 140 cm long, at an average radius of 15.5 cm. Each

counter is viewed at both ends by a photomultiplier. These are used

for the cosmic ray trigger.

Between a radius of 18 cm and 29 cm there is a cylindrical multi­

wire proportional chamber (CPC)2,l+ . The CPC is 170 cm long and has

four concentric layers, each with 480 anode wires and inner and outer

helical cathode strips.

Most of the remaining volume within the coil is occupied by a

large cylindrical drift chamber (DC) ' of length 350 cm and inner and

outer radii 32 cm and 128 cm, respectively. The DC has a total of

p - Chamber

- Chamber

Fig.2.2 TASSO (section)

+

drift chamber--------c o il----------------------iron yoke--------------|i-cham ber----------

4------------ 1-------------1------------ 1------------ 1-

2 3 A 5m

* ■■

r/~ r r 7 ‘ r 7 ’ > ' / / / 7/ / / / -’ 7 ' r~?/ ' ■ v / V >7 7 7 7 / 7 " '7 7 7 7 '7 "> V -

■ ■ ■ / / ' > / / ■ ■ /L . . .r- A / - .

p-chamber iron yoke

— shower counter - T O F

— Cerenkov counters C,,C2,C- Aerogel = Cj

— TOF— drift chamber— LA shower counter

< ^ =— beam pipe— beam pipe counter— p-chamber

— proportional chamber

Fig 2.3

plane view

( T A S S O )

Bz (

Tesl

a)11 -

Vertical

& Rg. 2.4TASSO coordinate system.

Rg. 2,5Magnetic field variation in the region of the d r ift chamber.

a) Bz on solenoid axis b) Bz vs. radius(R) at Z=0, 0=18(f

- 12 -

2340 sense wires in 15 equally spaced layers. In nine of these layers

the sense wires are parallel to the z axis (0°-layers), giving position

information in r(p only. In the other six, the wires are strung at a

small angle, a, to the z axis to give position measurements in z (stereo­

layers). More detail on the DC is given in Chapter 3.

Immediately outside the DC and mounted on the inner wall of the

coil, at a radius of 132 cm, are 48 time-of-flight counters (IT0F)2*6\

Each counter is made of scintillator plastic, measures 390 x 17 x 2 cm,

and is viewed at both ends by photomultiplier tubes. The ITOF covers

84% of 411 ster. and has a mean time resolution of about 380 ps, ^ 350 ps

at the ends and ^ 400 ps at z = 0. Coincidences from both ends of each

counter give 48 binary bits used for the triggering of.the experiment.

The solenoid coil is 440 cm long and has its axis parallel to z.

It provides an axial field of 0.5 T which is constant over most of the

volume. Small deviations occur at the edges of the solenoid (see

Fig. 2.5).

2.3,2 Luminos'Cty Monitor

The luminosity monitor consists of eight identical arrays of coun­

ters situated in the Forward Detector2*7) (see Fig. 2.6), four on either

side of the interaction region. Each array consists of lead glass

shower counters and plastic scintillator counters giving a well defined

acceptance. The luminosity is measured using Bhabha scattering events

identified by requiring a coincidence in diagonally opposite counters

accompanied by a minimum deposited energy in both lead glass counters.

The geometrical acceptance of the system is 1.4 x 10 3 ster. Statisti­

cal errors on the luminosity measurement are small and the systematic

shower counter S

iIt*lOI

- 14 -

2.4 Data Taking

The strobe for the experiment is derived from beam-pick-up elec­

trodes mounted in the beam pipe at 7.1 m from the interaction point.

In 2 + 2 bunch mode the time interval between beam crossings in PETRA is

3.96 ys. Triggers for the experiment are obtained from various compo­

nents of the detector. Only the charged-track trigger is considered

here.

error is estimated to be ^ 5% 2*8). Radiative corrections to 0(a3) 2*9^are taken into account.

2.4.1 CPC Processor

Information from the four anode layers of the CPC is passed to a

hardware processor2'10 which looks for coincidences, within 96 azi­

muthal sectors, between hits in at least three of the four layers. The

hits must be consistent with a track having a transverse momentum

greater than a preset minimum (y 100 MeV/c). Adjacent sectors are

then OR'd together to give 48 binary bits which are used in several

triggers.

2.4.2 DC Processor

The DC hardware processor2*11 gives fast track recognition for

use in the trigger. The 48 CPC and ITOF 'bits' are input to the pro­

cessor together with information from six specific layers of the DC.

The processor looks for correlated bits in at least five of these layers.

The allowed combinations of bits define a set of tracks of various

transverse momenta called masks. The requirement for a track is a

valid mask together with the corresponding CPC and ITOF 'bits'.

- 15 -

2,4.3 Multi-track trigger

This trigger required at least two tracks from the DC processor

with transverse momenta, p^, greater than a preset minimum value. Some

data were taken with a requirement of four tracks. The p^ was required

to be greater than 0.22 GeV/c at cm energies less than 25 GeV and also

for some of the high energy data where, usually, pT > 0.32 GeV/c was

demanded. The trigger efficiency, for events which subsequently pass

the hadronic event selection procedure is estimated to be ^ 98% or bet-o o ter at all energies '.

2.4.4 Data Acquisition

On receipt of a trigger the strobe is disabled and the data are

read into a Nord 10 computer via a CAMAC system. The input rate is

typically a few Hz. An on-line program * ' monitors the experiment,

reformats and checks the data and then transfers the data to an IBM

on-line disc at the central computing facility. The contents of the

disc are periodically written to magnetic tapes, called Dumptapes.

2.5 Data Processing

The large numbers of triggers accumulated on Dumptapes undergo

several stages of processing. The early stages are concerned with fast

and efficient background rejection using a minimum of event reconstruc­

tion. Data are then loosely categorised before undergoing further

selection and comprehensive reconstruction.

The processing chain to select data of the type e+e” hadrons is

described below.

- 16 -

2.5.1 Track Reconstruction

Two programs, FOREST and MILL2,13\ are used for the reconstruction

of tracks in the central detector. The FOREST program, used in the

first stage of processing, has been optimised for use as a fast event

filter. Full reconstruction is done later with the MILL program which

carries out exhaustive track finding in the central detector.

The FOREST program uses a link-and-tree2’ 1 3 3 2 * 1 method for track

finding. Links are formed between pairs of hits in different layers of

the DC. As a link has two hits it already determines the parameters of

a straight line or a circular track coming from the interaction point.

Elementary trees are formed by combining one link (trunk) with other

links, with similar track parameters, which share one hit with the

trunk (branches). A branch of one elementary tree can be the trunk of

another. Elementary trees are combined to form full trees and a fast

algorithm is used to find chains of links, within trees, that form

tracks. Track parameters (see Appendix 1) are found in two stages;

firstly hits in the 0° layers of the DC are used for track finding.

Parameters defining the projection of the track in the xy planes are

determined from a circle fit to these hits. Secondly, hits in the DC

stereo-layers together with the parameters from the circle fit are used

to find the trajectory in z.

Speed is achieved in the FOREST program by restricting the type of

links and elementary trees that are formed.

The MILL program uses both link-and-tree and conventional road

track finding methods to make a thorough search for tracks in the DC.

CPC anode hits are then added to the tracks by means of a road method

and the track is refitted using both DC and CPC hits.

17

2.5.2 Data Reduction

The stages in the hadronic event selection procedure are:

PASS 1

All events on the Dumptapes are put through the FOREST program.

The processing time per event, on an IBM 370/168, is ^ 60 ms including

^ 20 ms for reading, writing and decoding. The output is written to

PASS-1 tapes. Various data checks are also done.

PASS 2

Background rejection is performed on the basis of the tracks pro­

duced by FOREST. Events having > 2 tracks reconstructed in r<p each

with |d0| < 2.5 cm are selected and written to PASS 2 tapes. About 10%

of PASS 1 events satisfy these criteria.

PASS 3

Loose selection of possible hadronic candidates. Events having

a) > 3 tracks reconstructed in r<p each with | d0 | < 2.5 cm, or

b) > 2 tracks reconstructed in r(p and z each with | d0 j < 2.5 cm, and

|z0 | < 10 cmsare selected. These cuts reduce the data by a factor of ^ 20. The

remaining events are put through the MILL program and the output is

written to PASS 3 tapes. The time taken for the track reconstruction

of a high multiplicity event is ^ 10 s on an IBM 370/168.

PASS 4

Final selection of the hadronic event sample (HADSEL selection).

The data on the PASS 3 tapes contain not only hadronic events but also background from beam-gas and beam-pipe scattering, T pair production,

18 -

Bhabha scattering, y pair production and yy scattering. The following

event selection was used to purify the sample. The procedure reduces

the PASS 3 data by a factor ^ 10.

TRACK CUTS

For a charged track to be used for the final event selection it

had to satisfy:

1) It is reconstructed in three dimensions (r<}>z) with | do | < 5 cms.

2) The transverse momentum, p^, > 100 MeV/c.

3) |cos 0| < 0.87.

4) Izn-z I < 20 cm where z is the z coordinate of the event vertexv vaveraged over the tracks satisfying cuts 1-3.

EVENT CUTS

Events were required to satisfy the following:

1) At least 4(5) tracks for W < 25 GeV (W > 25 GeV). This removes

background from Bhabha and yy scattering, y pair and T pair production.

2) To remove background from T pair production the event was divided into two hemispheres wrt the sphericity axis. For W < 15 GeV

(W > 15 GeV) events having three tracks in one hemisphere and 1

(1 or 3) tracks in the other hemisphere were rejected if the effec­

tive mass of the 3-prong system was less than 1.78 GeV (t mass), assuming pion masses for the particles.

3) For W < 14 GeV the event was divided into two hemispheres wrt the

z-axis. To discriminate against beam-gas and beam-pipe scattering

the event was required to have at least one track in each hemisphere

and Q_jJ < 3 where is the charge of the i ^ particle.

- 19

4) jz l < 6 cm. This removes some beam-gas scatters.

5) The sum of the particle momenta, ^ | | , must satisfy

I |p.| > 0.265 W . i

This cut removes some of the contribution from beam-gas and yy

scattering.

A further few background events, ^ 3%, were rejected by means of

a visual inspection. Remaining background in the sample is estimated

to give a systematic uncertainty in the number of events of less than 2% at all energies2*8 .

2.5.3 Data Sample

The data used in this thesis were taken between July 1979 and

August 1982 and cover cm energies between 14.0 and 36.7 GeV. The inte­

grated luminosities and numbers of events are shown in Table 2.1.

- 20 -

Table 2.1

Data samples

Run period W Luminosity Events(GeV) (nb-1)

July 1979- August 1982

29.6 - 36.7 <34.4>

^ 73000 20832

June 1981 22.0 ^ 2800 1889July 1981 14.0 ^ 1600 2704

- 21 -

CHAPTER'3

DRIFT CHAMBER CALIBRATION

3.1 Introduction

The space drift-time relation in the TASSO central drift chamber

(DC) is non-linear. The form of this relation must be determined in

order to obtain a good spatial resolution and hence high track finding

efficiencies and a good momentum resolution.

The method used to determine the space time relation and the reso­

lution achieved are described below after a brief description of the DC

and the origins of the non-linearities.

3.2 Drift Chamber

3.2.1 Design

The TASSO central drift chamber (DC)3,1 has an active length of

3.23 m and is mounted inside a solenoidal coil providing a magnetic

field of 0.5 T parallel to the z-axis. There are 2340 drift cells

arranged in 15 equally spaced concentric layers. The inner and outer

layers being at radii of 36.7 cm and 122.2 cm, respectively. In each

layer adjacent sense wires are separated by three potential wires giving

drift cells of height 1.2 cm and width 3.2 cm measured along the arc.

In nine of the layers the wires are strung parallel to the z axis (0°-

layers) and provide coordinates in the plane perpendicular to this axis.

The other six layers (stereo-layers) are strung at small angles 4°)

with respect to the z axis to provide position measurements in z. The

- 22

chamber is strengthened by five layers of material which are held at

ground potential. The chamber is filled with a gas mixture of 50% argon

and 50% ethane at atmospheric pressure. Prior to July 1980 a 90:10 mix­

ture of argon-methane was used. The DC layout and cell structure is

shown in Figs. 3.1-3.2. The electric field configuration in a cell

adjacent to a stiffening layer is shown in Fig. 3.3.

3,2,2 Non-linearities

The DC position measurements are reconstructed from the drift-

times. For the purposes of track-finding the required position, within

a drift cell, is the distance, d, at which the track crosses the arc

through the sense wire (see Fig. 3.4).

The drift velocity, v(jr£ft> is ^ ^ yns-1 (27 Jins-1) in argon- ethane (argon-methane) giving drift times up to ^ 400 ns (^ 600 ns).

Under normal operating conditions in the TASSO DC the variations in the

electric field within the cells has little effect upon vcjr££t and so

this velocity can be assumed to be constant.

Drifting electrons follow complex paths due to the influence of

the electric and magnetic fields. The drift paths within a cell are

shown in Fig. 3.5 where it can be seen that the presence of the magnetic

field removes the left-right symmetry.

The measured drift-time, t(r££tJ will correspond to the shortest

time path from the track to the sense wire. It can be seen from Fig. 3.6

that the minimum drift-time path depends not only upon the distance d

and the side, left or right, but also upon the angle, a, at which the

track passes through the cell. Hence, in general

a

o°

* 9°.

0°

- U LS°

0*

sense wire (W 30 yum)

cathode wire (Mo 120xm)

v°

0°

♦ 3,36'

O'

- 3,35*

TASSO0

2560

*

Endplates ( A l )35 Outer Shell (A l)

ASeparating Cylinders(Rohacell Al Sandwich)

~T— :tt

Inner Tube (Epoxy Fibreglass)

15 Layers ,of Wires

1.

-3520

Fig . 3.1

Schematic diagram of the drift chamber: a) section;beam axis.

b) cut along

- 24 -

<o

o -

Potential Wires : 120 um^

v

\ T

Sense Wire: 30(Jm^Fig. 3 .2

Drift cell geometry.

Fig. 3 .3

Electric field lines in one drift cell. The separating cylinder is indicated below.

T TV.’.

- 25 -

Fig . 3 .4

Schematic diagram of tracking passing through a drift cell, showing the distance from track to sense wire, d.

TASSO drift cell

B = 0,5 Tesla

drift path mm \

F ig . 3.5

Electron drift paths within a drift cell with both electric and magnetic fields.

- 26 -

d f d'

where

d tdrift Vdrift

The extent to which the relation deviates from linearity can be seen

in Fig. 3.7 which shows the distribution of d7 obtained from cosmic ray

data. The cosmic ray tracks are randomly distributed in d and have

angles of incidence, a, between ^ ±0.4 rads. Ideally, if there were

no non-linearities, this distribution should be flat.

The method used to obtain accurate position measurements, within

the limitations discussed below, from the measured drift times is des­

cribed in Chapter 3.3

3.2.3 Spatial Resolution: Limitations

The resolution that can be achieved with the DC is limited by:

i) The chamber construction. This introduces both random and syste­

matic effects from wire sag, wire support construction, electro­

static deflection, etc.

ii) The time measurement. The drift time is affected by:

a) finite track width caused by 6-ray production;

b) ionization fluctuations, which dominate near (< 5 mm) the

sense wire;• c) diffusion, which dominates for drift paths > 1 cm;

d) finite time resolution of the electronics 2 ns).

The relative contributions of these effects are shown in

Fig. 3.8.

- 27

FieldWires

Incident Tracks a! Angle a Incident Tracks af Angle clFig. 3.6Minimum drift-time paths within a drift cell for tracks at a distance d and angle a.

Distribution of d ’ (see text) from a sample of cosmic ray data taken with an Argon-Ethane gas mixture.

- 28 -

The drift time is not measured directly. The time, which is

measured relative to the strobe (see Chapter 2), must be adjusted

to the beam-beam interaction time, and includes contributions from

the time-of-flight from the interaction point to the drift cell

(typically a few ns) and signal propagation time down the sense

wire (^ 4 ns m” 1) and in the external cabling.

iii) The accuracy with which the space drift-time relation can be

determined.

3.3 Space Drift-Time Relation

3.3.1 Introduction

As has been said in Chapter 3.2.2 the drift time, tcjr££t> depends

on the trajectory of a track through a drift cell, in particular on

the distance d and the angle a (see Fig. 3.6). Therefore tracking in­

formation is necessary for determining the space time relation. Cosmic

ray data are used as they are plentiful and sufficiently simple so that

the behaviour and efficiency of the track finding program is well

understood. Cosmic ray tracks are well distributed throughout the

volume of the DC and over the angle a.

An approximation to the distance d can be obtained by assuming a

linear space time relation

X = ^ d r i f t

where v is a mean velocity which gives an approximation to d for all

possible values of t(jr££t> i.e. for all possible trajectories through

the cell. Each drift time gives two possible DC hits at ±x. It is

left to the tracking program to resolve this ambiguity. These DC hits

- 29

can be used as a basis for track-finding and hence corrections to the

linear approximation

6x = d - x

can be determined.

Determination of the space-time relation is therefore a two-step

process:

i) Obtain a mean velocity, v, which gives a linear approximation to

d.

ii) Find corrections to the linear approximation as a function of x

and a.

3.3.2 Determination of the Mean Drift Velocity v

In order to determine v the drift times, t, . - , must be extracted1 driftfrom the time measurement, T, obtained from the DC. Ignoring small

random effects due to diffusion, ionization, etc., and after correc­

tions have been made for differences due to external cabling (typically

^ several ns), there are essentially four components in the time T,

T to + tTOF + tdrift + Cwire *

where t . is the signal propagation time down the sense wire (defined wireas zero at z = 0); t is the time-of-flight from the point oflUFclosest approach to the origin to the drift cell in question and t0 is

a timing offset which adjusts the measured time to the beam-beam inter­

action time or, for cosmic ray data, the time at which the particle

passes closest to the z axis. As tm-_ and t . are small compared to r TOF wire rtdrift and as they can only be determined after tracks have been found they are neglected initially.

- 30 -

200

ZL

b 100\\\\

L \ ^-V-- ^\ ✓y

__ ^-D iffusion^

---------------------------------- Electronics

/ \/ 'Prim ary sta tist ics

10 15Fia . 3 .8

x(mm)

Approximate relative contributions to the resolution as a function of the drift length, x, showing a constant electronics dispersion, a diffusion term « ix and a contribution due to primary ion pair statistics.

Fig. 3.9

6x as a function of a for fixed x.

06 (rads.)

Fig. 3.106x as a function of x for fixed a.

x (mm.)

- 31 -

The value of to for cosmic ray data is determined at the same

time as v. Initial approximate values of t0 and v, based on knowledge

of the gas, electronics, cable lengths, etc., are used in a linear

space-time relation

x = (T - t0)v .

Using these DC hits tracks are found and the sum of the squared resi­

duals ;. 6x2 , where

6x = x - xt , tr

and x is the distance of the track from the sense wire measured tralong the arc, is minimised with respect to t0 and v. This procedure

is repeated with the values of to and v obtained from the minimisation

until the values converge. Typically four passes are needed depending

upon the accuracy of the initial approximations.

The timing offset for e+e” data is found in a similar way but the

value of v is held fixed.

3.3.3 Parametrisation of the Space Drift-Time Relation

Corrections to the approximate linear relation are parametrised

in terms of x and a:

6x = f(x,a) .

For fixed x, 6x is a slowly varying function of a over the range of a

covered by the data (see Fig. 3.9). The variation as a function of x

(see Fig. 3.10) is more pronounced. Hence the parametrisation can be

reduced to a 1-dimensional form

6x = f(x)

- 32 -

for small intervals of a. The functional form used is a polynomial of

degree 44

f(x) = ^ a^x^ i=0

for positive and negative values of x separately with a intervals of

0.04 rads.

The linear space time relation is used to find approximate trajec­

tories with distance x^ and angle a (see Fig. 3.11). The residualstr tr

6x = x _ - xtr

are corrected for time-of-flight, t and signal propagation time,l U r

t . , and accumulated in the intervals of a and in 0.2 cm intervalswirein x for both positive and negative values of x and a. The polynomial

is fitted to the mean residuals for each a bin. The set of polynomials produced give the sign and magnitude of the correction to be applied

to a hit at x associated with a track with angle a. These corrections

are applied to the DC hits and the tracks are refitted. Again the

residuals are accumulated and a second set of polynomials obtained.

This procedure converges to give a final set of polynomials after about

six iterations.

Two sets of polynomials are determined; one for the 0°-layers and

another for the stereo layers.

Due to the strengthening layers at ground potential the electric

field configuration is not identical in all cells. For a given angle,

a, the correction for a track passing at a distance x in a cell outside and adjacent to a stiffening layer is the same as the correction needed

Corr

ectio

n (m

m.)

- 33 -

Fig. 3.11

Approximate trajectory through drift cell with distance xtr from sense wire and angle atr. Residual 5x = xtr-x, see text.

D (cm.) D (cm.)Fig. 3.12

Correction polynomials for the O-degree and stereo layers for Argon-Ethane gas (see text).

- 34 -

at-x in a cell inside the layer. The procedure takes this sign-change

into account when the residuals are accumulated.

Typical sets of polynomials for 0° and stereo layers in argon-

ethane are shown in Fig. 3.12.

3.3.4 Gas Mixture Dependence of Space Drift-Time Relation

The nature of the space-time relation depends upon the gas mixture

in the chamber. Not only is the drift velocity dependent upon the gas

but so also is the ionization potential, amount of 6-ray production

and the diffusion. The differences between argon-ethane and argon-

methane can be seen by comparing Figs. 3.7 and 3.13 which show the

distribution of hits across the cells calculated assuming a linear

space-time relation. The correction polynomials for argon-methane are

shown in Fig. 3.14. Comparing Figs. 3.12 and 3.14 it can be seen that

argon-ethane gives a reasonably linear relation over a large region of

the cell. For argon-methane large corrections are needed at the edges

of the cells and there is also a higher probability of a spurious sig­

nal in the adjacent cell (cross-talk) when the track passes close to

the field wires. The probability of cross-talk was ^ 20% in argon-

methane and < 10% in argon-ethane. The advantages of argon-ethane are

slightly offset by its higher drift velocity. The time resolution of

the electronics (2.5 ns) together with the drift velocity in argon-

methane limits the spatial resolution to ^ 70 ]Jm. For argon-ethane

the time resolution was improved to 2 ns giving a fundamental resolu­

tion of ^ 90 ym.

- 35 -

Distribution of d T (see text) from a sample of cosmic ray data taken with an Argon-Methane gas mixture.

D (cm.) D (cm.)Fig. 3.14

Correction polynomials for the O-degree and stereo layers for Argon-Methane gas (see text).

- 36

3.4 Results

The effects of the corrections were estimated by comparing the

spatial resolution both with and without correction. The improvement

can be judged qualitatively from the corrected d* distribution (see

Fig. 3.15). The distribution is approximately flat as expected.

To estimate the resolution one hit on a track was left out of the

fit and the residual, 6x, plotted. For data taken in the Argon-Ethane

gas mixture the width of this distribution for all tracks is 410 ym

which improves to 210 ym after correction. Additional fine corrections

have been applied in certain cases to improve the resolution further

(see Ref. 2.5). The resolution depends on the distance across the

cell, x, and on the entrance angle, a (see Fig. 3.16). After correction

the angular dependence is very small. As expected the resolution de­

teriorates in the region of the sense wire and, to a lesser extent, at

the field wires.

The resolution in Argon-Methane gas is shown in Fig. 3.17. Here

the resolution is approximately constant over two thirds of the cell

but deteriorates in the region of the field wires. The average resolu­

tion improves from 520 ym to 280 ym after correction.

Num

ber/

0.5

mm.

- 37 -

(cm)

Fig. 3.15

Corrected d ’ (see text) distribution from a sample of cosmic ray data taken in the Argon-Ethane gas mixture.

- 38 -

x (mm.)

Fig. 3.16

Spatial resolution, without and with correction, measured with data taken in the Argon-Ethane gas mixture. The resolution is plotted versus the position in the cell for various entrance angles.

- 39

Fig. 3.17Spatial resolution, without and with correction, measured with data taken in the Argon-Methane gas mixture. The resolution is plotted versus the position in the cell.

- 40 -

CHAPTER 4

BARYON PRODUCTION IN e+e" ANNIHILATION

4.1 Introduction

Hadron production in e+e” annihilation is not yet understood.

However, various models have been formulated which describe possible

mechanisms by which final state hadrons are formed. These models are

essential tools in e+e" experiments. They are used for describing par-

ton fragmentation into hadrons, so that the underlying parton distri­

butions can be unfolded from the observed final state particles and for

determining efficiencies and acceptances.

The most widely used fragmentation models are described after a

brief description of the Quark-Parton Model (QPM) and the modifications

to this due to the currently favoured strong interaction theory Quantum

Chromodynamics (QCD).

4.2 Quark-Parton Model

In 1964 Gell-Mann and Zweig proposed a scheme to explain the spec­

troscopy of hadronic states which involved hypothetical constituents

called quarks4,1 »4,2) . Independently the study of deep inelastic

lepton-nucleon scattering gave results which could be explained by as­

suming that hadrons are composed of point-like spin \ particles or par-

tons4,3 . The partons were later associated with quarks.

In the QPM hadron production in e+e” annihilations is assumed to

proceed via quark-antiquark pair production. The mediating current

(photon) couples directly to the charges of the quarks, the total

- 41 -

hadronic cross-section will therefore be proportional to the cross-

section for muon pair production:

a(e+e~ -*■ hadrons) „ „ _?• j L 6#/ J. + —• \ Xa(e+e •* y y )

where e^ is the quark charge and the factor 3 accounts for the fact that

all quarks come in 3 colour states.

Partons do not appear as final state particles. Showers of hadrons,

or jets, with small transverse momenta w.r.t. the parton directions,

are formed.

The model also predicts that inclusive single particle cross-

sections should be independent of energy (scaling).

Low energy data from the SPEAR and DORIS storage rings4*1 were

found to be in reasonable agreement with this model.

4.3 QCD

QCD is the currently favoured field theory of strong interactions.

The QPM of e+e“ annihilations is modified by the field quanta (gluons)

which mediate the strong force between quarks and couple directly to the

colour of the quarks. Quarks can radiate gluons which are expected to

also give rise to additional jets of hadrons in the final state. Emis­

sion of hard non-collinear gluons will lead to events with three jets

of hadrons unlike the more common two-jet qq events. Such events will

exhibit a broadening of the transverse momentum distribution w.r.t. the

2.jet axis. The produced hadrons should retain a planar configuration

due to energy-momentum conservation of the primary 3 partons. The

emission of more than one hard gluon will lead to more complicated

- 42 -

configurations but this is calculated to be a small effect at PETRA

energies.

Results from PETRA and PEP experiments are consistent with many of

the predictions of QCD.

The process by which quarks and gluons become jets of hadrons is

not calculable in perturbative QCD. Fragmentation models have to be

used to form complete descriptions of e+e“ annihilations to hadrons.

4.4 Fragmentation

The most widely used fragmentation models are the chain decay

model due to Feynman and Field4,5) and the colour-string model of the

LUND group4,6). Their wide usage is mostly due to the fact that much

work has been done on implementing them into full Monte Carlo (MC)

programs.

Various alternative models have recently been proposed to describe

fragmentation but as they tend to make specific predictions for limited

aspects of the data they will not be considered in detail.

4.4.1 Feyrman-F-ieId Fragmentation

Feynman-Field (FF) fragmentation is a parametrisation of the for­

mation of a jet of mesons generated by a fast outgoing quark or anti­

quark. In e+e” annihilation when a qq pair is produced the quark and

antiquark are assumed to fragment independently. The fragmentation

takes place by the generation of new quark-antiquark (qq) pairs in the

colour field. The initial quark combines with an antiquark from such a

pair to form a primary meson (see Fig. 4.1). Similarly the remaining

quark combines with the antiquark from a newly generated qq pair to

- 43

qq'

rank1 1

» primary mesons decay to

final s ta te hadrons

# *primary

mesonsFig. 4.1

Schematic diagram of Feynman-Field fragmentation, qq pairs are generated in the colour field and primary mesons, Mf_, are formed. The primary mesons decay to final state hadrons.

qFig. 4 .2

Colour field between outgoing quark and antiquark.

- v vq q' q' q

c££> & ....... <£££M, Ma m3

Fig. 4.3

Fragmentation in the colour-string model: the string’breaks’ forming a qq pair and hence mesons, M^, are formed.

- 44 -

produce another meson. This process continues until there is insuf­

ficient energy to produce further mesons. The primary mesons are then

decayed to form the final state hadrons.

The assumptions of the model are that:

i) Only uu, dd and ss pairs are created in the colour field and ss

pairs are suppressed so that the ratio uu:dd:ss = 2:2:1.

ii) At each step, the probability, f(z), that the meson takes a frac­

tion z of the available energy is given by

f (z) = 1 - ap + 3sLg (1-z)2

where

z (P., + E)meson

+ E)quark

(4.1)

(4.2)

iii) Only pseudoscalar and vector mesons are considered and they are

equally probable.

iv) qq pairs are produced with zero net transverse momentum. The

transverse momentum, p^, of the q(q) is Gaussian distributed:

exp

Lepton-nucleon scattering and low energy e+e“ data are well represented

with ap = 0.57 and a = 330 MeV/c.

Only pair production of u, d and s quarks were considered in the

initial FF model, however at PETRA energies heavy quarks (c and b) are

also produced. The FF model has consequently been extended by Ali et

al.4*7) to include the primary production of heavy quarks and their weak decays according to the six quark model of Kobayashi and Maskawa4* .

- 45 -

The fragmentation function for heavy quarks into mesons is expected

to differ from Eq. (4.1) as the meson containing the heavy quark is

expected to take most of the momentum. This is supported by various

data on charm production4* . The fragmentation function for c and b

quarks is taken as

f(z) = constant .

The weak decay of the heavy quarks includes both semileptonic and

non-leptonic decay modes. The semileptonic modes are assumed to account

for 10% of all modes.

Weak decays of heavy quarks are expected to lead to a broadening

of the p , of the observed jets similar to that produced by gluons.

Hence, heavy quark pair production will give a background to 3-jet

events.

4.4.2 Colour-String Fragmentation

The fragmentation model of the LUND group is based on the massless

•relativistic string model. The colour field between the outgoing q and

q is confined to a tube-like region because the exchanged gluons attract

each other and hence constrain the colour lines of force (unlike the

Coulomb field where the lines of force spread out). This linear colour

force field between the q and q is the 1 string1 of the model (see

Fig. 4.2). The string has a constant energy density per unit length so

that the energy increases as the q and q move apart. When there is

sufficient energy a qq pair can be created in the colour field (see

Fig. 4.3). This process continues until all the kinetic energy has been

degraded into qq pairs and hence mesons. Transverse momentum and mass

can be generated by allowing transverse motion in the colour field. A

- 46 -

tunneling probability

P « exp (- £ m2)

where k is the string energy density and is the transverse mass,

/m2 + p2, of the qq pair gives a Gaussian distribution in p^ and sup­

presses heavy quarks so that uu:dd:ss = 1:1:0.3. c and b quarks are so

heavily suppressed that they cannot be created in the colour field.

In the relativistic string model a small point-like part of the

string can carry a finite amount of energy and momentum, such a ’kink1

gives features similar to those of a gluon in QCD. Therefore for qqg

the model assumes that the string is stretched between q and q via a

gluon (see Fig. 4.4). The string breaks at the kink to a qq pair to

give two strings. It is assumed that each string contains equal energy.

Each string fragments independently so that the final state particles

are distributed around two hyperbolae, in momentum space, between q and

g and q and g (see Fig. 4.5). In this scheme qqg events will be less

3-jet-like than if the partons fragmented indpendently. More particles

are expected between q(q) and g than between q and q. Some data support

these features of the model14*10) .

4.5 Complete Monte Carlo Models

The most widely used models of e+e~ annihilations, using QCD with

a fragmentation parametrisation, are those of Hoyer et al.4*11 , Ali

et al.1*’12) and the LUND groups*6 .

4.5.1 Hoyer et aZ.3 A H et at.

These M.C.’s use QCD with a FF fragmentation. The basic differ­

ences are in the order to which QCD is taken, the treatment of gluon

fragmentation and how energy-momentum conservation is achieved.

- 47

/ / / / / y

g Jy & x

, ' S S \'\\ ' \jtf'

'V'\ \\

''tt.

q

Fig. 4 .4

qqg events in the colour string model. The string is stretched between the q and q via the gluon.

Fig. 4.5

Schematic diagram of the fragmentation of qqg events in the colour string model.

- 48 -

Only terms up to first order in ag (the strong coupling constant)

are used in the Hoyer M.C. whereas second order terms are also included

by Ali.

Gluons are assumed to materialise into a qq pair which are then

treated with the FF prescription for fragmentation. All the energy of

the gluon can be given to either the q or q (Hoyer et al.) so that a

gluon fragments exactly as a quark of the same energy. Alternatively

the energy can be split between the q and q (Ali et al.) using a frag­

mentation function

f ( z ) = z2 + (1 - z ) 2

where

gluonEquark

This produces softer particles and a higher multiplicity in the gluon

jet.

4.5.2 LUND M.C.

The LUND M.C. uses QCD up to first order in ag to give the parton

distribution. The fragmentation scheme described in Section 4.4.2 is

then applied. This model has certain features which are similar to

those in F.F. The transverse momentum of qq pairs produced in the

colour field is Gaussian distributed with a width ^ 350 MeV/c. The

fragmentation function favoured by the LUND group is

f (z ) = (1 - z ) 2

but in practice the FF fragmentation function is often used.

- 49 -

4.6 Baryon Production in Fragmentation Models

4.6.1 Introduction

Recent data from e+e“ annihilations at high energies have shown

copious baryon production4*18^. It had been assumed that baryon yields

would be small because of the need to generate three coloured quarks

(antiquarks) at a point in phase space. The fragmentation models des­

cribing meson production, discussed above, have therefore had to be

extended to include baryon production.

4.6.2 Baryons in the FF Chain Decay Model

FF-type fragmentation has been extended in the Ali and Hoyer M.C.Ts

for use by the TASSO collaboration, by T. Meyer4*13).

Baryons are assumed to result from the production in the colour

field of diquark-antidiquark pairs (see Fig. 4.6). The qq can then

align with a single quark to form a baryon. Similarly an antibaryon

is also produced. The probability to produce a diquark-antidiquark

pair in the colour field, P , is a parameter to be fixed from the data.

No assumptions are made about the compositeness of the diquarks produced

the flavour of each quark is determined independently and the transverse

momentum of the diquark is obtained from the sum of the transverse mo­

mentum of the two individual quarks.

To allow for the possibility of leading baryons in opposite jets

the model allows a finite probability, f°r Producing a qq pair

which aligns with the original qq pair (see Fig. 4.7) in such a way

that the two quarks initiate one jet and the two antiquarks the other.

This will lead to baryon-antibaryon correlations in opposite jets.

- 50 -

Fig. 4.6

Schematic diagram of baryon production in the model of Meyer4*13).

Fig. 4.7

Diagram for leading baryons in opposite jets in the model of Meyer4*13).

*---- C£z~ 7 " B ---->q d a q

Fig. 4.8

Diquark-antidiquark (dd) production in the colour string model.

- 51 -

The fragmentation function and transverse momentum dependence are

assumed to be the same as for mesons, and the ratio of octet to decuplet

baryons produced is assumed to be the same as the ratio of pseudoscalar

to vector mesons.

The parameters P_.. and P ~ were determined by comparing the pre-

dictions of the model with data on p,p production in the momentum range

0.5-2.0 GeV/c from the TASSO4*14 and JADE4,15) collaborations. A value

of PB1 =0.075 describes the p,p yield in this momentum range but the BIavailable data are not sensitive to the value of P 0.dZ

4 .6 .3 Baryons i n th e C o lo u r -S tr in g Model

The LUND model for fragmentation has been extended to include baryon

production by assuming that diquark-antidiquark pairs can be produced

in a colour field in a similar way to qq pairs (see Fig. 4.8). The di­

quark (antidiquark) is treated as a composite object, the production

probability being dependent on the mass as in the case of single quarks

(see Section 4.4.2), so that diquark production will be suppressed rela­

tive to quark production and, in particular, strange diquarks will be

heavily suppressed. This has the consequence that a strange baryon is

much more likely to be produced with a strange meson and a non-strange

antibaryon than with a strange antibaryon. Also doubly strange baryons

(for example, E), where strange diquark production must be involved,

will be heavily suppressed. Although the model agrees with p,p and

A,A data in the SPEAR energy region it fails to agree with data at

higher energies (see, for example, Bell et al.4’16)) unless the amount

of strange diquark production is increased relative to non-strange

diquark production.

- 52 -

The transverse momentum of the diquarks is assumed to have the same

distribution as for quarks and the ratio of octet to decuplet baryon

production is assumed to be the same as the ratio for pseudoscalar to

vector meson production. Recent results on A production4* indicate

that decuplet baryon production is suppressed.

The LUND model predicts a somewhat larger baryon yield in gluon

jets as compared to quark jets due to the finite probability of the

string TbreakingT at the gluon fkinkf into a diquark-antidiquark pair.

However this is a small effect and cannot account for the large baryon

yields observed in upsilon decay4*17\

- 53 -

CHAPTER 5

A(A) FINDING TECHNIQUES AND EFFICIENCIES

5.1 A(A) Finding

5 .1 .1 I n t r o d u c t io n

Charged particle tracks in the central detector were used to look

for candidates for A -> p7T~ and A -*■ pir+ decays. The basis of the search

was to use the fact that the tracks from the decay start from a vertex

remote from the primary interaction point. Therefore the procedure was

to try to find pairs of tracks which intersect in three dimensions away

from the primary vertex and to reject background decays, secondary

interactions and accidental vertices. Accidentally reconstructed ver­

tices occur when a track from a decay or secondary interaction inter­

sects with another track, usually from the primary vertex, at a space

point.

A preliminary selection of track pairs was made on the basis of

the vertex in the xy plane. A three dimensional vertex fit was per­

formed on those pairs which could conceivably give a A(A) candidate.

Finally, a series of cuts was applied to purify the sample. These pro­

cedures are described in detail below. In the following the term A(p)

will be used to refer to both A(p) and A(p) unless specifically stated.

5 .1 .2 P re lim in a ry S e le c t io n

The number of oppositely charged track pairs in each event can be

large. Preliminary selection criteria were applied in order to reduce

- 54 -

i) The track projections in the xy plane must intersect or the mini­

mum distance between them must be < 2 cms.

ii) The angle between the tine joining primary vertex and decay point

and the A candidate momentum vector in the xy plane, a2 , must

satisfy cos a2 > 0.8. For the A hypothesis the higher momentum

track was taken to be the proton. The primary interaction point

was determined from large-angle Bhabha scattering events taken

concurrently with the data. The technique used was to take one

track from a Bhabha event and intersect it, in the xy plane, with

a track from the next Bhabha event in the sample. Taking the

mean values of.the intersection point over short running periods

gives the primary vertex position with errors of less than 0.1 mm

in x and y. The z co-ordinate of the interaction point cannot be

determined by this method as the beam bunch lengths are typically

^ 4 cm.

iii) Track pairs having more than four hits in the tracking chambers

on either track before the intersection point were rejected.

5 .1 .3 V e r te x F i t

The fit, described in more detail in Appendix 2, constrained the

two tracks to pass through a common space point. Track parameters from

the reconstruction program MILL (see Chapter 2) together with an ini­

tial approximation for the decay vertex were input to the fitting pro­

gram. The sum of the squared residuals between the track trajectories

and the hits in the tracking chambers was minimised to give the

the number of track pairs which were submitted to the three dimensionalvertex fit. These criteria were:

- 55 -

co-ordinates of the decay vertex and new values of the track parameters.

Candidates with an unsuccessful fit were rejected. For the remaining

candidates a mini-DST, containing all relevant quantities, was made so

that the cuts could be quickly optimised. The track with the highest

momentum was taken to be the proton. Kinematically this is always true

when the A momentum is greater than 0.270 GeV/c.

5 .1 ,4 S e l e c t i o n o f A C an d id a tes

The selection criteria were based on knowledge of tracking in the

central detectors, the kinematics of A decay and on the nature of back­ground candidates.

a) Hits in tracking chambers

Candidates were rejected if the number of hits before the decay

vertex, on either track, was greater than could be considered as acci­

dental. There is a small probability that the track finding program,

MILL, will wrongly associate a hit with a track.

Similarly candidates having tracks with three or more hits missing

following the decay vertex were rejected. Missing hits may be caused

by chamber and track-finding inefficiencies.

b) Collinearity

The collinearity angle in the xy plane, QLz (see Chapter 5.1.2), was required to be less than 3°.

c) Proton and Pion Track Geometry

Tracks from A decay do not, in general, pass through the primary

interaction point. The distance of closest approach to the primary

vertex, h (see Fig. 5.1) was required to be greater than 1.5 mm for

- 56 -

Fig. 5.1

p and it track projections in the xy plane showing the distance between primary and decay vertices, d; the distance of closest approach of the track pro­jections to the primary vertex, h; and the angle between the line joining primary and decay vertices and the A momentum vector.

- 57 -

the proton track and greater than 3.0 mm for the pion track. The pion

from A decay has, on average, a significantly larger value of h than the proton. The distributions of h calculated from the kinematics of

A decay at momenta of 1 GeV/c and 5 GeV/c, ignoring vertex resolutions,

are shown in Fig. 5.2. Errors in track reconstruction and in the ver­

tex resolution introduce an error of about 1 mm in h.

These cuts remove a lot of background from accidentally recon­

structed candidates which have a primary track.

d) A Flight Path LengthA momentum dependent cut was made on the distance between primary

and decay vertices in the xy plane, d, see Fig. 5.1. The probability,

P, for a A to decay within the distance d was required to satisfy:

For a A transverse momentum of 1 GeV/c (5 GeV/c) this criterion is satisfied for 2.5 cm < d < 21.2 cm (12.6 cm < d < 105.9 cm).

e) Centre-of-Mass System Decay Angle

In the A centre-of-mass the proton decay distribution is isotropic.

of the A, measured w.r.t. the A direction of flight. Track pairs from

other decays or accidental combinations, when considered as a A decay, do not give a uniform distribution m cos 0 . The distribution tends

to be forward and backward peaked due to the assignment of proton and

0.3 < P < 0.95 .

Cuts were made on the decay angle 0* of the proton in the rest system

pion masses to the tracks. In particular K°'s misidentified as A's+

give a cos 0* distribution biased towards values of +1#

The forward peaking is more pronounced for low momentum K°'s.• • I ^ ISome background was removed by requiring |cos 0 | < 0.9.

Arb

itrar

y un

its

Arb

itrar

y un

its

- 58 -

Fig. 5.2

Distributions of h (see Fig. 5.1 and text), for the proton and pion tracks from A decay, for A momenta of 1 and 5 GeV/c.

- 59

Distribution of decay angle m the cm, cos 9 , for K0,s interpreted as A pir decays, for momenta of a) 5 GeV/c and b) 1 GeV/c.

- 60 -

f) Electron Pairs

Electron pairs from gamma conversions were removed by requiring

that the effective mass of the pair, when considered as e+e", is greater

than 50 MeV.

g) K° Background

A major source of non-accidental background came from K° decays.

K°'s when interpreted as A decays give a pTT effective mass spectrum

which peaks in the region of the A mass (see Fig. 5.4). Most K°1s were

removed by rejecting all candidates whose 7T+ tt“ effective mass was within

15 MeV of the K° mass.

h) Momentum Cuts

Low momentum particles have a higher probability of interaction in

the beam pipe and are more affected by multiple scattering. Therefore

the uncertainties in the efficiency of tracking such particles is large.

Candidates having one or both tracks with a transverse momentum less

than 0.1 GeV/c were rejected.

The tracking of low momentum primary particles can give trajec­

tories which miss the primary vertex due to interactions. These tracks

can give accidental candidates. A lot of such background was removed

by requiring the A momentum to be greater than 1 GeV/c.

i) Shared Tracks

If, after all other cuts had been made, candidates shared a common

track, the candidate with the lowest chi-squared/degree of freedom from

the fit was retained. This happened rarely.

- 61 -

J-------- 1_____ I_____ 1_____ I I I I1.1 1.2 1J 1.4

M,. (GeV/c*)

Fig. 5.4

Effective mass spectra of K®Ts at 1 GeV/c and 5 GeV/c interpreted as A pir decays.

- 62 -

5.1.5 Enhancement of High Momentum A Signal

The yield of high momentum A's is expected to be.small. An alter­

native set of selection criteria was used to enhance this signal.

Cuts (a), (b), (f), (g), (h) and (i) (see Chapter 5.1.4) were

still used.

In the decay of a fast A the proton tends to follow the direction

of flight of the A. Therefore the proton trajectory passes close to

the primary vertex. For this reason cut (c) was removed.

Fast A's decay, on average, far from the primary vertex. There­

fore cut (d) was replaced by a cut requiring the distance between pri­

mary and decay vertices in the xy plane, d (see Fig. 5.1) to be greater

than 25 cm. This distance was chosen so that the decay vertex was

beyond the first tracking layers.

5.1.6 A Signal

The A finding method described above was applied to the data at

14, 22 and 34 GeV cm energy (see Table 2.1). The cuts described in

Chapter 5.1.5 were only used for the high energy data as there were in­

sufficient data at 14 and 22 GeV to allow such tight cuts to be applied.

The raw effective mass spectrum, M , for a subsample of the high

energy data is shown in Fig. 5.5a. This large number of track pairs

was reduced by requiring a three dimensional vertex fit (see Fig. 5.5b).

Effective mass spectra obtained after the cuts are shown in

Fig. 5.6. For the high energy data, the spectrum obtained after apply­

ing the tight cuts is shown in Fig. 5.7. Clear A signals are seen at

all energies. A scatter plot of the A candidate momentum versus M ,

corresponding to Fig. 5.6c, is shown in Fig. 5.8.

Eve

nts

/10

M

eV

Even

ts/1

0

MeV

- 63 -

a) pn effective mass spectra for all +/- track pairs for a subsample of the data at 34 GeV cm energy.

b) The pn effective mass spectra after a 3-dimensional vertex fit.

Even

ts/1

0

MeV

E

ven

ts/1

0

MeV

Ev

ents

/10

M

eV

- 64 -

p7T effective mass spectra obtained after the cuts described in Section 5.1.4 for the data at a) 14 GeV, b) 22 GeV and c) 34 GeV cm energy.

P (G

eV/c

) -n

E

ven

ts/1

0 M

eV

- 65 -

pit effective mass spectra obtained after cuts described in Section 5.1.5.

A candidate momentum, p, versus the pir effective mass for A candidates from the 34 GeV data sample passing the cuts of Section 5.1.4.

- 66 -

5.2 Efficiency Determination

5.2.1 Introduction

The efficiency for finding A's was estimated from a Monte Carlo

program SIMPLE5,1 . This program incorporated *an event generator and

a comprehensive simulation of the central detector, tracking and event

selection procedure. A simulation of the A-finding techniques des­

cribed in Chapter 5.1 was applied to the M.C. data. The features of

the M.C. relevant to the A analysis are described below.

5.2.2 Event Generator

Events containing A's were generated using the prescription of

Hoyer et al. including baryon production by T. Meyer (see Chapter 4).

The generator includes effects due to initial state radiation calculated• 5 2 }by Berends and Kleiss ’ .

Some of the parameters, which describe fragmentation and baryon

production, used in this generator are shown in Table 5.1. The values

of these parameters were determined from TASSO data5* 3’5 * 4^. Alter­

native values, also shown in Table 5.1, were used to check that the

efficiency estimate was independent of these values. Finally, the

LUND generator was used with parameters as modified by Bell et al.5,5

to fit TASSO data.

Figure 5.9 shows the efficiency estimate for finding A's, with the

cuts of Chapter 5.1.4, as a function of the A momentum for each of the

three M.C.'s. The efficiencies agree within errors.

- 67 -

Table 5.1

Monte Carlo Parameter Values

Parameter Standardvalue

Alternativevalue

a-p (meson) 0.56 0.30apT 0.320 GeV/c 0.380 GeV/c

P/V 1.3 2.8

s/u+d+s 20% 13%ap (baryon) 0.56 0.80

0/D 1.3 2.8

PB 0.075 0.075

ap Fragmentation function parameter (see Chapter 4).

apT Intrinsic width of the transverse momentum distribution.

P/V Pseudoscalar to Vector Meson Ratio.

0/D Octet to Decuplet Baryon Ratio.

Pg Probability diquark/quark production.

- 68 -

>>O•c<D

• —

O

Ll I

Fig. 5.9

Efficiency for finding A's, with the cuts of Section 5.1.4, as a function of the A momentum, p, obtained from three Monte Carlo programs (see text).

- 69 -

5.2.3 Detector Simulation

The particles of the generated event were put through a simulation

of the central detector. The trajectory of each particle was followed

until it had decayed, been absorbed or left the fiducial volume. The

simulation included multiple scattering and interactions in the material

of the chambers and photon conversions. Decay products were also fol­

lowed through the detector.

Losses of A's and their decay products occur due to interactions

in the beam pipe and detector walls. The loss due to absorption as a

function of the A momentum is shown in Fig. 5.10. Above 1 GeV/c the

total loss is ^ 6%.

Hits were generated in the tracking chambers along the trajectory

of each charged particle. The resolution and efficiencies of the cham­

bers were included. An estimate of the overall drift chamber efficiency

for different running periods was made by comparing the distribution of

the number of hits associated with tracks with M.C. predictions. The

tracks used were required to have p^ > 0.1 GeV/c, ]cos 0| < 0.87,

|do| < 2.5 cm and |z0| < 6.0 cm (see Appendix 1). The hit distributions

for two different running periods are shown in Fig. 5.11. The overall

drift chamber efficiency, £, is the product of two efficiencies; the

hardware efficiency, due to electronics, gas, etc., and the software

efficiency which depends on the accuracy of the drift chamber

corrections.

The efficiency, £, was found to vary between 0.84 and 0.94 for the

data used in this analysis. Figure 5.13 shows the affect of this change

in £ on the A finding efficiency. The variation in £ for different

running periods was included in the M.C. simulation.

Fig. 5.10

Loss of ATs due to absorption of the A or its decay products in the detector walls as a function of the A momentum, p.

- 71 -

Fig. 5.11

Distributions of the number of drift chamber hits, in the O-degree and stereo layers, associated with tracks for two different running periods.

72 -

Fig. 5.12

Monte Carlo predictions for the number of drift chamber hits, in the O-degree and stereo layers, associated with tracks for two different drift chamber efficiencies, e (see text): a) e = 84%,b) e = 94%.

- 73 -

Fig. 5.13

A-finding efficiency as a function of the A momentum, p, obtained using two different drift chamber efficiencies, e (see text).

- 74 -

The performance of the track finding program, MILL, was simulated

by an algorithm. The algorithm, which gives the probability of finding

a track as a function of the number of hits (see Table 5.2), was ob­

tained by passing M.C. data through the program MILL.

The track parameters, ro, do, $o, Zq and tan A (see Appendix 1)

were determined from circle and line fits to the tracking chamber hits

in r(j) and z, respectively.

The hadronic event selection procedure, described in Chapter 2,

was applied to each event. This procedure is dependent upon the A

momentum (see Figs. 5.14) as the occurrence of a high momentum particle

in an event reduces the probability of producing sufficient charged

tracks to satisfy the selection criteria.

The fiducial volume and tracking efficiency of the central detec­

tor severely affect the A finding efficiency (see Fig. 5.15). The

losses are worse for the pion track as the momentum of pions from A

decay is usually small (see Fig. 5.16).

5.2.4 Simulation of A Finding

The A finding procedure described in Chapter 5.1 was applied to

A's in the M.C. Sample where both the proton and pion are successfully

tracked. However, a vertex fit was not performed. The effects of

successive cuts on the efficiency for some specific A momentum ranges

are given in Table 5.3.

The major source of errors in the efficiency determination comes

from the estimate of tracking losses of the proton and pion. The esti­

mated systematic error is about 10% of the value of the efficiency.

The final efficiencies at each energy are shown in Fig. 5.17.

- 75 -

Table 5.2

Monte Carlo Tracking Algorithm

0° layers

$ of hits 1-4 5 6 7 8 9

Probability track found 0.0 0.8 0.9 0.9 1.0 1.0

Stereo layers

# of hits 1-2 3 4 5 6

Probability track found 0.0 0.9 0.95 1.0 1.0

- 76 -

Fig. 5.14A momentum dependence of the hadronic selection procedure, HADSEL (see Chapter 2), for data at 14 and 34 GeV cm energies.

- 77 -

Fig. 5.15P (G eV/c)

a) Probability (as %) that both particles from A decays at W = 34 GeV are successfully tracked in the drift chamber as a function of the A momentum.

b) % loss of A's due to loss of the pion, proton or both through interactions or unsuccessful tracking as a function of the A momentum.

In both a) and b) the branching ratio is included but not the HADSEL efficiency.

Arb

itrar

y un

its

Arb

itrar

y un

its

- 78 -

Pion momentum spectra from A pit decays for A momenta of 1 and 5 GeV/c.

- 79 -

Table 5.3

Breakdown of A-finding efficiency for specific momentum ranges as a % of all generated A ’s at 34 GeV c.m. energy

Procedure% A’s surviving procedure

All momenta 1.0 - 2.0 GeV/c 5.0 - 7.0 GeV/c

All generated 100. 100. 100.

Hadronicselection

71. 73. 67.

Proton and pion tracks found

21. 23. 19.

Preliminaryselection

18.6 21.2 18.0

CUTS

Mq+q_e e 18.2 20.8 17.8

|cos 0*1 16.8 19.5 16.1

Decayprobability P

12.3 14.5 10.7

h 9.0 10.9 7.2

+ =i i 7.6 8.9 5.1

Collinearity 6.3 7.6 5.1

pT and pA 5.2 7.3 5.1

Effic

ienc

y (%

) Ef

ficie

ncy

(%)

Effic

ienc

y (%

)

- 80 -

P (G eV /c)

Fig. 5.17

Final efficiency estimates for finding A’s at a) W = 34 GeV for both the standard cuts and the alternative cuts of Section 5.1.5, b) W = 22 GeV and c) W = 14 GeV as a function of the A momentum, p. Branching ratios and HADSEL efficiencies are included.

- 81 -

CHAPTER 6

RESULTS ON A,A PRODUCTION

6.1 Introduction

In this chapter differential cross-sections for A,A production in

e+e" annihilations at 14, 22 and 34 GeV c.m. energies are presented to­

gether with A,A yields and p^ distributions. Finally a measurement of

the A(A) polarisation is presented in Chapter 6.5.

Comparisons are made of the production of A and A with that of

other baryons and mesons using results from this and other experiments.

The data are also compared with M.C. predictions.

6.2 Differential and Scaling Cross-Sections

The differential cross-section, da/dp, and the scaling cross-section,

(s/8) (da/dx) , where s = W2 and 3 = f°r the sum °f A and A pro­duction have been determined at 14, 22 and 34 GeV c.m. energies.

The total cross-section for e+e~ -»■ hadrons, G , at each energy

is obtained from the integrated luminosity, L:

atotNL 9

where N is the number of observed hadronic events, A is the acceptance

for hadronic events and f is a correction factor for radiative effects.

The measured luminosity, L, and number of hadronic events at each energy

is given in Table 2.1. The total A,A cross-section is then

- 82 -

A,A tot ,T . at0t “ — NA nb ’

where is the total number of A and A in the sample of N hadronic

events, or, expressing a in terms of the theoretical QED y pair

cross-section

a(e+e~ -*■ y+y”) =+ ..-N _ 4IIa'3s

and the ratio

R = tota(e+e -► ]i+\T)

then

A,A 4ITa2 „ NAn = ■ ■■ • R •-- .tot 3s N ( 6 . 1)

The cross-section was determined from the A,A signals and efficiencies

described in the previous chapter. At each energy the A and A signals

were found to be equal within errors. An estimate was made of the num-

ber of A(A)’s and the background under the signal in specific momentum

bins. The background varies rapidly in the region of the A mass as

this mass is close to the threshold value m + m = 1.078 GeV. To allowp 7Tfor the uncertainty in the background estimate the statistical error, e,

on the size of the signal in each momentum bin was taken to be

£ = /ej + ej , tot back

where e is the statistical error on the signal and background in the

A mass region and is the error on the background estimate. The

number of A and A in each bin was corrected for the efficiency of obser­

vation to obtain the total number in the bin. The efficiency estimate

t TKe 1\ jjir — I'Oq — l • l cA" . tlqpcA.WCv5> ■ ''vuA-jzA Vv acw- ~ 1-0 3 -\ l S f < - \

- 83

includes a correction for unobserved A,A decay modes and also for un­

accepted hadronic events. The systematic error was estimated to be 10%

and arises mostly from uncertainty in the tracking efficiency.

The cross-sections, da/dp, for the data at 14 and 22 GeV are shown

in Table 6.1 and Figs. 6.1 and 6.2. Also shown are the predictions for

the cross-sections from the M.C.'s of Hoyer et al., including baryons5,1^*+

and that of the LUND group modified by Bell et al.5*2''. Both M.C.’s

are in agreement with the data though the number of data points is small

and errors are large due to the low measured luminosities at these

energies.

The high energy data covers a spread of c.m. energies from

29.6-36.7 GeV. A correction was made in order to obtain the cross-

section at the mean c.m. energy of 34.4 GeV. If where

where N = T . N..L\ i

For this data sample two different A-finding methods were used

(see Chapter 5.1). They were found to agree within errors and so the

results were combined. The A-finding efficiency for the second method

(Chapter 5.1.5) is very low at low momenta and therefore the cross-

section below 4 GeV/c was calculated from the first method (Chapter 5.1.4)

alone. Above 4 GeV/c a weighted average was taken of the values

q(e+e -»• AX) + o(e+e~~ -» AX) a(e+e” ■* y+y“)

is assumed constant over this energy range and there are hadronic

events at each c.m. energy then

EOr/w?) n aN " N

- 84 -

Table 6.1

Differential cross-sections for A,A production at 14 and 22 GeV c.m. energy

W = 14 GeV

p(GeV/c)

da/dp(pb/GeV/c)

1.0 - 2.0

2.0 - 4.0

88.6 ± 33.5

21.1 ± 8.1

W = 22 GeV

P da/dp(GeV/c) (pb/GeV/c)

1.0 - 2.0 52.2 ± 14.3

2.0 - 3.0 32.1 ± 9.8

3.0 - 5.0 10.3 ± 4.1

o

oJ---------------------1_____________ L.1 2 3

J___4.P

J _____________S ©( G e V / c )

Fig. 6.1

Differential momentum cross-section for the sum of A and Aproduction at cm energy W = 14 GeV. Also shown are the pre­dictions of the LUND and Hoyer M.C.’s.

dff/dp (

pb/GeV/c

)

- 86 -

Fig. 6 .2

Differential momentum cross-section for the sum of A and Aproduction at cm energy W = 22 GeV. Also shown are the pre­dictions from the LUND and Hoyer M.C.Ts.

- 87

obtained by both methods. The weight being inversely proportional to

the statistical error.

The cross-section for the high energy data is given in Table 6.2

and Fig. 6.3. Also shown are results from the JADE experiment at PETRA

on A production6,3 , and M.C. predictions.

The scaling cross-section, (s/$) (da/dx), where $ = p^/E^ and

x = 2E^/W was determined in a similar way to that described above for

da/dp. An estimate was made of the weighted number of A and A in the

signal and of the background in specific x bins, the weight being 1/3.

Here

NAa A,A = 4IIa2 R y _1_6 tot 3 N L 3. *

i=l 1

The statistical and systematic errors were estimated as for the differ­

ential cross-section above.

The scaling cross-sections are given in Table 6.3 and Fig. 6.4.

The cross-sections scale within the errors.

6.3 and A,A yields

The total cross-section for A and A production was determined by

integrating the cross-section over the measured momentum range and

estimating the contribution from the unmeasured regions using a) M.C.

predictions and, for comparison, b) a parametrisation of the invariant

cross-section, (E/4IIp2)(da/dp), of the form a.exp (-bE). The latter

method cannot be reliably used on the data at 14 and 22 GeV because of

the limited momentum range over which the cross-section is measured,

the limited number of data points and the large errors. At these low

- 88 -

Table 6.2

Differential cross-section for A,A production at 34 GeV c.m. energy

W = 34.4 GeV

p(GeV/c)

da /dp (pb/GeV/c)

1.0 - 1.5 27.9 ± 5.6

1.5 - 2.0 24.0 ± 3.9

2.0 - 3.0 17.8 ± 1.9

3.0 - 4.0 8.1 ± 1.5

4.0 - 5.0 6.1 ± 1.2

5.0 - 7.0 3.1 ± 0.9

7.0 - 10.0 1.7 ± 0.6

dcr/

dp

(pb

/GeV

/c)

- 89 -

P (GeV/c)

Fig. 6.3

Differential momentum cross-section for the sum of A and A pro­duction at cm energy W = 34 GeV. Also shown are JADE resultson A production®* and predictions from the LUND and Hoyer M.C.fs.

- 90 -

Table 6.3

Scaling cross-sections, (s/(3) (da/dx), for A,A production

W = 14 GeV

X (s/B)(da/dx) ()Jb GeV2)

0.22 - 0.3 0.214 ± 0.074

0.3 - 0.4 0.089 ± 0.032

0.4 - 0.6 0.018 ± 0.012

W = 22 GeV

X (s/3)(da/dx) (yb GeV2)

0.14 - 0.2 0.420 ± 0.107

0.2 - 0.3 0.218 -± 0.053

0.3 - 0.4 0.062 ± 0.033

0.4 - 0.6 0.014 ± 0.013

- 91 -

Table 6.3 (contd)

Scaling cross-sections, (s/B)(da/dx), for A,A production

W = 34.4 GeV

X (s/B)(da/dx) (lib GeV2)

0.09 - 0.11 0.920 ± 0.190

0.11 - 0.15 0.599 ± 0.073

0.15 - 0.20 0.355 ± 0.044

0.2 - 0.3 0.138 ± 0.022

0.3 - 0.4 0.060 ± 0.018

0.4 - 0.6 0.032 ± 0.011

(jASO’q^) xp/op-£//s

- 92 -

Fig. 6 .4

The scaling cross-sections s/B do/dx for the sum of A, A production at cm energies 14, 22 and 34 GeV.

- 93 -

energies the contribution to the cross-section for A (A) momenta less

than 1 GeV/c is expected to be large. For the data at 34 GeV the in­

variant cross-section was parametrised over the range 1-5 GeV/c.

Both Hoyer and LUND M.C.'s were used to predict the fraction of

the cross-section outside the measured momentum range. These fractions

are given in Table 6.4. Also shown in Table 6.4 are the additional

contributions obtained from the parametrisation of the invariant cross-

section. The M.C.s predict a larger contribution than the parametrisa­

tion by a factor of about two at all energies. The JADE data points

for A production6*3 in the range 0.4-1.4 GeV/c are in closer agreement

with the M.C. predictions than the parametrisation and so the LUND M.C.

was used to obtain values of and the total yield of A and A over

the whole momentum range. These are shown in Table 6.5. The values of

R.t are plotted in Fig. 6.5 together with low energy data from other,6-6).experiments”*”J ; values of R..0 zo and R - are also shown from this 1C ,K p,p

and other experiments6,7). The average A,A multiplicity is shown in+ + — . . .Fig. 6.6 together with values for II , K and p(p) multiplicities. The

increase in A production between 7 GeV and 34 GeV c.m. energy is larger

than that for mesons; in particular the increase in R^o over this

energy range is about half the factor for R^+ —The scaling cross-sections at 34 GeV c.m. energy for K , A(A),

— +p(p) and II production from this experiment are shown in Fig. 6.7. For

values of x > 0.1 the slopes for both baryons and mesons are similar.

6.4 Transverse Momentum Distribution

The differential cross-section da/dp7, where p^ is the A transverse

momentum w.r.t. the sphericity axis, was determined for the data at

- 94 -

Table 6.4Predictions for % cross-section outside measured range from M.C. and parametrisation of invariant

cross-section

W = 14 GeV W = 22 GeV W = 34 GeV

< 1 GeV/c > 4 GeV/c < 1 GeV/c > 5 GeV/c < 1 GeV/c > 10 GeV/c

HOYER 38% 4% 33% 7% 29% 2%

HOYER + leading baryons

32% 7% 28% 8% 26% 3%

LUND 39% 4% 28% 7% 22% 2%

Invariantx-section 25% 2% 16% 3% 13% < 1%

- 95 -

Table 6.5

A,A yields per event and RA,AYield/event

w

(GeV)

Measuredmomentumrange(GeV/c)

Yield/event in measured

range

Yield/event extrapolated to

all momenta

14 ir—i 0.07 ± 0.02 0.13 ± 0.03 ± 0.0222 1 - 5 0.14 ± 0.03 0.22 ± 0.04 ± 0.03

34 1 - 1 0 0.24 ± 0.02 0.31 ± 0.02 ± 0.04

RA,A

w

(GeV)

Measuredmomentumrange(GeV/c)

ra ,s inmeasuredrange

Ra ][ extrapolated to all momenta

14 1 - 4 0.30 ± 0.07 0.52 ± 0.12 ± 0.0722 1 - 5 0.58 ± 0.11 0.89 ± 0.17 ± 0.11

34 1 - 1 0 0.95 ± 0.07 1.25 ± 0.09 ± 0.14(stat.) (stat.)(syst.)

- 96 -

10t*cz'£cz'51cz

• TASSO O MARK It

{<> 0

} of

♦ t I

♦

t

K°+K°

P+P

A+A

10

*

i

10-2 J__1— L 1 110

J_____ L... I. 1__I 1 1...110'

W(GeV)

Fig. 6.5

The ratio of the total cross-section for e+e” annihilations to the hadron h (h = A/A), p(p), K°(K0)) to the y pair cross-section ayy = 47ra2/3s for data from this equipment and MARK II.

Ave

rage

par

ticle

mul

tiplic

ity

- 97 -

W(GeV)

Fig. 6.6

The average number of tt+ + ir_ , K+ + K , p + p and A + A per event from this and other experiments.

s//3

.da/

dx

(/ib

.GeV

2)

•- 98 -

Fig. 6.7The scaling cross-sections, s/B da/dx, for tt+ + it , K + K , p + p and A + A production at 34 GeV cm energy from this experiment.

- 99 -

34 GeV. The sphericity, S, is defined to be

, l Pt .S = 4 MIN -----

l tili

where the sums run over all tracks in the event and the is measured

relative to the sphericity axis. In this analysis only charged tracks

coming from the region of the primary interaction point were used to

determine S and the axis. The method used to determine da/dp2 follows that for da/dp.

The cross-section is shown in Table 6.6 and Fig. 6.8. Also shown

are the cross-sections for all charged particles and for K° production.

The p2 distribution for A's and K0ls fall less steeply in the low p2 region than that for all charged particles. Parametrising the cross-

section in the form a.exp (-p2/2a2) over the range 0.0-0.5 (0.0-1.0) (GeV/c)2 for all charged particles (for K°’s and A ’s) gives values for

aT of

0.324 ± 0.007 GeV/c for all charged particles,

0.450 ± 0.025 GeV/c for K0,s,0.410 ± 0.026 GeV/c for A's.

The p2 dependence of A ’s in the LUND and Hoyer M.C.'s, using an

intrinsic p^ of 0.320 GeV/c for both quarks and diquarks, is also shown

in Fig. 6.8. The reasonable agreement between M.C. and data gives some

confidence in the fragmentation models used.

100 -

Table 6.6Differential cross-section, da/dp2, for A,A production at W = 34.4 GeV

PT(GeV/c2)

da/dp2(pb/(CeV/c)2)

0.0 - 0.1 230 ± 35

0.1 - 0.2 144 ± 28

0.2 - 0.3 120 ± 24

0.3 - 0.4 61 ± 200.4 - 0.5 69 ± 18

0.5 - 0.6 47 ± 16

0.6 - 0.8 37 ± 9

0.8 - 1.0 14.8 ± 7.9

1.0 - 2.0 10.6 ± 2.4

2.0 - 5.0 3.4 ± 0.7

da/

dp

r2

(nb

/(G

eV/c

)2)

- 101 -

• All charged

o K®+K°

A A+A

— LUND— Hoyer

♦

♦

5 6 7

pT2 ((G eV /c )2

Fig. 6.8The differential cross-section da/dp^, where pT is the transverse momentum wrt the sphericity axis, for all charged particles, K° + K° and A + A production at 34 GeV cm energy: from this experiment.

102 -

6.5 Polarisation

If A ’s are produced via the weak decay of heavy quark states then

polarisation will result. For a mean A polarisation P the angular de­

pendence for A -+■ ptt decays is

da --3-------- r* cc i + a p c o s 0dcosG

where 8 is the angle between the direction of flight of the A and the proton in the centre of mass of the A, and a is the decay parameter.

Hence a measurement of the asymmetry

A = F ~ B A F + B

where

and

8F = / (1 + aP cos 0) d cos 0

0

0B = / (1 + aP cos 0) d cos 0

-8

gives an estimate of the polarisation as

A = BaP 2 * ( 6 . 2)

The polarisation was determined for the data at 34 GeV. An esti­

mate was made of the number of A(A)Ts in the forward (0.0 < cos 0 < 0.9)

and backward (-0.9 < cos 0 < 0.0) regions surviving the cuts of section 5.1.4. The limits on cos 0 are due to the cut on this variable

in the A-finding procedure. Additional cuts on the A candidate momen­

tum were made such that 2.0 < p < 5.0 GeV/c as this region has the best signal/background ratio.

103 -

M.C. data were used to estimate the efficiency for finding A(A)Ts

in the forward and backward regions. The M.C. assumes zero polarisation.

The observed A(A) signals were corrected for the efficiency giving

values for the asymmetry, A, of -0.03 ± 0.13 for A’s and 0.06 ± 0.13 for

A’s. Hence, from Eq. (6.2), using B = 0.9 and a = 0.642 gives values

for the polarisation of -0.11 ± 0.45 for A fs and -0.19 ± 0.45 for A’s.

The polarisation is consistent with zero though the large errors, due

to the signal/background ratio and the efficiency estimate, make the

measurement somewhat insignificant.

- 104 -

CHAPTER 7

A PRODUCTION IN JETS

7.1 Introduction

Models used to describe e+e” annihilations to hadrons make various

assumptions about the fragmentation of quarks and gluons into jets of

particles (see Chapter 4). It is usually naively assumed that gluon

fragmentation is similar to that of quarks. However results have al­

ready been presented by the DASP7*1 and CESR7*2) collaborations which

indicate that the yield of baryons in gluon jets is higher than that

in quark jets. An excess of baryons has been observed at the T reso­

nance when compared to yields observed in the continuum. The T is

believed to decay predominantly to three gluons. There are also indi­

cations from the EMC experiment that planar events contain an excess

of protons (antiprotons)7 * 3^.

The data from this experiment have been used to look for differ­

ences in A production in quark and gluon jets. For this study it was

assumed that the data at 14, 22 and 34 GeV are predominantly composed

of 2-jet, i.e. qq events. Thus, values obtained for A yields (see Chapter 6) are essentially measurements of yields from quark jets.The high energy data contain a subsample of 3-jet, i.e. qqg events.

If such events can be isolated then one may be able to study A pro­duction in gluon jets. The 3-jet event selection procedure used in

this study and an evaluation of its reliability is presented in

Chapter 7.2. The results obtained are presented in Chapter 7.3.

- 105 -

7.2 3-Jet Analysis

A 3-jet analysis was performed on the data at 34 GeV cm energy.

The method used was that of generalised sphericity7,1* applied to

charged tracks in the central detector. This method determines an

event plane by minimising the transverse momentum out of the plane and

gives three jet axes in the plane. The energy of each of the jets is

determined from the angles between the axes in the plane on the assump

tion that the instigating partons have zero mass.

The analysis sorts the charged tracks into three groups, each

associated with one of the three axes.

A subsample of events consistent with having a 3-jet structure

was selected by demanding:

a) xi < 0.9 where xi = E /E, and E is the largest of themax beam max 6three jet energies (see Fig. 7.1).

b) The scalar sum of the momenta of the particles in each jet,

Y. Ip.I, satisfies J. .Ip.I > 1.5 GeV/c.^jet1*i1’ ^jet1*i1c) The normal to the event plane makes an angle, 0 , of less than 70°

to the beam axis, this ensures that the event plane, and hence the

jets, lie within the acceptance of the detector (see Fig. 7.2).

The selection criteria were chosen from M.C. studies to give a

reasonably large sub-sample of 3-jet events (^ 7%) while keeping the

contamination of qq events to a minimum. The M.C. generates ^ 28%

qqg events. M.C. data was also used to determine the accuracy of the

analysis. The analysis and selection procedure was applied to M.C.

events which had been passed through a detector simulation and hadroni

- 106 -

Fig. 7.1qig final state in the cm. XjL = Eparton/Ebeam.

Fig. 7.2Angle between normal to event plane and beam axis.

Reconstructed jets with energies E, at angles a wrt parton momenta in qqg events.

- 107 -

event selection procedure. The sub-sample of 3-jet M.C. events was

found to contain a contamination of 12% of qq events. To evaluate the

efficiency of the 3-jet analysis the reconstructed axes and energies

of the selected genuine 3-jet events in the M.C. sample were compared

to the initial parton directions and energies (see Fig. 7.3). The

cosine of the angle between the. reconstructed and parton axes is shown

in Fig. 7.4a, and the energy difference

AE Eparton_recon E . jet

is shown in Fig. 7.4b. It can be seen that, in general, the 3-jet

analysis reconstructs the parton directions and energies well. Over

75% of the axes are within 15° of the true parton direction and over

75% of the energies are within 2 GeV of the true energy. If the jets

are next ordered by energy there is good agreement between the recon­

structed and parton jets (see Table 7.1). Table 7.2 shows the M.C.

predictions for the fraction of jets where the underlying parton is a

gluon as a function of the jet energy, about 50% of the low energy

jets are predicted to be from gluons.

The analysis associates each charged track with one of the three

jets. These may be the proton and pion tracks from A decay and hence

A's can be assigned to a jet by the association of their decay pro­

ducts. M.C. studies showed that the proton track, and hence the A,

was correctly assigned in 85% of all cases where the A passed the

selection criteria described in Chapter 5.1.4.

7.3 A Production in 3-jet Events

The 3-jet selection described above was applied to the high

energy data giving a subsample of 1402 events. The A finding procedure

Nu

mb

er/

.0.5

GeV.

N

umbe

r/0.

01

- 108 -

- 6.0 - 3.0 0.0 3.0 6.0AE (GeV.)

Fig. 7.4D istr ib u tio n of a) the angle between the reconstructed j e t ax isand the parton d ir e c t io n , a , and b) the energy d ifferen ceAE = E - E?eJon*, for M.C. data,parton jet

109

Table 7.1

Matching of parton and reconstructed jet energies

Parton energy

Slow Medium Fast

Slow 79% 17% 4%Reconstructed

energy Med. 17% 63% 20%Fast 4% 20% 76%

Table 7.2

M.C. prediction for gluon fraction in reconstructed jets (Hoyer M.C.)

Reconstructedjet

Mean jet energy(GeV)

% gluon

Slow 7.7 52

Medium 12.4 24

Fast 14.5 12

The remaining 12% are qq events.

n o -

described in Chapter 5.1.4 was applied to these data and the resulting

effective mass spectrum, M , is shown in Fig. 7.5.

The efficiency for finding A's in the 3-jet subsample was deter­

mined from M.C. data. A 3-jet analysis and selection was performed on

the M.C. data and then the A-finding simulation (see Chapter 5.2.4)

was applied to the 3-jet subsample. The efficiency was found to be

the same, within errors, as for the total data sample.

From the efficiency and observed A signal the A yield per event

in the measured momentum range (> 1 GeV/c), and extrapolated to all

momenta (see Chapter 6.3), was obtained. These are shown in Table 7.3

together with the corresponding values for the whole data sample. The

yield in the 3-jet sample is higher by more than 2 std. dev. than that

in the whole data sample.

To try to compare A production in quark and gluon jets the yield

in the 3--jet sample was broken down into a yield per jet for specificre conreconstructed jet energies, Ejet . These were compared to half of

the yield/event from the whole data samples at 14, 22 and 34 GeV. As

the latter are predominantly 2-jet events this gives the yield/quark

jet for jet energies of 7, 11 and 17 GeV. These 2-jet yields are

shown in Table 7.4 and Fig. 7.6. For the 3-jet data each observed A

was associated with one of the jets as described in Chapter 7.2. The

jets were grouped in three energy bins from 4 to 17 GeV and the A

yield per bin was determined. M.C. data were used to determine the Areconefficiency as a function of Ejet • The overall efficiencies at 14,

22 and 34 GeV (see Chapter 5.2) were found to agree, within errors,reconwith the efficiency at the corresponding • The A yields in the

3-jet data are shown in Table 7.5 and Fig. 7.6. From Tables 7.4 and

- Ill -

Effective mass spectrum of A candidates in 3“jet events.

Ejef (GeV.)Fig. 7.6Observed A yield/jet as a function of the jet energy, Ejet events and all data (see text).

, for 3-jet

112 -

Table 7.3A,A yield/event in 3-jet and total data samples at 34 GeV

Data Observed3) Totalb)yield/event yield/event

3-jet 1402 events 0.046 ± 0.008 0.59 ± 0.12

All high energy data 0.025 ± 0.002 0.31 ± 0.0220832 events

a) The observed yield for A ’s passing the selection criteria of Chapter 5.1.4.

b) Corrected for efficiency and extrapolated to the whole momentum range.

Table 7.4

Observed A,A yields/jet for data at 14, 22 and 34 GeV c.m. energy

W Ejet(GeV)

Observed(GeV) yield/jet

14 7 0.007 ± 0.002

22 11 0.012 ± 0.00234 17 0.013 ± 0.001

113 -

Table 7.5

Observed A,A yields in 3-jet data sampleas a function of ETe2°njet

_reconEjet(GeV)

Mean value Observed yield/jet

4-9 7.0 0.014 ± 0.004

9-13 11.4 0.015 ± 0.004

13-17 14.5 0.017 ± 0.004

114 -

7.5 it can be seen that the yields in the 3-jet data are systematically

higher than the 2-jet yields, although the difference is not statisti­cally very significant. Overall the result is more significant (see

Table 7.3). These results can be used to make a simple estimate of

the relative yield of A's in quark and gluon jets. If it is assumed

that the ratio of A production in quark and gluon jets of the same

energy is a constant, C, for all jet energies, i.e.

c = yield/gluon jet yield/quark jet *

then the values for the quark-jet yields (Table 7.4) and the gluon

fraction in the reconstructed jets (Table 7.2) can be used together

with the total observed yield/event in 3-jet events (Table 7.3) to ob­

tain a value for C.

The contribution to the yield/event from the 12% contamination of

qq events is

0.24 Y(17) ,

where Y(Ejet) is the observed yield/jet at jet energy Ejet (see

Table 7.4). The remaining 88% of events contain equal numbers of slow, medium and fast jets. The contribution to the yield/event from the

slow jets, estimated to be comprised of 48% q(q) jets and 52% gluon

jets, is

0.88 Y(7)(0.48 + 0.52C) .

Similar contributions occur from the medium and fast jets. Equating

the sum of all contributions to the total observed yield/event for

the 3-jet sample of 0.046 ± 0.008 (Table 7.3) gives a value for C of

3.1 ± 1.2 (stat.). Therefore, with the assumptions as stated the data

- 115 -

indicate that the A yield in gluon jets is greater than that in quark

jets. However, many more data will be needed to improve the statisti­

cal significance of this observation.

7.4 Study of Systematic Bias

Possible sources of systematic bias have been studied in order to

ascertain whether the excess yield of A ’s in 3-jet events arises from

the analysis method or is due to a specific feature of A production.

Firstly, the 3-jet selection procedure described in Chapter 7.2

gives a reasonably pure sample of 3-jet events with axes and energies

well determined. Further M.C. studies showed that the fraction of M.C.

events satisfying the 3-jet selection criteria was the same for events

with and without a A. As has already been stated the efficiency for

finding A ’s within the 3-jet sample was not different from the effi­

ciency for the whole sample. Thus M.C. studies do not indicate any

inherent problems in the analysis-method.

The 3-jet data sample was also studied to see if the observed A ’s

within this sample were different in nature to those in the total data

sample although the limited statistics in the 3-jet sample make such

tests at best qualitative. The A momentum distribution within both

samples was found to be the same within errors (see Fig. 7.7). As has

been discussed in Chapter 6, the transverse momentum distribution is not inconsistent with that predicted by the M.C. The observed A ’s in

the 3-jet sample are consistent with having been produced within jets,

the transverse momenta of these A’s out of the event plane (see Fig. 7.8)

is small. Furthermore the distribution of A momenta in the event plane

show a 3-jet structure, this can be seen in Fig. 7.9b which shows the

(GeV

/c"’

116 -

Fig. 7.7Momentum distribution for observed A’s in the 3-jet and whole data samples at 34 GeV cm energy.

- 117 -

— ■ - i .. i , — . 1 . .-i . 1--------- * u* » » 10.0 1.0 20P* (GeV/cl )

Fig. 7.8Distribution of the transverse momentum out of the event plane for observed A fs in the 3~jet data sample.

- 118 -

(Degrees.)Fig. 7.9a)

b)

Angle <J>a between the direction of the fast jet axis and the A momentum vector projected onto the event plane, PThe A momentum flow, P^, as a function of for A candidates with effective mass, M , in the range 1.09-1.14 GeV/c2 in 3-jet events.pTT

119 -

A momentum flow in the event plane as a function of (j>, where c}) is

the angle between the fastest jet axis and the A momentum vector pro­

jected into the event plane, < it (see Fig. 7.9a). The A's are

clustered in the region of the jet axes and not elsewhere.

120 -

APPENDIX 1

Track parameters

The track parameters used in the track reconstruction programs are

shown in Figs. Al.l and AI.2. A right-handed Cartesian co-ordinate sys­tem is used (see Fig. 2.1).

In the plane perpendicular to the z-axis r is the radius of the

track circle centred at (xc,yc). The track passes through (xo,yo) at

its point of closest approach to the origin, do is the distance between

the origin and (xo,yo)* do is positive if the track encloses the origin

and negative otherwise. The tangent to the track at (xQ,yo) makes an

angle q with the x-axis. In 3-dimensions the dip angle of the track is

X. The z dependence of the track is given by

z = z q + s.tan X

where zq is the z co-ordinate at the point (xo,yo) and s — r\p.

- 121 -

+ve

Fig. A1.1xy projection of a track.

Fig. A1.2sz projection of a track.

122 -

APPENDIX 2

Vertex Fitting Program

A vertex fitting program, FITPT (FIT to a Point) was used in the

A finding procedure. The program can be used to fit up to 20 tracks

through a space point but only the two-track case is considered here,

though most of the description is generally applicable.

Two helices are constrained to pass through a common space point.

Track parameters from the reconstruction program MILL (see Chapter 2)

together with an initial approximation to the vertex point are input to

the fitting program. The sum of the squared residuals between the track

trajectories and the hits in the tracking chambers is minimised to give

new values for the track parameters and the vertex point.

For each track the parameters r, <J>q , do, tan X , z q and the charge

are supplied (see Appendix 1). The initial approximation to the vertex

point is taken as the intersection point (xv ,y ) of the two tracks in

the xy plane, or, if they do not intersect, the point midway between

the points of closest approach of the two circles. The z co-ordinate

of the vertex z^ is taken as the average of the z co-ordinates of the

tracks at the point (x ,y ).

Internally, and for the minimisation, the parameters 1/r, $ and

tan X are used, where <j> is the value of <J> (see Fig. Al.l) at the point

(x ,y ). The errors on these variables are taken as 1/40 r for 1/r,

0.002 for tan X and cf> , 0.1 cm for x and y , and 0.3 cm for z . Thev* v yv vprogram flow is shown schematically in Fig. A2.1. In the initial phase

the track parameters are stored in internal arrays and hit-lists con­

taining the DC and CPC hits associated with each track, and also close neighbour hits, are constructed.

123 -

Using the initial track parameters, and forcing both tracks to pass

through the vertex point, the distances, d, between the track trajec­

tories and the hits are calculated. The hits used may be neighbour hits

if these are closer to the trajectory than the original hits. Each

track is then checked: if the number of hits, N, is too small, or the

chi-squared/point

X2P

N d?2 (-t) i=l 4

N >

where ck is the spatial resolution of the tracking chamber, is greater

than a preset limit, the track is rejected. If one or both tracks

fails these checks the program returns with a Tfit-failed* condition,

otherwise the function

d?F = l (— ) ,„2

where the sum runs over all hits on all tracks, is minimised wrt the

track parameters and the vertex point using the Harwell Library routine

VA04A, thus giving new values for these parameters and for the vertex

point. Using the new parameters the distance d is calculated at each

hit. Hits are rejected if d is greater than a preset limit. The track­

checking procedure described above is then repeated. At this stage a

search is made for close hits in tracking chamber layers previously un­

used. Suitable hits are added to the hit-lists. If hits have been

added or rejected the program makes a second pass through the minimisa­

tion procedure (see Fig. A2.1). No more than two passes are made.

124 -

After the second minimisation or, if no hits were added or rejected

after the first, the overall chi-squared/degrees-of-freedom is calcu­

lated. The program returns with a ’fit-failed’ condition if this chi-

squared is too big or if the number of degrees of freedom is less than

7. If the fit is satisfactory the new values of the track and the ver­

tex point are returned to the user.

- 125 -

No

Fig. A2.1Flow chart of the program FITPT.

Fail fit. Return

- 126 -

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- 129 -

Acknowledgements

I am deeply indebted to all those whose efforts, support and

friendship have made this thesis possible. Firstly, my grateful thanks

are due to my supervisor, Dr. Peter Dornan, for his insight and guidance

over the years. I wish to express my gratitude to friends and colleagues

of the H.E.N.P. group at Imperial College with whom it has been a great

pleasure to work. I must also thank the many members of'the TASSO col­

laboration from whom I have learned much and amongst whom I have enjoyed

working. I thank Barbara Strasser for cheerful and efficient typing.

I thank Prof. Ian Butterworth for the opportunity of working in

the H.E.N.P. group.

I acknowledge financial assistance from the U.K. Science Research

Council.

Finally, I owe my deepest thanks to Annie and Carol without whom

nothing would have been possible.