A Study of Hyneron Production by

p Interactions at 10 GeV/c.

by :Ciehael Edward Merrnikides

A Thesis presented for the degree of Doctor

of Philosophy of the University of. London.

Del)artment of P4sies,

Imperial College,

London, S.W.7.

October 1968

- 2 -

,ABS1'HACT

The thes.is presents a survf}Y of b~'y"p0ron production

in 10 GeV/c K- p interactions. Two-bod.y processes of

the type K- + P--' hyperon + meson were found to be v~ry

weakly produced, constituting about 0.2% of the total

K- p cross-s~ction at 10 GeV/c. A comparison with

results at other p~e't'gi~s indicates that the decrease

of cross-sec tion i,;v'1 th 1ncr~asing energy is more rapid

in processes illvolving th~ exchange of strangenAss or

baryon number than in reactions which can proceed via

non-strange meson or Pomeron exchang~.

The fOl'ward prod.uc tion of lambda h~r perons, which

becomes mora pronounced wi th il'lcr~asinf~ mul tipliei ty

of final pa-rt1cl'3s, is described in terms of a

mul tiperiph~!,al model invol,\rj.ng thf:1 exchang(~ of a

Regg~ baryon trajectory. Redsonable fits a~c obtained

for the a.istributions ill the centre of r·~ass production

angle and momentum components. The general features

of 8 production are also suggestive of baryon ~~ccha.nge.

Four exarr21es of sa- production have boen

unambiguously identified and their propertip.s n.r.~

presented.

...

-3

TABLE OF CONTENTS

Page ABSTRACT 2

PREFACE 5 INTRODUCTION 6

CHAPTER I :

1.1 The beam 9

2.2 Principles of RF separation 11

1.3 The Bubble Chamber 14

CHAPTER II :

2.1 General description of the analysis 4y stem 20

2.2 Scanning and measuring 23

2.3 Geometry programme 25

2.4 Kinematics programme

2.5 Selection of kinematic interpretations 37

2.6 Statistics programmes 42

2.7 Variables and curvr, fitting 44

CHAPTER III

3.1 Beam purity 55

3.2 Scanning lossas 58

3.3 Decay weights and statistical biases 61

3.4 Contamination and channel separation 63

3.5 Cross-sections 66

Page CHAPTER IV

4.1 Introduction Bo

4,2 The peripheral model 82

4.3 The Regge-Dole model 85

4.4 The double Regge-pole model 92

4.5 The multi liegge-pole model 95

CHA21711 V

5.1 Introduction

5.2 The final state A.9e

101

101

5.3 The?. final states A9t-1-7c-, A7c4. qc° 102

5.4 Two-body processes 106

5.5 Throe-body procassos 1.11

5.6 Tiambda production in many-body ractions 11-j

CHP,PTEP VI

6.3 Introduction 144

6.2 The. channel Tc-v --> A K°E° 74.4

6.3 The channel Kp --> A KR ic 146

6.4 The c'.,annels AKK 2 146

6,5 Production Tn-chanism 148

CHAPTPR VII

production 158

7.2 2 production 161

A0KITO7LEDGWMIT 172

REFF7iENC1S & FOOTNOTES 17.7

5

PRRFACV

In September 1964 the au-nor joined the Im,erial

College High Fnergy Nuclear Physics group and was

initially engaged with the 6 Gev/c K- o ex:9eriment

alread', in progress. Ee also becdme involired

with part of the analysis of the 5.5 Gev/c K- p

experiment.

The 10 GeV/c K- p ex ieriment, which was a

co110)orative effort between five F,uropean groups,

commenced in April 1965 at C77.N where the author

-)articipated in the bea tuning and exposure of the

film. Fe lAas assisted in the ada:tation of tho

stanqard C7PN prograorles for use the Iiioeria1

College comuter.

The 1:ilesis is based on about 200,000 bhotograpbs

and the author nas party res:lonsible for

com;Alation and -9T.ocessin of the im,:erial College

share of the data. The author was largely. responsibae

for the aaalysis of hy.eraa production, whici:, constitutes

the Present thesis.

INTTIODUCTION

The 10 GeV/c r:-() 'which was a colla'horT.tiv)

effort botwela five 'uroJen groups , corm7;encell in Acril 2)

1965 when the 02 beam becane operative in the qlast

ex,e-Amental area of the CN proto.1 synchrotron. This

was at the time the highest eAerFA: Kp bunle chamber

ev.perient to be undertahen, and offered A.1 interestiniE;

scofie of study in the 1:iterto une)-,lored energy region.

The objectives of this experiment are rather broad,

the rain concern beinr- a .11")1"CL of new resonant states,

thv; study of production mec}_arlisls at high enen-,-

the possibility to r.est various tneoretici-.1

The exi,eri-,ent also offers to op,ortunit,,, of accmiriAg

more information about the 2- .-article.

Among the resllts pub]isiled the most in-eTesi-,in,c;

Wore the discovery of four unambi:xous cass of 2

prodection and that of a new strange 1-sonancr, in th:,

If 4t7C systm, nared the L-mPson, hrlYing a mass of 1790 p.T,

width 100 Mev and isoto9ic soin J. 7iork. is in rogress

for the det•Drmination of its s;in an(' j,arity.

This thesis (Teols with some of -io beron J -(orluction

processes. The emphasis is placed mainly on J.,,mbfi_a

irortuction in associatioxi with , ions here the statistics

re:tivly gocyl an Trarraat a cu.3pa.'ison With tlicwry.

The generally iyoor statistics of ,otner hyperon cliaaantals restrict tLe anAlYsin to p:euerAl observ.Atioas on

production mechanisms an-3 cross-sections.

The first clya;)ter gives a description of th., be;-1.m

and bubble chamber. We t:INen fiscribe me tTlods

used in scanning anl measuring; the film an4 the computlr

programves involved. Ia the data r9duction, togetbc)r witt

the criteria for the selection of the kinem,tic

interpretations of tile event.d.

The third. cha. ter fLoals with the luestion of

experimental bias and Iresents cross-sctions for final

states involving hy-peron proAletion. A brief outline

of some theoretical modlls curnt1.7 used is xriven in

the no-ct cha:ter. Th.) rie.go-pol model is (liscussed

in sir" i.e terns (oLitiur: some rr4c!nt develont 61.ich

as ncons: irecyn and I'evqsionh) insofar as it is relevJaat

to the extr;nsion to eac)enolot,ical models of th o- more

final particles.

Chapter V contains an anz1)-sis of rear :ions Involving

lambda production in association, witl, pions. CrosF1-

sections are given for resacce ,roduction and the

production mechanism of the lambda and Aons is4)

discus.$1

in terms of a multicparittheral Regfze-pole mOdll . The

Production of lambdas in association 4ith fK Pairs iS

8

presented in the followinc cauter and similarities with

lambda cirorimetion in association wil, .ions ,2.re discs d.

- _ . The 'iro61-uction oroprti'3s o± E an 2 tirons

aro ii.r.senti,=.:d in tho final chaptz,t?.

CYPITTER I

1.1. The Beam 2)

The 1102" beam was built in the East

Area of the CERN Proton Sv-ncbrotron (CPS) to provide the

1.5 metre British National PVdrogen Bubble Chamber (B1MBC)

with reasonably pure beams of kaons, pions, i.)rotons and

antiprotons up to a oomentum of about 15 GeV/c. The beam

incorporated two modes of mass separation t electrostatic

and radio-frequency. The latter rode, suitab2o for momenta

in the range of H to 15 CeV/c, was el:played in the present

experiment.

Sinae traversal torgetting was used, since the R.F.

cavities wore under power for a few microsecons on?-'. A 5)

kicker magnet was cieratd in the fast ejection scheme

to Aeflect the protons onto a rather large target insid-, 6)

the magnet unit 60 of the CPS. This arrangement ac7lieved

a low production angle in order to take al7antage of the

strong forward peaking of 'artic1,1 production at high energis.

The layout of no beam is shown in fig. 1.1. The

particles were confined 'werywhere to 4ithin 9 cm. of the

beam a.zis to minimise 'Iberrations arising from non-paraxial

optics. ReYotel; adjustalnle coUlmators ,vere use to

facilitate beam tuning. The lesiF:n of he IF beam has 7) been optimiser' for prodluction of Imons at 10 (NV/e,

-10-

The beam can he regarded as being composed of threo

sections. In the first part the uhaso s a.cc accetP.nc

and rr.owentum bite are defined. The second part irforrns

the mass analisis and in the third s;?ction the phase s 'ace

accetance and yomentum bite are roughly redefined and the

beam is shaped for entry into the bunle c17.amber.

Collimators Cl and C2 defined the phase spac.) acc,tiptince

in the horizontal and vertical planes and the nomentul. bite was defined by ghere bending magnets U, M2 produced

dispersion in the horizontal plane.

Horizontal and vertical images of the target were

produced in the first cavity, RF1, h: the lens Quadruplet

Q4, Q5, Q6, Q7, and in the second cavity, 1R72, by the

quadruplet 00 09, 010, 011. The "angle defining slit",

C5, was imaged almost to infinity in the two cavities.

The lens s)rstem between the cavities was symmetrical and

such as to give a transfer matrix the vertical plane

of the form:-

-1

0 Mass searation was achieved in the beam stopper, BS,

onto which C5 was imaged. Collimators C7, C8, C9, C10

were used to redefine the phase space acce-otance and C7,

C8 defined the angle in the vortical and horizontal piano,

respectively. C9 and C10 were at images of the target

in the two planes. C8 was used as source for redefining

a final momentum analysis in the horizontal _,lane with the

use of 75, M6 and Q16, 017, where the gap of acter3 as

the momentum defining slit. In the vertical plane a

divergent beam was produced by de-focussing Q16, 017.

This was nocessai7 in orer to avoid too many overlapping

tracks in the chamber.

1.2 RF Sep_' ration - Basic princiPles

Consider a syster of two RP ce.,, ities se. arated b:r an

optical system of magnification -1, the conjugate foci lying

at the centres of the cavities. Assume that a well collimated,

momentum analysed beam containing tifo tr,,es of partic2 ,,s enters

from the left (fig. 1.2a).

In RF1 a transverse forc a deflects the particles and

modulates thn exit anao at the frequency of the U. At a

certain time the particles have some angle e . The optical

system focus;;os the beam in the second cavity. Although both

types of particles are defl.,.!cted LI the sang way when they

:mass through thg ffrst cavity simulta,leously, their arrival

times at RF2 differ due to their mass difference.

If the relative RF ?hase between the two cavities is

such that ay. unwanted particle arrives at RF2 when the .011se

- 7_2 -

of the latter is the sane as that of. RF1, it lill be af.ain

deflected through 6 in the opposit,1 •liroction, thus

cancelling the overall deflection. The wanted particlr,

due to its qifferent arrival tioel loaves RF2 with some

residual deflection. Because of the relatively long

duration of the incowing plaSey all entry ,Jhases

probable. Thus a sa:.,arator of this 17ind can onlv e:asur

that the unwanted particle is near the optical a.;d_s vber-:las

the other one is swept across the whole aperture. The

unwanted particles are eliminated by placing a central beam

sto,oar. This is it 'GUI exiionso of a portion of the wf..nted

particles The vertical , hase plane is shown in fig. 1.2b,

where the cavities ar,'? considered as long sgur:r() pi es.

In the relativistic lirit the phase aiv,1-: bet.,oen the

two types of particles is

2 2

ti

I. w. (V1 - W2) 2c (pc)2

whore w = pulsatance of the IT

p = particle -comenturo

distance between t1 cavities

'1, 2 ri:st energies of the two oarticles

Tho deflection of tie w,_:nted Darticle at the e7Lit of RF2 is

- 6 sin w t e sin( w t+

= 2 e cos( w t + T/2) sin rc• /2

- 13 -

Hence the deflection is P. m,ximum whorl thc) phase angTh

between the 4;40 i‘articl..?s is an od'I mu?tiplo of x. It

is thus desirable to adjust tb--; phaso to one of these valu,s.

The design monntun, is definod by

2 = LM WT - or p = —

2c (0c)2 cj L(w2 ,?3

2

For the n021! sovarator L = 50v., W = 0.105m, pc, = 10.2 Gr?Vitc

for K- x so,raration.

It is a:ISO ol () .avo l'ont,. &ere T = 2,F.n

where the r-9 ef1ections of the wanted particT'us cmc,?1,

care has to 1) L. seThctinr the P7

For Qractici-a 1)r)oses 1:;i.a initial b--)an 11,st occu -7 a

finit;) arl„,.. in ehase s ace. :;no for:"us:,;

in Rrl (fig 3.2b). Tht.: 17e-tic-tT! coor-;sond

targt and th,1 hor5.zoatal to Sort a.)ortur:,

say a collittor. T13 Tarr:Aping area is for

rief:1 -?ction. If oui starts with ;=1 vet! sm,.111 ar-a

ons. over a 3-.1.rvt frction of

thi wacit,31 lardicl,.is is lost in 4; -1,7) Unifo;m

Dartic1-! lailsity in phas,-; slac a is ac'i‘nriid b: the

tota?, acc.- Inc,:: in r,i-Ao 1:111,

We Lay': so rr,,.r discussHI. sopaca..ion of tv,o paric*!,i

r).;...is • In practice :i hav ree tv ,1:,; of pr:r!31-,'1 in th

- 14 -

beam: p K and It , if we ignore muon contamination arising

mainlcay in fliclit of pions. This contamination is

rath9r 1ar(2,(4 at high cuer:i..)s '.ocaus of th,4 forw-Lrrt

as th,) pton momentum incrs,-,.s and also blcaus) of the

rath;.ir large phase spac,-? acc!,tanc of t 11owiy-r,

as tso are not strongJ. intracting ,Articl)s tLv- pri-sont

no ph7sical bias, provided cross-sactions aro not to 13-4

based on direct beam counts, apart from spoiling th

clarity of the bubble chambur picGures.

If ,r.1 want to llt.inett-! two types of articles at a

time) rsto choose ti“,?, drift s!)ac,) pomontum such that

phaso differinca b,etwf!In t.11 tvo unwant“ par ticl,,s is can

ev,In multipl.) of i . is th cas,1 for p and it at

10.12 GeV/c, which fortunate]. ; is _aso vry n)ar to 10,32 GeV/c, th,) d. ?sign mom-mtum for K-it sfiaration; hence' the

8)

0) Tha 150 cm B.N.H.B.C. was (.1 sign, for us() with th

C.P.S. and th) 7 GeV/c Rutharford T,aboratory Proton

Synchrotron of N.I.R.N.S. at Harwell.

Th..) dimensions inert: 150 cm. length, 50 cm. height,

and 45 cm. (1,:Tth provided with a nagnetic field of 13 KGauss

and enclosiJg a liquid vo:111mo of 300 litt%ls. The ov9rall

choice of 10.12 (. aV/c for th,„; initial tuning of th. II0219.

1.3 The Bub7)1,-.? Chamber

-15-

precision of measur,Im -Int aimed. at was +20 microns in th-!

chamber. A plan view of the chambor is shown in fig. 1.:7.

Th ,) ourating t-,m1p3raturi) ws 270K, maintain--'d by hydrogm

rofrigr4ration loops. Radiation losses ;,vir reduced by

hydrog.m, nitrogen and vacuum shiolds consquetiv,.41y

surrounding chambn..

The chambor was expand,id upaards, all moving parts

boing outsides vacuum tank, &hich enabl -A maintnnanc

without the n'a-d to empt7 tho bublle chamber. A uni-axial

flow of tho liquid is dsirab17-) during tne oxiAnsio.1 in

ordar to minimise thermal siisturbancos and turbulance. A

gas phase exjansion systeE was adopted, al'r.) on of the

main difficulties is the inher:mt instability of larg-J gas-

liquid int.rfacos subjected to abrupt p-i7essure changs.

This aff-,ct was minimisod by porfoming the expansion through

3 bo.nks of 16 tubes uniformely distributed ow=r trie surfac.

A si:i7nal from t1bra lin ini'7iatod the expansion so

that th pulso arrived at the chamber during th,;

snsitiv time. Th'..) photographs wt1r11 taken ap,:roxizaately

1.5 msocs. after the arrival of tho 1 -am pulse, to allow

the bubbles to grow to tho desired size. The PS c rcling

tirn was about 2 sec.

Th' optical sy.stem is ialt with in detail in the 10)

litoratur,:. 7e r,:produco of rho salient faturs.

A condenser system was used to acl. ieve even illumination. The condenslr was ivielefl o tically- into 3 1,arts to avoid

the use of an impracticall7 co-idenser 1.1ns nocessar7

for a single axis optical s;-stem. The system had a 2:1

magnification ra'Ao and the illumination was achieved by

3 ring flash tubas par condenser section. The ring tubes

were focussed around the camera lenses in the fashion

depicted in fig. 1.3. For maximum illumination the angle

at which the lirht is scattered off a bubble must be kept

as small as possible. However, aberrations set a lower

limit of about 2° for the scattering angle. The

photographs were taken on 35.mn unperforated film. A

data-board was photographed alongside each frame displaying

Information such as reel number, frame number, magnetic

field, etc. On the inner surfaces of the bubble chamber windows

were engraved fiducial marks necessary for the initial

calibration of the optical system. These also prOvidw1

a frame of reference for the measurements of interactions.

RF1

08,9 /1 010,11

1/

RF2

Q1,2 Q3 04 // I 05,6,7

\\ / I M1,2 d 3A5 1ii

M3,4

MAGNETS o 2m.quadrupole

1 m. rr

11 0.5m. MS

B.C.

•

012,13,14,15 //as. m567Q16,17

\\ it! g o C .7,8,

\9,10

2m. horiz bending magnet

C11

CI

1 m. vertical

COLLIMATORS

horiz. colliMator

I vertical

T = target

B.S. beam stopper

= bubble chamber

RF1,2 = R.F. separators

*FIG. 1.1

R F1 RF2 BS

F'777, //77i

Y

Available

y phase space

/

/

/entrance/

1'

-18 -

Wanted particles

Unwanted

(A)

wanted _particles

Wi./77 Unwanted

B )

t2

CAMERA ARRANGEMENT

•

SCALE (FEET)

SSA

ARRANGEMENT OF LiG!-IT SOURCES

• 1 • ;-

SCALE:- (METERS)

{IM, •

/

•

A

•

ni

\

ss,

• • . MAGNET COILS

• i MAGNET YOKE

4.

FIG. 1.3

-20-

C1fAPT7P 2

2.1 Genera] doscriction of Emalvsis system

The basic objecive of anal;sis is to offer

kinematical inter,)roations, as complete as possible,

of interactions occuring in th,- bubbll chamb -x, st,7,rting

from measurefzents of vortic.es tracks on potograjhs.

The film was first inspected (fiscannedu) with

aid of a projector and the events under study recorded

for measuremmt. Then the film was transferrrA to a

moasuring mncbino. Tito lattor essentially consists of

a moving stage bearing i\ToirL fringe degitisers. A

projection system transfnr,ed a magnified image of tho

film to a screen at a convenient posil:io for the

1.3,2)asurr4r. The x-coorinate was recorded by the

displacwmt of stage, and the carriage bearing the

projection lenses measured tho y-coordinate. The

measurer recorded the coordinates of interaction

vertices and of a number of points, s,aced evenly along

each track, on the three sterosco, Ac views. The

measurements were taken relative to a coordinate s',,sten

formed by measuring the position of fiducial marks

engraved o:1 the bub7111 chamber winAows. The coorlinates

were punched on pao:r tape as binary cod, octal numbers

along with information about t1-1 evmt typeand laly,2s

-21-

for thy? identification of tracks and vertic,:s.

The major part of the subscau-mt analysis was

performed b:r co,_putor. The computation up to, and

including, the kinematica: fitting was card-A out on

th.o Coillegc,, IBM 1401 and IBM 7090 machines.

The post-kinematics programy-)s have been run mainly on

the CrRli C7)C6600 on the combined collaboration data.

The first stage involved conversion of the )

tape output from the measuring machines to magnetic tape,

which is a _lore convenient r,:edium for further processing.

This was done on the IBM 1401, and the paper tae image

then us„,d, as input to tha IBM 7090 programme, PIgG.

This was initially written for the Mercury com2uter. for

Rutherford Tabora CorypY:ogrm-)s, but mo':ified to a

version suitable for the running of CSRE programres on

the IBM 7090. The purpose of this DroFramr! was to

assemble the data in the format re uird for thc=,

subsequ.,,nt processimr and to check for labelling =ors,

completeness of measurements, etc.

The rri,maini:Ig procassing was done by ith) chain of

CMN programmes THB7SH-GRIND-SLIG51-SUMX. The first of

these is resl,onsible for the E:esem;etrical reconstruction

of events. It pLoduc,is a binary ta)e containing

geometrical parameters for each track and vertex, and

-22 -

this is usad as inimt for the kinematics progranm, GnIND.

A series of hr)oth9.sos is propos,)d program; c for

the doscri:tioil of each &vent. A "12st souarf4s" `'it

is )F3r.forci.ed for oacl-_ h po-ftesis is turn and all leasable

solutions are gen:rated. Th:) criteria adcytd for th,-,

selection off';'Lle corrct int?r,vrotation ara discussd later .

For each interpretation of an evmt a card is punch=ad

by GRIND and binary information is written on a magnetic

tape (theIGRIAD library ta-)e"). The physicist chooses

a,,propriate cards which aro then usld b:. SLICE to select

the corresi.oniing fits from the GIIIND tape.

SLICE produces a data suKzary tape (DST) which

consists of one binary record for each fit, cotaining

physical information such as Eolmanta and angles in th

laboratory and centri,! of rass

The sr,atistical analysis was p;,rformed h thr final_

prograw.ne in tho chain, STW. 1:32 .feans of data cards

prograrri::: can he instructad to producn istogrampos,

scatter plots and oth;?r displays of plysical cuantitins

recorded on the WA' under thel control of th- user.

Thy k; -)norz-11 flow of the analysis is il'ustrated in

fis. 2.1.

-23-

2.2 Scanning and Measuring

The film was scan:;ed with the intention of measuring

the following event types:-

0 Two- and four-prongs with no visible: strange

particle decays.

ii) Zero-, two- and four-prongs with ono Vo decay.

iii) Events of all multiplicities with two or more

strango particle decays. This category includes 2- candidates.

Other event types wore scanned for in order to normalise

the total number of interactioJs to the total cross-section

known from counter el-erim,;:lts.

For 1)urposos of scanAing thR chamber was :ivied into

3 rions viose boundaries Here the junctions between the

condens'Yr lenses as Vii1W=?1 fro camera 1 (fig. 2.2). Event:,,

of type i) were 111.)asured in region 1 only; category ii)

were moasured wher-wer they appeared in regions 1 and 2.

The last type (known as ',rarest° were rileasureJ wherever

they appeared in the ,ntir- volume of the chamber.

Two independent scans were carried out using views 2+:1';

for the first and views 14.2 for the second. The rlsults

from those two scans were comar.Rd in a chct scan and

cards were made out containing roll and frame number,

topology, region, sketch of try :i 917,Int an any oth,Yr

- 24-

information useful to the malsurer. The topology was

expressed as a 3-ligit numbar, ABC, where A gave the number

of visible tracks leaving the a.(3, B the nub -' of cbaT,':',d +

decays (V ), observed as ukinks” in tracks, and C th;,

number of V0 decays. 7,v-3nts were moasured onl if all t'-rree

views existe, eIrc,vt for 2 - candiates for wiAcl only taro

good views anr.. avAilabla.

Incident 1.p-?.am tracks ere accepted if thw

para11e1 to within 1 dogre with resct to tba ganeral

beam dir;?.ction. At l-ast 2 c71 of baam track of measurable

quality wero requird on view 1 to obtain its dip add

azimuth anrJos and a rough value of its mompAtum.

Electron pairs associated wit an interaction

recorded in the scan as thse could drovide

"sical information. Th,n...a was occassionallv som:= oubt

that the susected electron .pair micub h a Sr

Two cviteLia wera adorAel to recognise electron-ositrcn

.airs. Firstly the an-1e. botw;!n 'L.J.1) two tracks as r,quirA

to 1.)-.= zero o.i all 3 views This is not a sufficient

conition as V°'s can also have a zn:lo opming aril. Th'7,

s.)cond critrion 4as that at least ono of tTi= alctrons could

1.),) 1L1 ionisation. Eelo a nomntun of 150 P:V/c

-0 a track, wLich couU be a :Ioton. or pion, is of at 11)

1ast twic rinimuf ionisation , 71:12.,as an f)1:?ctron is

-25-

always minimum ionising.

Confusion as to r:ultivJicit- of an ov!nt can

from t1,0 .res:.4co of a D,l'itz fair, which is a

vaml.a co averted to a,1 electron-)csitien ,air at the;

int.eractioil v,Irtza, Only ionisation information can

be us-1d to 1dentif3r t. electron tl':acks tnis case.

Tau-d.c3cays of, t-c". Lacident particlos were a2 3o

recoree'A. Ti.:eso have the appearanca of :,---prongs, and

are useful for the detrminatioJa of the tota2 I path langth.

2.1 The Geomqtro P ofTairrLe

The 1.rogramrp,t THESIT was originary. d,3viset by 12) 13)

G. R. McLeod and G. Moorhead to perform the

goometAcal reconstruction of curved tracks in a bubble

chamber; it later und,mwent various improvlmnts and

modifications for wlicn te CERN DD divisl.on is mainly 14)

responsible.

The in,ut acceited by THRECr consisted of a magnetic

ta.:.e onto which tl-e ftor ti.J) rplasuring

u,achines had been transferred by the 17'1 1401 computer.

THRESH ,:.su&-.s thc, Oh_1(Dbor is in a uniform

magnetic fi-,1d, per.,Jeudiculr to th.3 plFnes of the qinciows,

and that chargq particlls (1,.4scribo gur h:ilicQs. Th2

- 26 -

coordinate systea„ MI us-0 in thn reconstruction is

shown La fig. 2.3. Th-.3 XY f)lal (back surfac of front

glass) is us,O_ as a refac,..1 onto tvflici

film coordin,it)s •,r4 trar,sor--1. tralsrormation

is r1it,3rmine for .lach view by70ans of th -. strInl',rd

reflrlac., fiducials for that N7-1', as Ncvi)nt17

in tha constants (1,-no,n as 'titles"). TYie trans:

is assum,A to b.,2 lin'ar

Xi al

+ a2 xi +

0.3 1.

Yt

04 + 4c( x

i + a6 Yi

A last squares fit giv.s co.Iffick:alts a .

4 fiducial marks are measured to give some ov:Irdetermillation.

This transformation is imme1.iately ap.died to all

measureaents in the view (fiducials, points, tracks).

The transformed fiducial coorlinates aro comparyl with

th title r7,1favmc=3 coordinates to cbeck th measur,ront

quality.

Lens 'llstortioA an'3 filr tilt aro rellhovd by aaving

th tralisfornation:

Xi\

7. Yi X, Yi

[ 1 + 13 -2= 4" P

1 • 2 d 3 d v2l e

+ d2 d

4 6 13 5

0 (X2 y'?)

_27_

where d is the camera Z—coordinate. The set of coefl:icients

is determined separately, and fel_ in as (IL:ta to the

programme.

The programme calculates the s.,-eace coordina tes of a

point in the chamber (such as an interaction apex or end

point of a stogi_ing track) by first forming a *reconstruction

linen, described by

X = Fz + G x x Y =Fz+ G

This is the segment of the light ray, inside the

liquid of the bubble chamber, joining the point of interest

to a given camera. F and G are functions of the a,parent

positions and are calculated by the yrograNme. If a point

is measured on at least 2 views its coordinates (XYZ) are

found by the closest approach of its reconstruction lines.

Solving the above by least squares, using all available

views, one obtains (XYZ) and their standard errors A X,

AY, A Z. If the sum of the errors exceeds a constant

given in th.. titles the result is rejected and the

reconstruction is tried again using one view less. If

none of the possible combinations gives a satisfactory

result the measurements of the ;;pint are ignored.

The method .iescAbed above to,: ttg reeoagtrUCtiOn

- 28

of points c..nnot be Ined for measurements on tracts as

there is no correspondence between the keasurei,!ent of a

point on one tract: on one view with a eoixit measured on

the same track- on anoter view. One uses instead the

method of near corresponding points.

For each track the followin5,. steps are followed:

1) The reconstruction lines are calculated for

each measurement on each view.

2) A helix is constructed through some points

along the track (1st ap-roximation).

3) The best helix is found by least squares

fitting.

Let the reconstruction line associated witl' a .!!oint

on view a be

a X = P G

x x y = y

Assume that the image in the view a is a point lying

somewhere between the jth and (j+l)th measurements on

that view. The progranme finds a set of coefficients

F Gx Fy, Gy by linear interpolation between the x coefficients coreesoonding to the jth and (j+l)th

reconstruction lines with the condition that

X = Fxz +

Y = Fr3z GP

29

intersects the a line in space. If te interpolation

does not suceed, an extr,polation is attomptcy'i. 4nie

choice of views a and is such as to ensure good

stereoscopic separation for each point along the track.

A helix is now fitted, described by

X p(cos e -1)

Y psin 8

7," p e tans

where the axis system (X"Y"Z") is the original system

(1 .Z) rotated through an angle p about the Z axis and

translated to a new origin, (ABC) (fig. 2.3). The

T'arameterF to be found are :

P = radius of the helix

dip angle

P = azimuthal angle of the starting point

with respect to the X-axis.

A, B, C = coordinates of the starting point of

the track.

P and P are found by fitting a circle through the

orthogonal projection (X,Y) of the spatial points on the

plane Z = 0 :

(Xi-A)2 (Yi-B)2 X 1 (Xi-A) + x 2 (Yi-B) = 0

-30 -

The final fit consists in finding small corrections

to the parameters of :iAe helix so that the es-uatlons of

all the reconstruction lines corrosonrling to all good

measurements in all views, and the corresponding helix

equations are simultaneously satisfied to the of.timum,

in the sense of least sqvAres.

An approximate value 0.. of e has to be associated 1.J with each measurement i on view I, using

from the first approximation; an iterative methoM is used

to find a bet tor. estimate of 6 . To each eij there

corresnonds a set of re onstruction line coefficients

(F

(1)4 Fyii Gyii.). e ij deter. mines a point M • (fig. 2.3) on the helix in a given 7, = Zij plane. This

piano is intersected by the reconstruction ine at N.

Fora given cacorrectionAeto0ii may be 2 computed by minimising qE.ml. f 2 where f l ( 0 p , 0

tam. A, C), f 2 ( eij, p (3 tanm , B, C) are the

X, Y components of NM.

Th,4.! distance NM is given by D2 . = f 2 ( 0 ,e ) 2

ij 2 ( 6 + De ij 1 ij.

When projecting back to the film plane we have

dij = Dijr

where r is the demagnification to first order optics.

p, P,

- 31 -

THRESH minimises the sum of d2j over all ij. The

helix parameters are then corrected and the procedure

repeated until the corroctions are sufficiently small,

which normally requires two or throe iterations. The

moan value of the residuals constitutes a good test of

the quality of reconstruction. Fig. 2.4 shows we.:90z.t mean o the Sij

distributions of the . for a sample of well

reconstructed tracks. Distributions of apex measurement

errors are also displayed in the same figure.

2.4 rinomatics Programme

The kinematic fitting of the events is performed by 15)

the programme GRIND. This programme has been modified

to make it compatible with the Imperial College IBM 7090

computer, especially in view of the limited core storage

of the latter.

The input to GRIND is normally a binary tape produc-18

by THRESH, although there is a provision for card input,

known as "GRIND illtryn. This last mode is useful in the

respect that successfully reconstructed tracks from several

measurements may be combined. The need for this often

arises in the case of rare events where measurement is

difficult (wing to their topological complexity. To save

the effort of punching cards, and eliminate punching errors

-32-

a progrEaram • hfts b!en devised by the author to generat,)

GRIND entry' cards from the library tape. These can then

be merged by hand.

The programme proposes a series of hypotheses for the

description of an event and performs a statistical fit to

each hypothesis. The %2

probability of the fit provides

a measure of the confidence that may be placed upon it.

The definition of the hypotheses is under the control of

the user.

Run cards read by the programme specify gneral

information such as date and experiment number, ltc..

Experiment dependent titles are also provided. Th.)si,

consist of blocks of data necessary for the fitting

procedure, and contain constants governing the convcrg- mce

criteria, paramet,Yrs of the incident beam, range momentum

conversion tables and magnetic field table. In the titles

are also included the mass-hypotheses to be tested for each

vertex in an event. Finally, information about the

individual events is provided by a magnetic tape (the normal

THERSH output), or cards, containing the coordinates for

each point and the dip, curvature and azimuth angle at the

centre of each track.

The output from GRIND is normally a binary taw:, a

listing for all hypotheses attempted, and 51= cards

- 33 -

giving details of all satisfactory fits obtained. The

library tar) is used as inuut to STJCF which produces the

DST. One ST,IC7 card is punch.=d per attempted hypothesis

and the physicist communicates to SLICE the fits to be

accepted by means of the appropriate SLICE' cards. For

each evmt there are several binary records on the library

tape:

i) The first is an exact copy of the geometry input.

ii) Next there is a more complete version of the abov-:,,

containing the momentum of each wel] recoAstructed

track and information to guide the fitting.

iii) A record of the outcome of each hypothesis tried

containing mass, fitted and unfitted momentum,

dig and azimuth angles of all tracks, also fittd

and unfitted error matrics ess-intial for error

Propagation.

iv) A summary record containing abbreviated information

on all attempted fits.

An event is completely described if the momentum v3ctor

p and tl mass of each particle involved are known. The

momentum vectors are derived from the measured parameters

in conjunction with a knowledge of the magnetic field,

using a range-energy relation in the title to correct the

centre of track values to the values at the interaction

apex.

-- 54-

Th variables chosen to roprosent th m,:asurrannts are

1/1 n (1ip) and p (azimuth) for which th- error

Oistributions ncar to aaussian, which justifis the u

of x2 thory. ?7?. havc to satisfy tbn constraint 3(luations

2 p= =p = It3 = 0

for ail i,articlos participating in th, r-action.

corr:.aations xist btvn th.,! we us• an error

matrix to dscrib th varianc.ls and covarianc-is. Variabl'.n

can b either fixed (zaro variance) or wal m-,,asured whcra

they can be described by a vector (mi). Tho error matrix

for th:-.)s -,; is

G-1 ij

a a U 12 •••• 0 a 21 22

(32 = A mi. L mj ij

furthr dcfinc (ci) as tho vector of corrections to (mi)

to b,? found by th,_ it. ';!: can also bavo badly m=.asuod

(ag. tracks too short) or unm3asurd (neutral tracks or

unknown massr4s) variabls. For tho last two catogorios

wa dnfin

(16k)

= vctor of badly masurcd variablr:s. (for

unnrInsurcd variabl-)s first gusses arn assumcd)

Gk = ,yrror matrix for m . 77.0onts referring to

variabl)s arn zero and the) matrix is

assumed to "tv. diagonal, sine() correlations ara

moaningless in this casn.

(Ck) = vector of corrections to m .

-35—

The constraint equations above can bc! expressed by a

vector (fk) which is to be reduced to zero by the fit. The

basis of th fit is to find the Imctors (c) and. (c*) which

minimise the scalar

X2T

= cGc + c G*c (1)

subjct to the constraints f(m+co m * +c ) = 0, whore T

indicates the transpose of a matrix. If we neglect

correlations the expression above reduces to the well-known

form 2

X 2 ;on%)

The parameter %2 der) ends only on the number of degrees of

freedom.

The main complication arises from the non-].inoar

denendonc of the variables used on the constraint nnuations.

V:e linearise them and adopt an itarativa procedure. Given

an approximation c o c for c and c , we expand f in a Taylor

series

... f x (c, ) = fx * (6, c ) + Bw iii + (c—E.) B (4- ' ck)

7. k :, a fw a f7s- Where B and B are the derivative matrices J171 andi-g-

%i 7kk k respectively. For a 2.articular stet, in the iteration, 2 X = cTGc + & TG'' c* = minimum

,- -4:: f(c,c ) = Bc + B* C* + r'A = 0, where r7 = fkc,c: - B: c

Taking derivatives, 2 T

liax -+ 8 ci (G- ,10)(c ) (B )

T J %

0 (2)

L 'fa2C 2,T a ck)

,

f(c,c )

(G;,:'e) (4) (Ilhk)

= 0

‘T = =

aaxi ld k

(3)

(4)

-36-

Using the method of Lagranvan multipliers, we define the

vector a of rfultipliers to combino the two equations:

2 T x = cTGc +c G c + 2af= minimum

where

1,j = 1,2, • • nc (number of well measured variables)

= 3,2, • • • g nc- (number of poorly measured variables)

= 3,2, • • • g no, (numbor of constraints)

The matrices G and G* are symmetric.

This is a system of n + n + na

linear equations for c"'

an equal number of unknowns, c, c* and a.

From (2) we have

c = -G-1 BT a (5)

Substituting into (4) and subtracting (3) multiplied by tB*

why r t is a scalar, we obtain

- (BG-1BT + B.T) + (B! tB*G*):

r = 0

= -Gm- a + B (P te): + r =

where E is the unit matrix and Gd,1 = BG-1BT tB* 11

-37-

Therefore,

= G m [Bs(E tG*)c* + r) (6)

Substitution into (3) gives

Kc* + B*T Gar = 0

where

K = B*T Gm e (E - te) +

This yields

c* = - K-1 e4T Q/r

Substitution into (6) gives a which in turn gives c using (5),..

and hence 2 from (1), an9 the iteration step is completed.

The programme generates ia turn all feasable

combinations of charged and neutral tracks and for each of

these allocates each of the pormissable mass combinations,

incorporated by the user in the titles, and enters the fit

section which performs the calculations outlined above.

When one interaction point of an event has been tried

with each hypothesis in sequence, the programme uses the

additional information thus obtained at any adjacent

vertices. Finally, for combinations of single vertex fits

which have been successful, multivertex combinations are

constructed and overall fits tried.

2,5 Seection of !.:inem4tic intorprotfttions

Having obtained all possible fits for each event, the

-38-

w)xt step is the selection of tlw; correct int.q.pretations.

We broadly classify events as "fits" and "nofits". In

the former case there is at most one missing particle (or

three unmeasured auantities) and a x2 analysis is possible.

In the nofit category more than one neutral particle is

missing. K,.r thJ numb,Yr of constraints is unsuffici ,nt to

permit a fit. We repros-mt thz! missing particles by a

fictitious Darticle, denoted by Z0, having mass and energy

eual to the corresponding missing quantities and emitted

in a direction rieded to balance the momentum-energy eouations.

Thr.;) mass of this "particle" is then the "effective mass" of

the set of all missing particles.

There is also a category of events there four parawlt,ers

are unknown, called "zero constraints". ktt-mpts are made

to solve these 1-), using information from secondary fits.

This is often rdossib]e vdth charg.)d sigma or xi production

with one neutral, ?here the 13ngth of the hyperon track is

too short for a measurom.mt of its moor

With a view to selecting the most probabl,,, fits and

reducing ambiguities to a minimum, the following criteria

have been adopted and applied with the specified hi)rarchy:

1) Ionisation predicted by the fit must be consistent

with the observed value.

2) One-constraLet fits are rejected in favour of any

existing four-constraint fits.

-39-

3) x 2 probabi]ity limits were 1% for 3-and 4-constraint fits

and 5% for 1--any? 2-constraint fits. The limits were

initially chosen on the basis of experience with other

high energy experiments. They were found to be reasonable

for this ex::,eriment (see fig. 3.4a).

4) Missing mass limits for one constraint fits:'

-.12

.10

.40

<

<

<

m2

m -k m2 <

.10

.35 1.20

(GeV/c) 2

(GeV/c) 2

(GeV/c) 2

The upl)er limits were chosen at a value where events

with one missing particle in the appropriate, riissing mass

squared distribution is approximately equal to the number

of events with an extra missing neutral pion. The lower

limit is made sufficiently generous to accommodate

measurement errors. Fig. 2.5a shows the missing mass

squarod distribution for the A litxk° and ILIJIc72

channels to illustrate the case of the lc° limits.

For rare events the criterion used was that the

square of the mass of the missing particle lay in the

range mm2 + 3 Am2 -+ mm2 3AI=2. No missing mass

restriction was imposed on four-constraint fits.

5) Ono-constraint fits involving missing A° or Z° 1,/,?r,1?

rejected. A comparison between the number of fits

involving an unobserved A ° andttnnumber involving a seen

-40 -

A °, gave a ratio of the former to th) latter of about

20 times larger than ,)xoected from the known cicay

branching ratio of tho lambda. This is becausc: a

considerable number of events with a missing neutron,

or nofits can simulate these channels. As cross-

sections for hypron production are known to be a =all

fraction of the total cross-section, it has been decided

not to accept fits with missing lambda's and sigma's.

6) Limits on proton. momentum.

From high energy experiments in meson-baryon

scattering it has been found that nucleons are generally :6)

produced with low momentum in the laboratory system,

the momentum distribution for protons extending to about

2 GeV/c. This affords a possibility of discriminating

between ''ion and proton tracits, whore th(- laborato

momenta of the former extend well beyond this limit.

For low multiplicity reactions at 2 GeV/c laboratory

mom,,Intum a track is r-,10 times more probable of b3ing a

pion than a proton. This limit increases with

multiplicity. The limits docided upon were 2 GoV/c for

Less than four bodies in tho final state and 3 GeV/c for

higher multiplicities, where nofits are assumed to contain

two missing neutral particlos. This criterion was not

applied for rare events, where the reactions are not

- 41 -

necessarily predominantly peripheral, nor in the case

of four constraint fits so as not to eliminate an

interesting class of processes where the proton mny

indeed be fast, as in a baryon exchange process.

vie show in fig. 2.5b laborator7 momentum plots for

protons and pions to Mustrato thr. choice of th

above limits.

7) Any fit having a x 2 probability less than owl-third

of that of the best fit existing was reject(,:d.

Up to three ambiguous fits were acc-TtA, and if wore

than this number survived the above criteria then the throe

with the highest probabilities were taken. The most

frequent source of ambiguity arises from the failure to

distinguish between fast pion and kaon tracks due to the

relatively small mass difference between these particles.

The re also exists a momentum region just below the limit

discussed in section 6, but not low enough for a proton to

have an ionisation discernably more than minimum, where we

often meet a 7c4./p ambiguity. As a consequence of these

ambiguities we have a category of nofit,ev-nts having mor.:

than three interprtations, which cannot be rlduc-,d RS

probability criteria are not applicabl-. have not

been used in the analysis, and their exclusion is liable

to introduce a bias. How,,v.-?r, reactions involving lambda

-42 -

hyperon production in association with pions, with which

this thasis is mainly concerned, are free from such bias.

The possibility of oxistancil of positive kaons and

antibaryons is ignored in the normal class of events,

oxcept when wa are forced to accept these assignments on

tho basis of ionisation, ns th,1 cross-scletions for such

procassas constitute a very small fraction of tha total

cross-section. Many ambiguitis exist amongst the rar

events whore we cannot exclude tho possibility of L)ositiva

kaons. Lifetime consid.;rations wara often useful to

discriminate batwoan chargPd 2snd K decays, as, for ,acampla,

the mean path ratio of 2 to K+ at 1 GeV/c momentum is

1:240.

2.6 Statistics programmes

Tha first programme in the post-kinematics chain is 17)

SLICE, Tha GRIND library tape is used as input, together

with SLICF, cards which communicate to SLICE the accapted

interpretations. In tho mode used in the praant experiment

up to three fits could be accepted per event. 'Each

ambiguous fit was taken with weight equal to l/(numbar of

ambiguous fits).

From the fitted masses and momentum vectors SLICE

calculates quantities, such as rasoaanca affactiv.. mass,:s,

-43-

centre of mass momenta, decay weights, etc, to be used in

the statistical analysis. A binary record is written

on the DST for each. fit. Unfitted events are treated in

exactly the same way as fitted ones, the missing neutral

mass being treated as a single particle. This concludes

the single-,,,vent analysis.

The statistical analysis is performed by SUM X, a

programme originally written in Fortran 2 and FAP in 18)

Berkeley and introduced to CRRN in 1963. The programme 20)

was complet-ily rewritten the following year at CERN,

incoroorating dymanic storage which avoided unecessary

waste of cocoon area which occured by storing variables

in fixed arrays of maximal size. Several refinements

have been introduced since then.

The _programme reads DST and accumulats information

which can ba entered in histogrammes, scatter plots, etc.

The definition of the information to be display-)d is

communicated to the programme by data cards supplied by the

user. In practically all applications of. SUMX it is

necessary to select various different subsets of events.

The conditions under which a particular paramtor may entEr

a plot can be defined by a series of tests under the control

of the user. The information is convyed in an array,

known as the test vector, which contains during the

- 44 -

processing of a given event the truth values of all

d4,fined tests.

Provision is made for the user to perform auxiliary

computations, which may necessary if the r.,:levant

information does not already exist on the DST. Due to

th,! finite size of the core store it may happen that th-,re

is insufficient dyYn-xic store to compile the information

required in ono job. STThX has been programmed to cocc

with the situation by automatically breaking down a logical

pass into as many phsical passes as may be needd.

2.7 Variables and curve fitting

We define in this section kinematic and dynamic

variables commonly used in the description of elementary

particle proc-Dsses. An outline of the maximum likelihood

method is also pr,Ilsented.

It is obviously advantageous to employ a relativistic

framework and we use the 4-vector notation. We also adopt

for convenience th) system of units often uet in el-Jc.entary

particle physics in which: -z = c = 1. A particl,e is

represented by its "our-v.cto-; p = (F,i)9 where p2 = E2 2 (ii)- is the snuare of the rest mass of the °article

( to th , square of the energy in th- rst frame) and

is a useful invariant,

- 45 -

4-vectors are exploited elegantly in the Mandelstam

roprosentation. Consider a two-body process in the centr

of mass system of the type 1 + 2 3 + 4, where pl...p4

repres,mt the 4-vectors of the particles involved.

s-channel

-channel

p2 p4

u-channel

The centre of mass energy squared is defined as , s = (p1 + p2) 2 = (1)7 + IDA)2

VI-1 also defin the square ,2 ,2

of the 4-momentum transfer, t = - p3) = (p2 1)) .

To complete the representation we dr)fIne a third variable

u = - p4)2 = (p2 13)21 the 4-momentum transftr in

the crossed channel. This leads to the relation 4 2

s + t + u = 2 mi. The scattering angle, 6*, in the i =1

centre of mass system is defined by

1)1.P3 = 11)1111)31 cos 61*

and is related to the 4-momentum transfer by 2 t = 21pAp 'cos + m1

2 + 1/1 - 2E1E 1 3

The absolute values of the momenta are obtained from

2 2 , .2+ 2. 2 E = s = Cp1; mi) + (!p2 , A 1 2)

-46

IP1I -P2 1P31 =I-P4

2 2 - , I = -----7 W ;. k's'IniPm2) 2E 1 1= 1 x 7?;(8,4,m)

21-E,

where wr) have introduced the conveni•mt notation

(x,y,z) = (x-y-7,) 2- 4yz

which is symmetric in all its three argumTnts.

The invariant liffective mass; M of a system of n

particles is defined by

m2 2,11 E) 2 - I d i.=1

and is a useful , tur,ntity for the s,,arch of resonant states.

If the n partic2es originatr- from a resonance: rcay, tIrm

the total (7.T.Hrgy in the c=mtro of mass of th,e partic:H

system is if-mai to the energy of the resonance in its rest

franc, ie. to its mass.

A reson2nc,, of mas h maniets its ,-Lf as .n ,_ I, res

in the r ,ff sctivo mass (listribu'Aon at M = M having a res Breit-Wign,r saps:

,2 f(V) (m-m )24. wr 2

res where r is the full width at half height. A serious

rroblth encountered iu the search for resoAancas is the

assessment of the background shape. In the simplest

treatment ono assumes that tLe effective mass follows a

,hase space -Astribution, as calculated on the basis of

-47—

the statistics] -alodol, and the experi,Jental effectiv? mass

spectrum is fitt;.A to phase s:.acY, weighted by Brit-Wigner

shapes corres:.onr3ing to the r.)sonancos which are assumed

to be present. However, the statistical phase spac.?

assumption is questionabl,- as hi 01 energy collisions are

generally of a ";,,lancinc" (p,?.riphlra]) natue, with

major dart of the cross-seetion being restricted to low

t values. Moreover, no account is tak,:n of final state

interactions which may be present or of resonances in another channel

The way in which t,11 phase space can he distorted by

the peripheral nature of th,e interactions has been 2] )

illustrated in the discussion of the so-call -A "Deck effect"

which invokes diffractive scattering of the exchanged particle

at th, baryon v..117ex.

A sini-r,mpirial to rIal,:e phase space r;,c).ri

consist;:nt 4ith high energy observations is to weight the

distribution by an exponential factor -Amax

tnin

do where A represents the naximum slope of the elastic —

max dt

versustdistributionandtmin the minimum value of the

4-mom'entum transfer corresponding to each value of the

effectivc mass.

-48-

Moro information about resonance production in three-body

final states is contained in a so-called Dalitz plot in

which on plots the ,:ffectiv , mass seuared of one

two-particle combination versus that of another two-body

system. The statistical model predicts a uniform density

of events in the kinematically allowed region. A resonance

in a particular particle pair manifests itself as a strongly

populated band across th plot centred about the value

corresponding to the square of the resonanc,i mass.

The main methods of comparing experimental results to

various theortical predictions are the X 2 fit, which was

briefly dealt with in connection with the geometric and

kinematic analyses, and the maicimum likelihood technique,

the latter being more suitable to cases with limited

statistics.

Considor a distribution of n events depmding on the

parameters xl, x2 ....c x which W: compare to a theoretical

distribution V' (xl, x2 ..... x ). The likelihood function

for the experiment is defined by

n (x, x

2 x

r) = n w (xi, x2 x

r )

1- v=1

For a given set of values (xi, x2 Zr) one 4,

calculates with a computer4,(xi, r) inserting the

experimental values of the v th event into the distribution

-49-

function FTrand computing the product. By varying (x„...xr)

one finds the l set of paraneters (x11, x ...xp that gives the

maximum value of the likelihood function. This set is then

taken as the best estimate for tho param-!tnrs. Usually thr., n

maximum of anj, =- 2,W is taken to fa e ci)itat-1 th computation. v=u. Th,-) =or matrix (ox Ox.J ) of the paray-)t ers (for n not

too small) is the invors of the matrix H with th.. elerents

Hid= a 23..n„ (xi ,...xr )

a x• ax- a X•

1 a X. (H

1r

X2 Y xr The maximum lik,.aihood method is not suitable for

deciding which of a set of theoretical prclictions fits the

data best, for we hav--) no theory to d-A•ina tho ngoodnss"

of a fit as we have in the cash, of % 2 analysis.

CDC6600

SLICE

magnetic tape

paper tape

1---) cards

R events for remeasurement

Ell' prints

- 50 -

scan cards

1

Scanning I=

Measur- ing

Editing

1 IBM7090

R I.N.G.

iBM1401 paper tape

conVer

IBM 7090 IBM 7090

THRESH GRIND

selection of fits v

1 > CDC6600

SUMX

FIG. 2.1

paper output

film

Beam -->oentry

SCANNING REGIONS OF BUBBLE CHAMBER PHOTOGRAPH

Region 2

1<

Recion3 >1

FIG. 2.2

al trac k

(A,B,C)

,, N

\ reconstruction \ line (ij)

11

I- I G. 2.3

chamio-gr --_( x,Y ) plane windows

\I

x flashes

>Y *---- projection

of track on ( X,Y ) plane

- 52-

x cameras

-53-

Apex position measurement errors (cm)

60- 60- 60-

40- 40- U) .,--, c a) > a) 4-20-o d z

40-

-I-,

20-

.02 .04 .06 Ax

.02 .04 .06 dy

.1 .2 .3 Az

20-

Weighted mean of residuals du

40-

30-

u) ...-, 20- c e > w "5 0 10- z

-1 6 10 15 20 microns

FIG. 2.4

K p Tc++Tc-+Tc

E21 „ Ao+ rt++ rc-+ Z

p (

TT+ (channel K13-> n Kit+ ) „ TC 2 GeVJc cut-off

40 tr) 420 a) a) 0

_ G eV/c

-54-

(a) Missing mass squared distribution

(t 20- > a) O

z 10-

P771 -.12 0

30 Mms.limits forte -rt.°

( b)

Laboratory momentum distributions

140

120 3-body final state

5-body final state

TC + ( channel K p -› n K

P p K7i-t+-rti-E°)

200-

100- 3.GeV/c cut-off

2 4 6 8 GeVic

FIG. 2.5

-55-

CHAPTER III

In this chapter discuss various sources of bias

and error introduced by the instrumentation and analysis

system. Tho discussion will treat these in the

"chronological" order in which they arise, starting with

considerations on the quality of the beam, then the

scanning biass and the quality of measurement and

reconstruction, finally the decay weights and statistical

biases will be treated. The chaptt-r concludes with a

presentation of cross-sections for the channels studied.

3.1 Beam purity

We have to ensure that all interactions studi!d are

due to incident negative kaons at th,1 nominal momentum.

Measuraments of high energy tracks are rather inaccurate

and it is thus possible to accoamodate within the errors

tracks at a wrong momentum. In view of this a large number 2)

of beam tracks has been measured in a separate experim,-nt •

to obtain accurate values of the momentum, dip and azimuth

angles, and the variation of those parameters over the

volume of the chamber. The incident beam parameters thus

obtained are inserted in the GRIND titles and are used for

comparison with the measured quantities for each event.

If the comparison is satisfactory within three standard

- 56 -

deviations of the measured values, a weighted average is

taken between the measured and titlo parameters, otherwise

the event is rejected as off-beam.

Fig. 3.1 displays histogrammes of fitted momentum,

dip and azimuth for beam tracks of a sample of four-constraint fits. The title values averaged over the liducial region

in which these events have been measured are

p = 9.98 -+ .08 GeV/c

% = 10 + 6 mrad.

9 = 3.145 + .005 rad.

The distributions are reasonably centred about the

nominal values and we conclude that the contamination from

off-beam tracks, and the loss of genuine tracks, are

negligible.

We next have to investigate the possibility of

interactions due to non-kaon tracks. Since the rest nass

of incident particle makes only a small contribution

to the energy it is often possible to obtain a good fit to

an hypothesis involving an incident K for an interaction

induced by a 7C -. Pion hypotheses have not been included

in the titles: these would in alinost all cases also give

fits which would be impossible to discriminate from a Y.--

hypothesis, so we must rely on independent estimates of the 7c contamination.

-57-

An estimate of the beam composition was made from a

knowledge of the total. Kp cross-section at 10 GeV/c.

We expect one interaction every 12.2 metres of beam track,

which corresponds to about 10 tracks observed in the chamber.

From a scan of samples of film, taken from each roll of

film during the exposure, the non-interacting background

was found to be about 30%. This consists mainly of muons

from pion decays in flight. The pion contamination was

estimated to be below 5% from a count of interactions occuring

with the RF switched off. This was in agreement with the

ratio of the number of events with associated V(p ts to the

number without decaying tracks expected from an extrapolation

of Kp cross-sections for such processes at ]0 GeV/c. Thf,

tuning of the beam virtually eliminated any antiproton

contamination.

There is no serious bias from pion contamination in the

channels involving a seen lambda, studied in this thesis,

since hyperon production induced by non-strange mesons is

much less copious than in the case of incident kaons.

However, the possibility of associated production from pion

contamination cannot be ruled out in the rare events where

we have more than one strange particle produced, as the

cross-sections for these processes are now comparable.

Whenever unorthodoxies arose with rare events, these were also

processed assuming incident pion and antiproton beams.

-58-

75.2 Scanning losses

For cross-section calculations it is necessary to have

a knowlelge of the numbsIr of events missed dueing tho

scanning state. Te d'fine

N = total number of events.

Ni = number of events seen by the first scanner.

N2 = number of events seen by the second scanner.

E2 = probability of finding an event in scans

1 &nd 2.

N12 lutnlber o( fAten.s seen bd ccanntv's Then

N= N1 =

N2

N12

E1 E2 E1E2

The total number of distinct events seen in both scans is

N1 + N2 - N12' overall scanning efficiency is

F - 1

+ N2 N12 (N1 N2 - N12) N12

N N1 N2

It has been implicitly assumed that the probability of

finrling each event is the same. This is a questionable

assumption as the geometric configuration plays an important

role. For instance elastic reactions with very short recoil

proton tracks are often missed.. This manifests itself as a

dip in the t-distribution at low 4-momentum transfer values.

Scanning corrections were made for a series of t intervals as

a function of the polar angle of the normal to the production

-59-

plane. The total number of elastic events was found by an

extrapolation of the data to the optical point.

For rare events the procedure adopted was to express

separately the probabilities of finding positive, negative

and neutral decays as P1, P2, 5

P_, respectively. The

efficiency for finding the non-decaying content of the

event was taken to be the same as for ordinary events of the

corresponding multiplicity, This was taken to be 1.0 for

simplicity (see table3.1). The probability that an event

with two decays is observed is reoresented by a 3x3 matrix

P = (PiP0), i,j = 1,3, for each scan on the assumption that

if one decay is missed the event is classified as a non-rare.

This is perhaps not justified for events where a charged

decay is missed, as this is quite likely to be observed in

a later part of the analysis, eg., during the measurement

where a decaying track measured as a continuous one will

most probably fail to be reconstructed properly and lead to

further investigation.

An event with three decays is considered as found even

if only two decays are seen, since this is sufficient to

classify the event as rare. In this case we have

P = P1P2P3 P1r2(1-P3) P2P3(1-p1) + p

1P3(1-P

2) (3x3x3 elements)

- 60

Each matrix element represlnts a particular topology with

corresponding scanning efficiencies El = N12/N2' E2 N12/111 as defined previously.

As the number of events in c:ach topology is rather small

the statistical errors Rre large and fluctuate strongly. It

has therefore been decided to obtain the P1 by minimising E (N 4R. i ,L 1E -74E1 2) 2 A E 4( 12 1, 12 2,1 1,2

1,2 ' - X - E N211' N N211 2,1 / over all topologies for each scan slparately.

For zero-pronged rares the scanning efficiency for the

001 topo?ogy has been incorporatd since this is significantly

less than 1.

Table 3.1 displays the scanning totals and corrected

numbers for all types of events scanned in region 1.

To investigate loss' of charged and neutral decaying

particles due to the decay configuration, We haw) plotted

in fig. 3.2 the azimuthal decay angle Y given by

cos y = (14 )

where

= unit vector along the line of flight the

decaying particle.

= unit vector along the line of flight of the decay

product (charged for V positive for Vo) 2 = unit vector along the z-direction of the chamber.

- 61 -

All vectors are defined in the laboratory system. In the

absence of any biases this angle should be isotropic, which

is consistent with the data, except for 017E where

scanning losses occur due to the orientation of the decay

plane along the line of sight. This loss amounts to about

3% for A decays, 8% for charged sigmas and 7% for the

E - case.

3.3 Decay weights and statistical biases

Due to the finite size of the bubble chamber ther is

a bias against observing strange particle decays of long

lifetime. Short decays are also liable to be lost due to

scanning and measuring difficulties. A correction for

those losses is made by multiplying each event with a decay

by a potential weight factor

1/(e10/AcosX e-L/N)

where

Acos7‘. = projected decay length.

L = potential length (distance between production

vertex of the strange particle and the end of

the fiducial region)

1o = minimum detectable length of the strange

particle track (taken as 3mm)

To find the losses of short decays we plot the reduced

length (l/p) distribution for hyperon decays (fig. 3.3);

62

the corrections for these losses are: found to be in the

region of 8%, 20%, 20% and 15% for A., ; - and E -

decays, respectively.

Rare events, with two or more -locays, fl.;?(-) givm a

composite weight equal to the product of the individual

decay weights.

Each event entered in a histogramme is given a total

weight equal to the product of 'Tie deco weight and

hy.dothesis weight (a, or For rare events one has

to be cautious in intertinc-, bumps in histogr,-mnes, as

we can have very large decay weights due to the presence of

charged kaon decays.

The average d..3cay weights were found to he as follows:

Particle Decay weight

A 1.08 + .o3 + 1,18 + .14

2- 1.12 + .l2

1.50 + .15

For the Z- and E decays there seems to be a loss of evnts

beyond the minimum cut-off length, as suggested by the large

depletion of events r.t Tow 1/p values.

To investigate biases- arising from the probability

selection criterir.discussed in the previous chapter we have

plotted the probability and chi-squad distributions for

-63-

one- and four-constraint fits (fig. 3.4a1b) and compare

these with th,- theort,, tical predictions. The probability

distributions exhibit a strong peak at low values, presumably due to misidentified events. There is also

a tendency towards high probability values. This

behaviour is to be expected if the measurement errors are

over-estimated. The loss of events from the tail of the

chi-squared distribution is found to be negligible for

the lambda channels.

A test for statistical bias is afforded by thl stretch

function distribution. The stretch function for a

variable x is defined as

_ - S - x m

xf

(A x2 - A x2f) t-

m where the suffices m and f refer to measured and fitted

values, respective]y. For unbiased fits this quantity is

expected to follow a normal distribution with its mean at

zero, assuming the variable x to have a Gaussian distribution.

This condition is well satisfied by the data. Fig. 3.4c

disnlays the stretch function distributions for l/p, A and

P for tracks from four-constraint fits.

3.4 Contamination and channel separation

Misentorpretation of reactions can occur in many ways

for instance the presence of pions in the bc,a.m could give

64

rise to interactions which can be accommodated in a Y-p

hypothesis but, as discussed earlier in this chapter, this

has a negligible effect on channels involving observed

lambdas. Another form of contamination coms from the difficulty

of distinguishing between A and Z° h7peron.s. It was

found that 5% of the events fitting channels of the type

A °+ + charged pions also satisfied the hy.iothesis 2o

charged pions, where the fit is performed by constraining

A °+ Y to the 2° mass. This ambiguity was much higher

between the channels A0+ charged pions and Z°+ charged

pions. Missing mass considerations have proved fruitless

in resolving this ambiguity owing to the rather large

measurement errors involved at this energy, in addition to

the inherent 80 MeV/c error on the beam mowentum. In this

case we have favoured the lambda fit (four-constraint) over

the latter, two-constraint fit on the grounds of our

selection criteria. The A°/ Z° ambiguity is most serious

in the nofit channels where there is no way to distinguish

the difference between the two particles.

There also ecists a small ambiguity between e and

lambda fits, especially when the V° has fast tracks where

ionisation information is of no assistance. It has been

found that this ambiguity occurs in 5% of the cases.

-65-

To facilitate the selection of the fits in the non-rare

A o channels, only hypotheses of the type A o + pions were

incorporated. A search was made later for events involving

a K+K pair which may have been fitted as a It % pair.

There is some indication of this occuring in the channels

involving one or more missing neutral pions. We illustrate + - o

the case for the channel A7c+ % % % % in fig. 3.5a, showing

the laboratory momentum distribution of the neutral pion where there is a large peak of near-stationary pions. The

_ most likely cause of this is the misfitting ofAK K % % events which when treated as A 441F7F have missing mass,

to account for the %/K mass difference, but no missing momentum. The lambda channel s involving one or more els have been refitted using the hvpothesfs AAA and AAilit'n

+ - o + - o 20 events from channels Alt it It and AA AZ gave satisfactory

A° - 0

fits to the hypothesis. The A it it it channel

contributed 4AK Y events (as 'lisplayed in fig. 3.5b, showing the mass distribution of "particles' A). An additionalAK

+K- event and 9App events came from channel

+ - o _ + - A it it Z . The analysis of channel. AAA% it is comaicated

by the presence of background from the 4 possible (+ -)

combinations. Only combinations corresponding to values

of A lying in the K and p mass regions were retained. If

an event contributed more than one combination in these

-66

regions, then each entry was accepted with an equal w,Adat, _ _

/1 I 1\ k r ,j or Fig. 3.5b shows 29.5/1K K 7c it events and

8.5 App 49T events. It is interesting to no:t that the

number of AK+K- andA-K+F- It 7r events found by this method

compares re,,sonably witll the number of near stationary it°'s

in the laboratory momentum distributions, (fig. 3.5a).

3.5 Cross-sections

There are two aproaches open to us for the determination

of cross-sections. One can either cbaculatr, the total K-

path length (eg. from a count of tau decays), or use the

total numbest of events observed in conjunction with the

known total Kp cross-section at 10 GeV/c. The former

method is subject to a rather large statisticn1 error due

to the small number of soon tau decays. A count of beam

tracks would also be inaccurate as the muon/pion ratio is

not exactly known. Tine the total cross-sGetion method

was used where the total K-p cross-section at our momentum 24)

was taken from an accurate spark c}-amber determination

to be 22.5 + .2 mb. The scaniing results dive a total of

31,227 events in region 1 of the chamber afte7, correction

for scanning losses (see Table 3.1). The scanning results

have not been used for the zero-prong interactions as the

scanning efficiency is very low. 7-10 number of zero-prong

-67.-

K and zero-prong + lambda events was used to calculate 25)

the number of unseen decay modes.

There is an additional, significant loss of events

(z‘i33%) in the elastic channel due to the difficulty of

observing short recoil 9rotons. The elastic channel has

received si;ocial treatment in view of this bias, as discussed

earlier in this chapter, and the cross-section obtained was 26)

3.2 + .14 mb. If we exc:!.ude this channel, we ara :left

with 27,700 events observed in region 1, corresT,onding to

19.3 + .2 mb. Tbis gives an equivalent of .700 + .01

microbarns per event in this region.

To obtain the effective lengths of the scanning regions

we have plotted in fig. 3.6 the production apex x-coordinate

distribution. The mean height of the distribution was used

to normalise to the number of events in the region tnd hence

obtain its affective length. A cut-off was imposed at the

plane x = 70 cm, as bey.ond t1-.is point secondary tracks were

genarary found to be too short for accurate measurement.

The effective lens the and corresponding microbarn equivaThmts

are given in table 3.2.

Table 3.3 gives cross-sections for some final states

involving hyperon production, where corrections have been

made for scanning loss, unseen hyperon decay modes, escape

probability and incompleteness of data. The decay weight

-68-

for the charged sigma and xi channels was found not to

account for all the losses, for a significant numb.:r of

events corresponding to hyperon track lengths of ovr

(which is the cut-off imposed in the decay welc,ht cal_culation)

escape d -ytection; this additional loss tias corrected for.

Corrections wore also mad for unseen K° d-cays and

Ko decay weights. Ev-mts Involving decaying K tracks

have not bean used in the cross-section cdlculations as

these have very large decay weights and there are too few

of them to give statistically significant results.

In the A K°K° channels, where it is demanded that at

least two of the strong() .article decays are observed, Iv,

have used the rough branching ratios of and for A°

and K° decay modes, respectively, which yid a fraction

of 11/27 observable configurations out of the total numbnr.

K0o K states. This figure was used to correct for the of

unseen decay modes.

- 69 -

Topolomr

TABLE 3.1

Scanning efficiency

Corrected number

Number of events seen in region 1

000

001

306

572

-

.92

567

415

200 10,072 .985 10,122

201 2,689 .991 2,718

400 8,565 .997 8,600

401 2,202 .995 2,220

210 385 .996 387 410 949 .990 959 6-prongs 4,195 .996 4,220 + +

V V - 7 .92 8 + - v v : 17 .92 19 + 0 v V 142 .96 148

Irv- 3 .91 4

V-V° o o V V

159

603

.96

.99

166

608

3v 68 1.00 68 Total 31,227

TABLE 3.2 Microbarn

Region Length (cm) Toologies measured eauiva1ent

1 40.3 + .5 All .700 + .01

1+2 81.2 + 1.8 Fvents with V .348 + .008 and rare s

1+2+5 103 + 2 Rares .274 + .008

- 70 -

Channel

TABLE 3.3

STATES

Corrected cross-section (11.1)

CROSS-SECTIONS FOP HYTT=!ON FINAL

Number of observed events

A.9° 25 14 ± 3

Aeit- 82 50 + 8

Alt+.7c-70 213 133 ± 15

Aen+w-.)t- 80 52 ± 8

A70e9t-7c-70 277 170 ± a9

Az° 275 144 + 18

AeA-Z° 1,378 8o ± 8

A90-7E+%-%-z° 1,017 59 ± 6

AK4a- 4 2 + 1 _

AK°K° 22 16 ± 4

AK°K°7c° 5 3 ± 2

AK°K1-7t- 16 5 ± 2

AK°K-70- 20 7 .± 2

AK°R°29t 66 35 + 5

AR°K+29t 42 13 ± 3

AK°K-2% 41 11 + 2 _

AK-la-27c 30 17 + 4

AK°V>21t 28 20 + 5

AR°K4->29t 45 12 + 2

AR°K->29c 4g 13 + 2 ±

AK°Z° 51 /6 + 2 -

(Conttd)

- 71 -

Number of Corrected Channel observed evept s = oas - s ? c ti 00KIL (.11. 1

A10171>%-r 19 6 + 2

AK °K-n+ Z° 22 6 + 2

AK°e%-Z° 41 12 ± 3

A PP 9 5 + 2

A pii 2'n 9 5 + 2

g41°K- 3 3 + 2

ZI-K°K-ic° 19 21 ± 5

241C°17°n- 't) 26 + 4 _

24-VIT°29t 5 12 ± 6

el7°K-1-21.c 10 11 ± 4

24-K°K-2% 18 20 ± 5

141°1e>2% 18 19 ± 4

2-1-K°K>27c 14 16 ± 5

zl-K°K° >2n 5 12 ± 5

rit °K+ 5 6 + 5

fR°K+ /c° 4 4 + 2 _

2-KoRoe 11 9 ± 3

zVii° 2/c 5 12+6 _

2—K-FR ° 2% 12 1 ± 4

z—z°K-2% 5 6 + 3

34 + 7

19 ± 5

20 + 4

(Cont'd)

2-170K+> 2/c 31

z-K°K->27z 17

z-10/70>27c 23

- 72 -

Channel Number of

observed events Corrector:

cross-section ( µb

Z+K°7cZ°

z+x°39cz°

11

1

10 ± 3

1 + 1 _ elckz° 7 6 + 2 _

1711z° 2 4 ± 3 .

2KliZ? 10 _, 9 + 3

Z7K3ICZ° 3 2.5 ± 11-- • 5

z-KITz° 5 4.5 + 2

riC.INZ° 2 2 + 1 • 5

raR2itz° 7 6 + 2.5 _

2.:,', -Vic+ 0 4 2

E. Ka 2% 0 .6

27,-K° 3% 5 2.6 + 1 ±

2-3-K°149t 10 13 + 3

E-K° >14% 1 _< 2

5-7-K+ 0 < .6

17 -1c±7K 2 < 1.5

23 K+2% 2 < 1.5

23-1C+39K 11 5 + 1.7

-K+Lyn 1 < 1. E-K+>4% 7 3 ± 1

s.-7c+z° 7 2.5 + 1.3

E-3/tZ° 15 4.3 ± 1.5

(Cant d )

- 73 -

Number of Corrects' Channel observed. events cross-section (µ b)

2.-3-57tZ° 4 1 . ± .7

ai-Kc'icZ° 8 11 ± 2.5

a' -103itz° 5 6 ± 1.:5 53-1C°59tZ° 0/

.‘ -1- E-14-Z° 5 2 + 1

.3 -K+27EZ° 20 8 + 2

s-1+49a° 7 2.5 + • 7

10

Beam parameters

9.98 ti) 10 3.145

400

500

200

U)

z • a)

'fa

z 312 3.16 3.20

radians

400

I I I

10 20 m rad.

9.8 10.0 10.2 GeV/c

•F I G . 3.1

Ae decay

Thi2

-75--

No.

of

even

ts

Decay azimuth angle, y

20-

+ E decay

10-

Tc/2

20-

10-

_— :-.. decay

TEI2

FIG. 3.2

10 20 30 40 cm/(GeV/c)

1.4-

1.0

0.6

0.6 1.2 1.8 0:6 1.2 cm/(GeV/c)

FIG. 3.3

-76 -

1/p distributions for hyperon decays

A°

1.8

1.4-

1.0

0.6-

1-C fits 48; 0 z

( b) 10 40

0 • z

1/p

- 77-

Probability distributions

100-

1-C fits (a) 50

200

100 1

4-C fits

0 50 100 °/0 0 50 100 °/0

X2 distributions of A° production fits

a) 80 20

Stretch functions of tracks from 4 -C fits

(c)

200 200

x

-

4-, M .100 100 100

U (U L.

-3 -2 -1 0 2 3 -3 -2 - 0 1 .2 3 -3-2 -i 6

FIG. 3.4

Kp -0. A° TE4-rt.4. TEtc rc°

( a )

1

30

20

10

30

20

10

-78-

Kp -+ A it+ rt- Tc°

r

Laboratory momentum of 0

noi GeWc --->

0

1

Kp->t AA IC+ TL

eit.+Tc- rcr Ti

u TL+ Tr.+ TC- Z° 10-

z

Mass of -A •

GeV;c2

•8

Fl G. 3.5

-79 -

400-

REGION 1

200-

-30 -20 -10 0 +10.

20-

I —71

REGIONS 1+2+3

x -coordinate of apeX

30 -10 410 +30 +50 *70

cm

FIG. 3.6

- 8o -

CITAPTFP TV

An outline of sorce of the theory of elementary particle

processes is ,riven iA this chapter. A survey of various

phenomenological models is Alqo presented, emphasis being

placed on treatments relevant to the analysis of high-energy

data.

4.1 Introduction

In the study of elementary particles it is customary to

classify the interactions involved in three categories.

i) 'electromagnetic interaction, characterised by a

coupling constant 2

1

137

ii) Weak interactions of coupling constant G2 10-15

iii) Strong interactions of coupling constant g2 14

Only the electromagnetic interaction has a correspondence

in classical and atomic physics, and arises from the Coulomb

force between charges and magnetic moments, the• photon. being

regarded as the carrier of the e.m. force. This is the

only class of interactions where we are equipped with a

',complete theory!' inasmuch as it is possible, in principle,

to obtain any degree of accuracy in terms of an expansion

in powers of the fine structure constant, a .

a

-St_

Weak interactions are responsible for leptonic, semi-leptonic and non-leptonic decays of elementary particles,

excluding strong parity-conserving decays of resonances,a,hd

cte oty orAcko -v-ti &ix-6T All of the existing experimental evidence can be

described in terms of a weak Lagrangian with a local current-current structure:

gx) = G X [ 1 1X JX X j7) 4j2

1 and J correspond to the lepton and hadron currents,

respectively, and the 3 current-current terms above corr?spond respectively to pure-leptonic, semi-leptonic and non-leptonic

processes. It is, however, possible that the coupling is

not really local, but mediated by the so-called intermw3iate vector boson (7), in which case the structure of weak interactions would resemble that of strong and electromagnetic

ones. From present estimates of the W. mass, the possible

non-locality is 51.0-14cm. An excellent review of the theoretical developments

27) and comparison with experiment is given by Marshak.

Strong interactions govern processes between hadrons, such as scattering, resonance decays and nuclear binding forces. The main difficulty here arises from our ignorance of the exact nature of the force, and perturbation theory

obviously cannot be applied due to the large coupling constant.

-82-

Instead of starting with a potential to define a basic

Lagrangian, and deriving consequences which can be subjected

to experimental test, the usual procedure is the reverse.

One tries to gain some insight into the nature of the

potential from phenomenological interpretations of

experimental data, mainly from scattering experiments.

4.2 The peripheral mode]

During the last few years a large quantity of high

energy data has been accumulated and studied at various

primary momenta above 1 GeV/c. It has been generally

observed that inelastic processes are frequently of the type

a + b c + d

where c and d may be darticles stable against strong decay,

or may be resonances. Many reactions also exhibit a

tendency of the secondary particles to follow the directions

of the incident particles in the centre of mass system (ems).

This dominance of small momentum transfers increases with

increasing primary momentum and becomes less pronounced as

the number of secondary articles increases. This feature

has led to the development of the peripheral model which

has been successful in describing the main characteristics

of many quasi two-body processes in the energy range between

about 1 and 10 GeV.

83

The theoretical formulation of the peripheral model

is based on the Feynman diagram shown below,

A a

x

where we assume the interaction to 1.roceed via the exchange

of a virtual particle x . The four-momentum transfer at

the vertex A is given by ,

= (Pc - Pa) 2

which can be interpreted as the square of the mass of the

exchanged particle. At the point t = m2 the exchanged

particle becomes real ("on the mass shell"), but this lies

in the unphysical .region of t since t is normally negative

for two-body reactions.

We write the matrix element for the process, following

the Feynman rules, as

1 M = MA (t/mc) 2 MB (t,md) t - m_

4.

2 At t = Mx we have a pole in the propagator term and the

MA and MB become the matrix elements for the process

a + x--4c and b + x respectively, which are proportional

to the coupling constants of the two vertices. The exchanged

particle must conserve all relevant quantum numbers at each

vertex.

t

-84

Perturbation theory has been used to calculate the

vertex functions and these are found to be increasing

functions of t, the increase being stronger when the spins

of the final particles are hillier. This inhibits the

rapid fall-off of the propagator as we move away from the

pole. Ali two-body reactions studied so far exhibit a

much steeper fall-off of t and a lower overall cross-section

than predicted by the peripheral model.

Two apa•roaches have been used in an attempt to overcome 28)

this difficulty. The first is the form factor method

where a t-dependent form factor is introduced in the matrix

element for each vertex and the propagator, expressed as a

product, F (t).

The form factors are equal to unity on the mass shell

and are supposed to take into account high order effects due

to a ,resumed internal structure of the vertices and

perturbative connections of the propagator. The main

criticism is that no theory exists for the calculation of

form factors and these are parametrised in a more-or-less

arbitrary fashion.

Several one-pion exchange reactions can be reproduced

by an empirical form factor, while processes where pion

exchange is forbidden have led to much less satisfactory

results.

-85 -

The alternative modification of the simple periohera:

model is the absorption model. Unitarity, so far neglected,

has been introduced to take into account the many channels

which are open at high energies and contribute to the total

cross-section. These tend to reduce the quasi-two-body

channels, the reduction being stronger as the impact

parameter becomes smaller. This means that the main

contribution to absorption comes from low angular momentum

partial waves, correst_onding to high t values. This has

the desired effect of reducing the cross-section at high t

and brin:-;ing the t distribution in closer agreement with

exeriment. The simple Pefnman diagram is complicated by

an interaction of the particles in the initial and final

states to take the absorptive effects into account.

29) 4.3 The Pegge pole model

The peripheral model encounters a serious difficulty

When we consider the exchange of particles of spin J),1.

This can be seen from the s dependence of the scattering

amplitude. This strong energy dependence on spin is

contrary to experience and also leads to a violation of

the unitarity bound at high spins, and high s.

The need to suppress this violent energy dependence

has led to considerable interest in the Regge pole model

- 86 -

which originated in potential theory. Regge and his

collaborators conside.:ed the analytic continuation of

angular momentum, 1, in the comelex domain. -athin such

a framework Reggels original analysis showed the existence

of poles in the scattering amplitude, .f(1,F,) for complex 1

and complex momentum, k. For physical values of k the

poles describe a locus, a (k) (known as a T1ege trajectory)

in the complex angular monentum plane. a pole

approaches a positive, integer value of 1, a resonance or

bound state results in the scattering amplitude for that

particular 1 and k. A bound state occurs if the energy

is below the scattering threshold Pith. We have a resonance

if F > Eth„ provided Im a (E) is small and Rem (F) increases

through its value at the energy considered. A iegge

trajectory connects a family of hound stLtes and resonances

having the same internal quantum numbers. The set of

resonances associated with a trajectory are called Regge

recurrences. The concept of single iarticle exchange is

now replaced by the hypothesis that a whole trajectory of

particles is exchanged in the t—channel.

The aim was to investigate the conseruenccs of the

analyticity of T(102) and in particular' the existence of

Regge poles on the total scattering amplitude, F(cose , 2),

given by the usual partial wave expansion.

- 87 - N

F(cos e E) = (21 + 1)f(1,E)P1(cos e 1=0

By applying the Sonmerfeld - Watson transform and the

Cauchy integral theorem, the partial wave sum is replaced

by a contour integration in the complex I plane. V.e

arrive at the final expression:

(2 mi(E)+1) F(cos 02E) = p P(-cos a )

k i sin w (E)

background integral

The fil,(10 are residue functions and c.i.(E) is the

position of the ith pole in the 1 plane.

Due to the existence of exchange potentials (liajorana

force) in strong interactions, the forces in even and odd

anaular momentum states are different. In the Regge

terminology this means that we should have t%o trajectories

corresponding to even and odd 1-states with recurrences

occuring at intervals of Al = (Re a (E)) = 2, corresponding (±)

to two amplitudes F of positive and negative signature,

This is accounted for by replacing the Legendre polynomial

in the Sommerfegei - "atson'represqlatation by a factor

Pai(E) (-cos0) 'GI. Pai(E) (cos 0)]

In the high energy region it is necessary to use the

relativistic scattering amplitude

T (s,t) cclis F (E, case)

-88-

Using crossing symmetry in the t-channel the Legendre polynomial reduces to

s a(t)

9 (t) ti" for s

where Q (t) contains kinematic factors and do is an arbitrary scale factor, usually taken to be 1 GeV.

be shown that the background integral tends to E as k • -11

At high s-channel energy the scattering amplitude reads a (0 a(t)

T(s,t) = 2 y (t) —S [ + + 0 (s

i sin is(t) So s 0 iS (t)

y i(t) 41(0 t = z ..0 y i contains residue functions and kinematic factors.

It turns out that Y i can be written as a product of couplings of the Regge poles to thethovertices in the t-channel, in

analogy with the vertex functions and propagator of the

peripheral model. This factorisation property has important

consequences as we may use different internal symmetry

schemes, such as 'SU(3), to relate the coupling of one

exchanged particle to different members of the mulltiplet.

4 .(t) is the signature factor giving rise to the Al = 2

spacing rule and contains the phase dependence. a,1(t)

From the d dependence of the scattering amplitude

we see that a limited number of exchanges (namely those w-ith

It can

— 89 —

the highest a(t) values) are expected to dominate the

amplitude at high energies. Using the optical theorem,

which relates the total cross-section to the imaginary

part of the amplitude in the forward (t = 0) direction,

we have Is ‘9.(0)-1

total °c v--)

From the Froissard bound the restriction (o) '<1

is obtained, which avoids the divergence we had with high

spin exchange in the .!,eripheral model.

There is indication from cosmic ray data that thq

total cross-section tends to a constant value at ultra high

energies, in agreement with the Pomeranchuk theorems. The

situation is represented by a unitary simJet Pomeranchuk

trajectory P, of maximal strength, a (0) = 1. Successful

fits30have been made to all total cross-section data at

high energies using the Pomeranchuk trajectory in addition

to the non-strange members of the 1-(p, co, 9) and 24*(4, f l f ,)

meson nonets with the incorporation of SU(3) symmetry for

the vertices to reduce the number of parameters.

A very stringent test for the validity of the T?egge model

comes from 9tp charge exchange scattering, as only the p

trajectory satisfies the ouantum number selection rules.

The prediction of the characteristic Regge energy dependence F.1 _13,,2 ap(0-2 do ,

dt \Eo

90

seems to be completrily consistent with all high energy data

on the reaction 9t p--on A° and yields

2 ap(t) = 0.57 + .914 in the range 0 ..5kti < 1 (GeV/c)

The situation is sketched in rho Chew-Frautschi plot

shown below rf

31 -

727" g ?

Re

Scattering

Particles region t

t >0

For boson trajectories a(t) is real, and the

trajectory is linear. Extrapolating the trajectory to

the t> 0 region we find that the Re m(t) = 1 value occurs

at t = (760 VeV)2 which closely corresponds to the square

of the rho-meson mass. The first possible candidate for

a Rege recurrence of the p must have spin 3 which seems

to corres.:)ond to the g-meson of mass 1.65 GeV on

continuing the extrapolation. This remarkable correlation

- 91 -

of high-energy scattering data with the particle spectrum

exchanged in the scattering process achieved by the Regge

trajectory is the most appealing feature of the Regge pole

concept.

Considerations of t-chanuel helicity amplitudes predict

a turnover of the cross-section at t = 0 and a minimum at

m (t) = 0 (t , -0.6) for the charge exchange process.

These features are observed exeerimentally.

Experimental data have been fitted to a variety of

channels, although here the predictions are not as clear-cut

as many trajectories can contribute.

At present the only unsatisfactory aspect of the

rho-meson Regge description of the IcN charge exchange

reaction is the erediction of zero polarisation at high

energies (where both helicity amplitudes have the same

phase) in disagreement with recent CERN measurements at

6 and 11 GeV/c where 10-15% polarisation at small t is

observed. Moreover the 1,olarisation seems to increase

rather than decrease with increasing energy. Several

explanations involving, for instance, interference from

s-channel resonances have been proposed to explain this

discrepancy. However, some evidence has recently been 7" )

presented, indicating that direct-channel resonances are

already contained in the Regge amplitude of the crossed

-92-

channel and the interference model therefore involves

severe double counting.

4.4 Double Regge-pole model

The concept of extending our knowledge of two-particle

reactions to production ,,rocesses with three or more final

particles is not a new one. The original multiperipheral

model of Amati, Fubini and Stranghellini was developed as

an elaboration of the peripheral model.

The generalisation of the Regge model to processes

involving more than one exchanged Regge pole has been 32)

considered theoretically by many authors in the asymptotic

region and in the case of three-body reactions some

applications to ex-nrimental dr.ta analysis have been made 33)

with encouraging results,

The double Regge-pole model of Chan, Kajantie and

Ranft is based on the graph shown in fig. e..1a. The

amplitude is a function of five independent variables,

three of which may he chosen as

s34 = (p3 + p4) 2 , s45 and s35

2 2 2 while, s =s35 - m3 - m4 - m5 (p1 + p2

)2 = 534 + 545 +

is the total cms energy squared. The shaded regions of

the Dalitz plot (fig. 4.lb) correspond to

-93 -

(I) small s34 , (II) small s45 (III) small q 535 These regions are usually populated by resonance production

in peripheral quasi-two-body reactions. Region IV

corresponds to events with all sij large. The amlitude

for the process depicted in fig. 4.]a is taken as

aa ) A n) Ya(tiN(t2Mtlyt2 ,9) a(t1)534(t1 ID(t2)S45ab(t2)

where t1 and t2 are the squares of the four-momentum transfers

at the two external vertices and yl, Yb re:present the

coupling of the Regge poles a, b to the external particles.

1 + exp(-i/ca a,b(t1,2)) (ti 2) - a,b' sinwa (t1,2) a l E

are the signature factors and ma, mb the trajectory

parameters of the Regge poles, as in the traditional two-body

Regge model. The new factor Y(t1l t210 represents the

coupling of the two Regge poles to particle 4. It can

be shown that this factor depends only upon the nmassesti

t1 and t2 of the Regge poles and on the azimuthal angle cP,

defined in the rest frame of particle 4 as

(11143) (p24;5)

1 fix-153 1 I 112x1515 I 1 2 -1 2 2 2 2.[ (t/+t2-m4) +g (ti+t2-2t1t2-2m4t1 2(-t1M-t2)7'?, 2

-21114t2+1134)

cos q) =

where s34s45

-94-

As a consequence of three-particle kinematics and the

udiffractiv-!I, character of the Reg:,e vertices, it turns

out that the graph of fig. 4.1a is appreciable only in one

corner of the Dalitz plot where is small (fig. t.lc).

Consider, for example, the reaction Alt-tic - where the

graphs shown in fig. 4.2a may ty:ically contribute. One

can thus label the corners occupied by the middle particle

as shown in fig. 4.2b. This property leads to a

de-population of the central region of the Dalitz plot.

An investigation of interference effects has shown that

these are generally negligible. From the kinematics the

contribution to the cross-section is a strong function of

the mass, m4, of the middle particle. This feature makes

baryon-exchange effects quite significant. It can also

be shown that the amplitude strongly favours the value

p =ic, with the distribution exhibiting a roughly

exponential peak at this value,

Averaging over spin and absorbing all spin indices,

the amplitude reduces to

2 2aa(t1) b(t2) I A I = (3 (t, ) (t2)15 (til t2,1p )534 s45

a ' b

The distribution of events in the Dalitz plot can

be calculated by making the assumptions that the Regge

- 95 -

trajectories are linear and that Pa and (fi b, which are

related to residue functions for two-body processes, can

be approximated by expon-vitials. A smooth clpend-nco of

T on (3(tl,t2,9) is assumed, as the strong pealcing at 9 =7c

is already contained in the diffractive character of the

vertices. Amplitudes arising from various Pegge graphs

are added to give directly the distribution function on

the Dalitz plot.

The cornering effect and diffractive nature of the

vertices give rise to an ordering p >p >p -1

with 3 ; L respect to the cms longitudinal momentum, p .

4.5 Multi-Regge pole model 4)

A phenomenological model for reactions of the type

A + B 1 + 2 + 3 + has recently been proposed for the cualitativu description

of reactions at energies >, 5 Gev/c. Three-body models considered so far apply only to events

in that rePion of phase space where every pair of final

particles has a high effective mass, which is a condition

satisfied by a generally small fraction of events at present

experimental energies. The present model supplements the

multi-Pegge model with the assumption that the structure of

non resonant, low mass clusters is governed only by phase

space.

- 96 -

The total ems energy is given by

s = Z ij sij

2 (n-2)Em. , where sij = (pi

2 +

is the energy of a particle .pair. At low multiplicities,

the sli ts are likely to be large, since the energy is shared

among a small number of particle pairs, und we expect a

multi-peripheral reaction to prevail. At high multiplicities

less energy will be available for each particle pair which

leads to a "statistical" picture. The amplitude for the

multi-peripheral graph (fig. 4.3) is parametrised as follows: Q. t n-1 , g.s. + ea\ /si +

II (Si A ei k jF

1=1 \ si + a a bi

s = (Pi Pi+1)2 (mi mi+1)

i 2 (PA - Pr)

r=1 = intercept of ith Rogge pole.

constant a (taken to he 1 GeV2) defines in a rough

sense the boundary between the high energy, Regge-type

behaviour and the low energy, phase space region. When

all sits are >> a, the amplitude reduces to the form

ngii--1 exp (Bi + log si)ti with Bi = -log hi Na

gi here play the role of coupling constants and Bi describe

the assumed exponential t-dependence of the vertices and

the Regge trajectories are assumed to be linear. When

ti

a. 1

The

-97-

any of the sits << a, however, then the corresponding term

in the amplitude is replaced by the constant, c. The

amplitude thus contains th-) phenomenological features of

high and low energy processes and interpolates smoothly

between the two cases.

The amplitude for a given process is obtained by

adding incoherently amplitudes corresponding to all

permutations of final particles, consistent with quantum

number selections rules. This is justifiable as it 32)

can be shown that interference between graphs is

negligible. Good ripyeement with experiment has bean 4)

obtained for the distribution of both baryons and pions

in the cosine of the cms scattering angle and the cms

momentum components for high energy reactions between

5 and 16 GeV/c.

St's

tEs

q

.17

(e)

17Es

(q)

Sts

91 +11

3i 'Old

1-LV - 917s + 6 -

17E u) w s + - z

•

(q )

(e)

=

-100-

Multiperipheral Regge-pole diagram

1

2

3

2

3

4

FIG. 4.3

CHAPTER V

5.1 Introduction

This chapter is devoted to a study of reactions

producing a lambda hyperon. We first look for resonance

production in the various channels and presenterotsrisections.

Two-body reactions of the type K-+p-* Y + M (where Y is a

lambda hyperon or hyperon resonance decaying into a lambda,

and M represents a meson or meson resonance) are compared

with observations at other energies.

A Regge pole model is used to describe the production

properties of the lambda and associated pions.

5.2 The final state A7c0

re have 25 events satisfying the hypothesis

K -+ p-a A + 7E°. This channel is likely to be contaminated

from two-pion production, as the fitting errors are rather

large in zero-pronged interactions where we do not have

secondary charged tracks to determine the apex position to

a high degree of accuracy. This contamination was

estimated from a consideration of the missing mass

distribution obtained by deleting the charged tracks from

A 7E+7E-

events. A comparison was also made with the missing

mass squared distribution of zero-prong, nofits. Fig. 5.1a

shows these distributions, from which it is deduced that

the contamination is negligible.

- 102 -

The cross-section for the final state A1P was found to

be 13 + 51-Lb. The production angular distribution of the

lambda exhibits a strong backward peak (ie. a peak in the

direction of the target particle in the centre of mass system);

correspondingly the t-distribution has a peak at small values

of iti. This is indicative of a peripheral interaction (fl4g.54:

.3 The final states loct-0 A itiFie

A search was made for resonances decaying into two

bodies giving rise to the final state A 1t 7. Fig.5.2 shows

the Dalitz plot of M2( A It) versus M2(it+TT) and effective

mass distributions of all two-body combinations of this channel.

The effective mass distribution for the A it system shows

a pronounced peak in the region of the well-known Y1(1385).

The productfon of this state is very peripheral with 60% of

the enhancement remaining after restricting the four-momentum

squared to less than .3 (GeV/c)2. There is also some

evidence for a small peak in the region of 1680 MeV, also

Peripherally produced. This enhancement could be associated 34)

with the recently reported Y (1680) state. We observe this

enhancement in the A w system at all pion multiplicities

studied. The sum of the A It effective mass spectra between

threshold and 1.88 GeV/c has been plotted (fig. 5.3) for

the four-constraint channels A it is and A •

- 103 -

where the resolution is ex9cted to be good. The enhancement

appears in the combined ,lot as a 4 standard deviation effect

at 1650 MeV, which is somewhat lower than previously

reported values. The full width at half height is of the

order of 80 YeV and is inconsistent with the value of 120 LeV

given by the above authors. Our data show no convincing

evidence for the decay modes Y (1385)% or NK of this

state. If we assume that this enhancement is a resonance,

we obtain a cross-section of (3 + 2)µb for the process

m+ K-+ p --> Y (2650) +

L....4->A IC

Some rho production is evident from the effective w+

mass distribution, amounting to (3 ± 2)µb. The Y (1385)

and rho bands are well-separated, as can be seen from the

Dalitz plot, and hence there are no complications arising

from interference effects. 3-

The absence of Y production is not surprising as this

requires the exchange of a baryon or of - a doubly-charged

strange meson. However, some evidence does exist for

baryon exchange in final states of higher multiplicity as

will be discussed later.

The cross-section for the reaction K-+ fiLit%-%°

was found to be (133 ± 15)1) after the usual corrections

for losses.

-104-

To look for meson resonances decaying into two or three

pions we have studied the relevant effective mass plots

(fig. 5.4). The prominent feature is the r-)lative:117 strong

rho production in the negative and neutral states, as

displayed in th3 7E79 and - effective mass spectra. The

amount of p - and p° production was estimated by fitting a

Breit-aligner curve to each enhancement over a smooth,

hand-drawn background, using the maximum likelihood method.

The background was reduced by excluding events in the Y

omega and rho bands which could interfere with the production

of the two states above. The values obtained for the masses

and percentages of these enhancements are given in Table 5.1.

There is no evidence for rho production 1) the positive state.

TABLE 5.1

Particle Mass (GeV) Percentage

.748 + .020 9 + 2

p .729 + .022 10 ± 5.4

A visual estimate gives 4 events above background in the

region of the omega resonance in the lz+7t-it° effective mass

spectrum. This yields a cross-section of (2.2 + 1)11b for

the process K-+ p + le-7770

-105-

Pig. 5.5 shows effective mass plots corresponding to

S = -1, B = 1 combinations. Y1(1385) production is evident

in the positive and neutral states.

A comparison was made between the ex ,erimental effective

mass distributions and phase space predictions, taking into m+ mo

account 5% Y (1385), d Y (1385), 9% p° and 10% p production.

To allow for the peripheral nature of the interaction, an -At

empirical factor e was introduced in the phase space

calculation, where A is the slope of the tedistribution to m+ .-2

the Y (1385) (taken as 4 (GeV/c) ). 10,000 "events" were 44)

generated on the computer by a Monte Carlo method and the

resulting curves are shown superimposed on the corresponding

effective mass distributions. The agreement is within the

statistical significance of the results.

To investigate double resonance production of the type -

K + p--> Yp we have looked at the M(A IP) versus M7t 3E+ -

scatter plots (fig. 5.6). The Y p overlap region contains

5 events, where from the density of events in the adjacent

regions of the individual resonance bands and background we mo 0

expect about 4 events. For the Y p overlap region we

corresfondingly expect about 5 events and find 6. Y p

production is therefore insignificant and an upper limit

of e'llab may be placed on the cross-section for this process.

- 106 -

It is interesting to note the very weak prouction of + o

quasi two-body processes in the Alt is it final state, while

the three-body reactions

+o 2%)

K-+ p p°%0

constitute about a ttl.rd of the channel.

5.4 Two-body qocesses

Table 5.2 shows cross-sections for werious tio-body

processes associated witT, hyperon froduction, a?) of which

are corrected for unobserved decay modes and other lossos.

The cross-section for the process K-+ p -.M.X° was + o

obtained from the (w w 7 ) effective mass in the channel + o

K + p Z , by vostricting the mis,,ing mass Z to lie

in the region of the eta-meson mass. The 11,,,pr limit on

thy. Ace cross-section was obtained from events of the type

K-+ p -->Aerr where only one K° was observed. Other

modes wore estimated by using the branchinc, ratios given 25)

in the tables of Rosenfeld et al. The relevant effective

mass plots are shown in fig. 5.7.

To compare our results .with those at w;ber euergies we

have plotted in fig. 5.8 cross-sections as a function of the 5)

incident r laboratory -zomntum for the two-body processs.

-107 -

K-p -* K-p

Kap K (890)p

K-p --> A p°

K-D A w°

It may be seen that while the elastic cross-section

decreases very slowly with primary momentum, the cross-sections

for processes which can proceed via meson exchange (eg.

K-p-laKK--) decrease more rapidly with primary momentum.

The decrease is faster for exchange of strange mesons (in

K-p-*AP/w) than for non-strange meson exchange. This

latter feature gives rise to the generally weak hyperon

production observed in two-body processes in this exp,,rim,,nt.

The results may be expr.essed quantitatively by the

empirical formula-' -n p

a = 'n

Do where K and n are constants for a given reaction and po is

a scale factor, taken as 1 GeV/c. The fitted values of K

and n are given in Table 5.,;. This 1?q.r=lmetrisation is 2a (o)-2

equivalent to the ReFge pole model prediction s

in the forward direction (w_ Le most events in two-body

reactions are concentrated) since poc s at high energy.

The cross-sections shown in fig. 5.8 for the reactions

K-p AP° and K-p are consistent with the prediction

of the independent quark model37) that

lo8

(Kp Ape) = (K-p -> Aw Moe

whore a is proportional to the square of the transition

matrix element. If we assume only K and K exchange the

quark model connects Ac with AP and Am cross-sections as

follows :

(K-p ) = 2-o (K-p -oap) = 2 3(K-p-- A4

This expression is also consistent with our results summarised

in Table 5.2.

The production angular distribution for the weakly

produced Y (1385) shows a forward peak, corr-Isponding to the

baryon exchange process. In no other quasi two-body channel

is there any evidence for a forward peak. The absence of a

backward (p peak is to be expected from the weak NlIcp coupling

as predicted by the quark and w-c mixing models. 40)

In figure 5.9 the cross-sections are plotted as a

function of the incident laboratory momentum for the two-body

processes:

K- Y (1385)A- m-

K-p Y (l385Ye

The fall-off of cross-section for the production of the

negative hyperon state is more rapid (it is characterised m+

by an exponent n = 4.0 + .4) than that for Y production

(with n = 2.7 + .2). This behaviour is to be expected

as the negative hyperon state can be produced only by baryon

- 109 -

exchange (as we have no evidence for a doubly charged strange

meson) if we assumd that the Y is not produced by a final

state interaction. It is interestinq. to note that below

A/1.5 GeV/c incident momentum, (near threshold) where

s-channel effects are exii3cted tc be strong, the two states

are produced with roughly the same cross-section.

Important information cancerging the exchanged particle

in two-body peripheral processes can be obtained from a

study of the decay angular distributions of resonances m+

produced. The decay an:les of the Y (1385) produced in

the reaction m+

-> y (1385) t--> Mt+

have been calculated and are shown in figure 5.10, where

the frame of reference in the Gottfried and Jackson

formalism is also displayed.

Although the sample was small (20 events) we feel the

analysis is justified due to the almost complete absence of

background under the resonance reion, defined as

1.36 <m < 1.40 GeV.

The decay distribution for the process

(J. = ) (er = (J = 0) 2 is given by the function

w(co. e „p) = [1'0.4'4 p3 (1-4 p33 00320

23 (13k1 p3, sin215cos2p + Re p31 sin2ecosp )1

- 110 -

where the trace condition Pr = - P33 is incorporated.

The density matrix elements were calculated using the method

of moments, where the average value, f, of a function

f(cose,T) of the decay angles e and pis given by 21c

? d p fp(coSOf(coSepOW(c0S019)

OTT is normalised)

Inserting the distribution function defined above, we have

COS2e = — 8p33) 15

sin ecos2T = 8 Rep 5/3 3,-1

1'77 -2 3' The errors arn given by Af =E(f f ) where n is the

number of events. 42)

Our results are compared with the Stodolski-Sakurai m+

predictions on the density matrix elements for Y production

by exchange in a M1 transition, in analogy with the

photoproduction process yp -;11.37 at the baryon vertex.

The comparison is fiven in Table 5.4.

TABLE 5.4

Re p Re p p 33 3,-i 31

Stodolski-Sakurai prediction .375 .216 Experimental values .26 ± .12 .64 + .20 -.01 ± .03

sin2e cosp 8 2,

= 543-e P31

The disagreement, observed especially in the case of

ReP3 _1 may be accounted for by the exchange of the K (1420)

and complications arising from absorption effects which

have been ignored.

5.5 Three-body processes

Reactions producing three final particles have been

isolated and the following channels were found to b= most

frequently produced

Cross-section (11b)

(i) K-p A7C1-1Z- 38 4-

- K-p Ap 17 5

(iii) K-p -* Ap°7e 20 + 4

3E+

(iv) K-p ->y (1385)C z° 7 4- 3 MO

(v) K p (1385)7c 7c 7 + 3

The background was reduced by excluding events lying

in the Y and rho resonance bands competing with the above

processes.

Fig. 5.11 shows longitudinal momentum distributions in

the centre of mass system for particles involved in channeln

(i) to (v). From the ordering of the p values the double

peripheral graphs shown in the figures are suggested. A

qualitative comparison with the predictions of the double 7,2)

Regge pole model eas made. The cornering effect predicted

- 112 -

by the mode? for the Dalit% Plot distributions for the

region where the nnergies of a21 partic2e pairs are large

is evident from fig. 5.12a.

The azimuthal angle 9 (defined as the angle between

the normals to the production planes of the external particles,

as viewed from the rest frame of the centrcll particle) is

displayed in fig. 5.12b for reactions (1), (ii) and (iii),

above. The model predicts that the value 9= w should be

strongly favoured, which is qualitatively consistent with our

results, especially in the reaction K-p A 9t+w- where

more statistics are available. This behaviour, however, is

not conclusive evidence for the double 'Rogge picture, as a

peaking at q) =7E is expected on the grounds of periph,:,ra3

phase space :alone,

In all casus it is alarent that thrl negative or neutral

meson is emitted from the uppTr vertex. This feature may be

understood from the fact that an I =2 strange meson would

have to he exchanged to proluce a 1Jositive meson as th

leading particle, and so far no evidence exists for such a

doubly-charged state. There is also a tendency for th2

light-1st :)article, p-)rmitted by the quantum number selection

rules, to be produced in the centre of the double Regge

graph, as can be seen from the ording of t'ee p values

(fig. 5.11).

-113-

5.6 A production in many-body orocesses Here we consider processes where more than two particles

(or resonances) are produced. Table 5.5 gives appro:Amat,7.

cross-sections for resonance production in the following

channels: K-p --> Aeic-it°

K-p 11‹l'/t+ic79t-

K-p A7c4-% Z°

K p A7tIcE%-%-e

K-p A7CI-ef'qz-Z°

The errors cuoted are st4tistical and include uncertainties in estimating the number of events in the

resonance peaks. Figs. 5.13, 5.14 show (Aid- ) and ( AMC) effective mass

distributions for various multiplicities. These demonstrate that the the production of the Y (1385) resonanc,,, increases v.ith

increasing multiplicity. multiplicity. Mile there is negligible 7 Droduction in the quasi two-body reaction, at the highest

multiplicity the production of the Y and Y states have

comparable cross-sections. To study the production ropertics of A hyparonswc

e have plotted in fig. 5.155 the distributions of the A and

associated 4ons for channels of varying multiplicity,

where the symbol Z° in the nofit channels is taken to

- 114 -

represent two n.Jutral pions. Resonances have not ben *4-

removed except for the Y (185) in the channel K-p Aew

as in all other cases this would involve the removal of a

com:farabl7 amount of background.

It is seen that for multiplicities of less than 5

the lambdas are produced mainly backwards in the cl-ntre of

mass system, diilst at high v.ultiplicities a pronounced 47,)

forward pak is obs,:rved. The behaviour of the nec;ativ,d

pions s'ems to be complmentary, while the positive. and

neutral pions are ganerally ,moduced'symmetrically in tho

centre of mass without displaying strong forward or backward

peaks.

Peyrou plots (transverse momentum,

longitu'iinal momentum, p ) ar-, shown in

state mu:Itiplicities between 3 and 7.

evident in these distributions :

(±) The transverse momenta are generally small, 1Pading

to a de-population of the upper regions of th,,, Peyrou

plots.

(ii) There is a changc, in the distribution of p as 7r,

multiplicity changes. At low multiplicities thi lambdas

are strongly peaked backwards and th') distribution

generally spreads out untia at th- highest rultiplicity

there are roughly equal numbers of forward and backward

lambdas.

pT

versus ems

fig. 5.17 for final

Two Matures are

- 115 -

This latter feature is apparently in contradiction with

the distributions of the cosine of the production angle in

the centre of mass system of fig. 5.1f, where we observe

quite a sharp backward peak. However, this may understood

from kinematical considerations (a given interval of cos (Y;

represents a much large' area of the Peyrou plot near the

extremeties than in the central region and thus enhances the

number of events in the revions cos e.. ti + 1).

The feature of increasing longitudinal momentum of the

lambda may be understood in terms of th(-: onset of baryon

exchange processes in the lambda reactions for multiplicities

greater than 4. The increase of Y production with

increasing multiplicity may be taken as sul)porting evidence m-

for the baryon exchange process if we assume that the Y

is produce-Jd bv single particle exchange and not by some

final state A intcyraction.

Further sup,,ort for the baryon exchange hypotbsis comes

from a comparison of transverse momenta and forward/backwa r.

asymmetries between A channels and proc.,sss producing

nucleons where we '10 Aot expect baryon exchange mechanisms

to contribute significantly. Fig. 5.18 shows the forward/

backward asymmetry in the case ofA and N production channels

K-p —> A + (n)w

N + E + (n-1)7t

-116 -

The asymmetry is expressed as the ratio a, = (F-B)/(F+B)

where F and B represent the number of events producd

respectively in the forward and backward hemispheres in

the centre of mass. It is seen that there are generally

f events with the baryon in the forward hemisphere in the case of nucleon production, in contrast to the lambda

case. If we express the asymmetry as a linear function

of the multiplicity: a = A + Bn, the slopes obtained

for proton, neutron and lambda production arc roughly

.03, .1, .4, respectively.

Fig. 5.19 shows the mean pT values for the lambda

produced in various mnitiplicities. A slight increase

is observed in <pm> as we progress in the forward hemisphere

which is again suggestive of a central type of collision.

Analysis along the lines of the multiperipberal

Regge-pole model of Chan et al, described in Chapter IV,

was carried out for the final states

K-p --> A+ (n-1)7

with multiplicities n varying from 3 to 6, in order to

describe the features of the proauction of the lambdas and

associated pions. The method consists of generating a 44) large number of "events" by a Monte Carlo method and

weighting these by the amplitude

17;rf r

= 1 A l2 r = number of permutations

-117-

where Ai is the amplitude corresponding to the ith

1-)rmutation of final oarticlm and is parametrisoo as

ad: ti n-1 ,s1 ca + a

s. -4- a .0 a . ai "I

The, constants bi

d4 scribe the dxpon.,ntial t-d. pend.ince

of t114) Regg.i couAinc;v. For r-!g;geons attach -O. to too

extIrnal particlBs tho correcl.mling constttnts can be

stimated from thrrle-boar .7eactions. Nothing is 'mown

about the intc,rnal coup rings which occur in highr,

r.3actions. These couplings ar

by an eff.,etiv?. average bT.

If wa assure that no~I = strap -e masons' exist, then 2

only I = ,ncchang wre vossibl l which corr,isponf2 to th-

E: (890) and K (2420) trajectoi.i-)s. Among the barvon

exchangs both the N(940) anti N (12'56) trajectorii-s may

contribute;. How:ver, thr N trnjectory is known f-rom

backward 7t p scattering to vry weakly couiar-4 to

the. 1N system, and has li.)en neglo!ct thow:h it hns

a higher intercept in th Chew-Frautschi plot. Th,)so

arguments rs:strict us to I = only. and admit only

graphs in which, irr(Islictiv of the :,osItioa of th? A and

, tha charg..,,d pions altornat::. down the chttin„ b,,ginning

with a R. Th) possible gradhs are illustrate.d in fig. 5.20.

Since in our param-)trisation. we cannot distinguish between

- 118 -

the pions W:? need calculate each of the graphs shown only 4- - once. The actual distributions for 'K % and %o can be

obtained as appropriately weighted averages of the distribution of lEltic2,7c3...

The larger possible number of graphs for channls involving a e, over the corresponding "four-constraint" channels may explain the differ nce between tian cross-sections for the production of these channels. (Se'? Tabl 3.2)

The trajectory was taken to he mm

The to be bA

bB = 0.5

parameters for meson and baryon exchange 45)

= a ..:: 0.30 Kff

were taken N = -.35

Regge coupling to the external particles =

and the suggested values

gN = 1.3

gM 2 gm = 1.4 bI • = 3.2

were used. These are crude ap.roximation determined by visual fits to the data.

The Monte Carlo results, smoothed by hand, shown

superimposed on the experimental distributions in cos 6, pT and p of various lambda channels. (tie. 5.15, 5.16, 21-23). The agreement is reasonably good in all cases even

though the effects of resonance production have not been taken into account.

- 219 -

Channel

TABLE 5.2 TWO-BODY PflOCESSES

Cross-section (lib) Number of events

Mt°

Y (1385) 7c ,

Y1(1385) e

Y3Et165.0) ic-

Ap°

A f°

A 0

A n° m+

Y (1385) p- NO

Y (1385) p°

AX° 4. - --> 1% 'K

26

20

2

5 ..,

6

4

4

2.3

‘2

2

4

+ 5

+ 5

+ 3

+ 4

±3

+2 _2.2

+ 2

+ 3

13

12

< 1

3

3

6

4

4 1

( 1

2.5

4- 5

± 4

+ 2

+ 2 _

±5

t 1

+4 _

+ 1.5

Acp

Reaction

+ 1

TABLE 5.3

K (mb)

6

Exponent n Kap -÷ K-p 7.4 + .7 .x8± .01

K-p plc (890) 8.75 ± .9 2.01 ± .14

K-p A p 1.8 + 1.6 2.8 ± 1.6

Kap A w m+

4.3 + 2.0 3.0 + 0.2

Kap -› Y (1385) 7c" m-

2.2 + 0.2 2.7 + 0.2

Y (1385)7t+ 5.1 + 0.4 4.0 + .4

7

7 15 10

8

± ±

4-

3 )

5 4

8

Resonance

- 126 L

TABLE 5.5

MANY-BODY PTOCFISSF.9.

Number of events

K1) A ic-1-n-7t°

Cross-section (14,10)

(231 events)

7173'T381 4.7, 1385 Y-- 1385 ' 11 + 6

11 + 6 2

P 25± 9 p° 19 1,, 7

f° 5± 5

Km ---4 A 70-70-- (91 events) Y3°-(1385) 13 + 6 8 ± 4 YN-(1385) 12 T 6 7 ± 4

K-u --4 A n+w-Z° (1399 events) Ym4.(1385) 84 + 14 51 + 9 YN-(1585) 26± 9 16 T 6

(296 events)

10 + 4

7 T 4 5.5 + 4

15 +4 20 T 8 16 ±5 21 ± 9 16 + 5

‘ (15 i 5)

K-13 A 7C+70.9t-n-Z°

Y:(1385) 60 ± 20 Y- -(1385) 100 ± 20

(2023 events) 35 + 12 55 ± 12

P+ not significant

000fo not significant

CD -4 A 90-90-%-ic-e 1

0

1381 l2+, 7

v1E 1 85 YN- 2.85 17 + 8

10 T 7 .,0 w 26 -T- 8 n lo + 4 P+ 30 ; 10 P° 40 + 16

r, p- 30 + 10 fw (10 T- 6)

10- (a) K p 3 A°n

+

Tc 0 0

n° limits mits K p-> A

0 TC

AZ0 ° limits (pion tracks deleted)

.3 0, 1 Missing mass squared (GeV-)

3

15- ( b)

No•

of e

ven

ts

10

6 K p -› A it

0

t -distribution

5

-1 Fl . 5 2

-t (GeV )

FIG. 5.1

m2(Aon+) 12 GeV2 n - 1 1.4 2= -2_ 0 ...

m ( A )

Itl < .6(GeV)2 10-

1 r-

K • 13 --> A n+ .Tc-

10

5-

20

'10

+- 2,4 m (run)

rT

GeV

FIG. 5.2

n 2.8

3,0

No. o

f ev

ents

, • , 1:t < kGe\/)

2

0 n+) 3'0 3.3 1.4

ii

-123-

No.

of

co

mbi

natio

ns

1.385

1

K p A Tc4- 1-c- _.

K p ---> A it+ Tc+-rcn

1.650

20-

10-

30-

1.32 1.48 1.e,4

1.80 GeV m (A° n)

FIG. 5.3

T m(-1-) 1.2

m(nn) 20

P O

(r)

z a) > a)

4-6 20 U z

10

1.2 +0 2.0 fi 1.4 +_ 0 2.2 m (Tvrt ) m (-it TT.TL )

Effective mass (GeV) ______>

FIG. 5.4

3.0

0 w

20

10

2

10

20

20

10

K A TC+ 11-:" IC°

m (A Tt-Ti') ..

—

m (A Tt÷)

1141 _

m (A Tin)

ma --al nry

bp

m(Art +

rt. 0)

_

r ,

m(An)

3 . 4 1.4 2.2

3.0

3.8 Effective mass ( GeV) —>

-126-

kicY'(1385)

H. 11\ 1 ,

, i 24

., 1 a..) , CD I .,• •

I... I , 1. c :•• . .

c)^ 1.6- 111 • ic • • • . •

I ' VI l• • .• ,. , • ...

I

E • • • •

, .1. - . • • •• • • •• • . •. , ; . ... . . • •

0.8-- --'rtr..7:.-;.,-*•---•-•- --:"-...-....---.. •-.: .•._.._..

_ L..,:;•• : . :: . • • . ,..1 .--; - -.. - - - - _ _• ,. • . .• •• . • . 1 1 • • • •.• , , • . . • 1 . • .

I I I

1.4 2.'2 0 + 3:0 3.8 m (A Tc ) GeV -->

Y *(13 85) •

1.6-

E 0.8

I i i • .

•

• I i n't

• 4F i I •• •

I el • • • •

If I

I • 1 . •

•

I 1• • . • • ••

•,••I • • • • • • le .1 .% . • • I .1, • : •

1••i• • • S. •

1 •I 16 .1 • . ••.. • : • • • . • ••• : .

I- -`• -••-•-s c —`-.-. -. - - a- a--J.-- a--• ,r --- -' , •

t

11 ..•• .•

• . . 0 . • •

•• •• • • • • •

- --. C.:-I. r•a- -- i - -a ...7- -•-•-•-.2 -4' .-- - "-. , •. • . ••• :. • :• ...' ••

1 .1 . •••• • • . .. •

.::• !GI • 0 ft •

I' , 1.4 2.2 0 0

m(Am) 3.0 3.8

GeV

FIG. 5.6

1

(r) C a) a)

0 c5 z

-127-

X°(958)

1

.80 1.60 2.40 GeV ---->

Effective mass (i-c÷ ft-Z0)

0 0_0 Kp-->AKK

D All K0-K0

K° K° fitted decaying

1.0 1.4 1.8 2.2

2.6

3.0

Effective mass (K°R°)

GeV

FIG- 5.7

10

10

5

K pArr.i-cZ0

•50< m(f)<•62 GeV

INCIDENT LAB. MOMENTUM (GeV/c)

FIG. 5.8

1 4 6 8 10 20

CR

OS

S- SE

CT

ION

E

-128-

10 —

1-0-

0-1-

x K -p —> p K -

o K p —>p Klc(890)

• K. p ---> A°

A K p --> A° p°

-01

.001

1 . I

10 .2 4 INCIDENT LAB. MOMENTUM (GeV/c)

X K p —>Y*(1385) it-

o K p --> Y* ( 1 3 8 5) ic + 1 .0-

.0 E

....-...•

0.1 —

SEC

TIO

N

.001

-130

K-p -->Y‘+(1385)

Y decay angular distributions

>K n_

xe

p

cos 0 =

* • p <

Ipl ixl

. (1-3A 5Z) coscp =

tn

oi 4 a)

2

d z

+1

cos0

LP

FIG. 5.10

K rc K_

K n _ K

7+ n0 + Tt K no IT

P

r-n-i

+ r

_ nn

n il

P Yk0 P

_ A

A P A

P0

r--) ri r —Li_

_

P A

_ n

rt+ It

+

1--

n

r—i r

o 7

ri r-

0

n

Tc +

A

so

A A

.1 •

. + Y

i

* 0 Y .

I

20

10

20

10

20

-2

b

2-2 0 2 2 0

2 2

0

2-2 •

b

2

Cms longitudinal momentum (GeV/c)

FIG. 5.1!

(b)

10 10- 0 A p

- +

5

A' ono

0 It n/2 it 0 Distribution of angle tp

A0rc+11-

it/2

T10

0.1 4-, C CL) 0 5.

0 z 0

-1132-

K

A°

1 I

K s- 1 ...

. . t . , , .. . c'l 4 -; .. E , •

. • . .

2 - I, i* .

t3. ' • . • . • • .. t--

u) (s 10 115 „....45 m2( A Tu+), G eV2

FIG. 5.12

FIG. 5.13

NO

. OF C

OM

BI

NA

TIO

NS

/40 M

eV

10- 50

20- A n+ n - - A 7+ nrcnn0

J

40

20-if

0

10

20- -

Arc n+n nr 100-

200-

0 A n+n+TL TL Z

100 -

A rc+ n 20 +

n rc

rU11-11-9 r--t r-t rl n 0 r-

10-

Arrlpr-r) 3

( An+) EFFECTIVE MASS (GeV)

( A Tc--) EFFECTIVE MASS (GeV)

FIG. 5.14

NO

. OF C

OM

BIN

ATIO

N S

/40 M

eV

40-

20

0 2 00

100-

20 - + - A Tc Tc

20 + + - - A rc it 7 7

ir 3

n

10-

rt n n nn nn ran

+ - 0 A itrcr.

10 -

n1

10

0

20-

100 - 0

A rc Z rc

A rc rt rt rc rt

50

A it rc rt rt Z

200

c <l.l 0"'--­> <l.l

30

- 135-

+ -Ann:

and + _ 0

An:n:n:

, i

i4CO

+ _ 0

Ann: Z

I

i

I ! :200

I ~~=r==~_::=-~.Jl O.L.--.------,-----

+ + - -I\n:n:n:n and

+ + - - 0

Arrnnnn: 160

80

o ~=--.---, --,------....jj 0 ~j ~--r---, --.------1 0 + 1 - 1 0

Cos e· of A .. 1

FI G. 5.15

2

100

+ 1t

-135 -o 0

1t/Z

OTI--~~~~C-~~~~~~~-~~~~~~~~

2001

+ -A1t1tZ

100

Or-------~-------~------~--------~------~----~

200

100

+ + - -A1t1t1tTl:

and + + - - 0

A 1t1tTt1t1t

+ + 0

A1t1t1t1tZ

0_1-1-----0-.-----+ 1+---:1----0..-----+-1-1--1---- 6----+---1

1

Cos e*' distributions

FIG. 5.15

<t-

o o z

-137-

1.5 + - A TE TC and

Annie

0.5

1.5- + 0

A It Tt Z 1-00

-

0.5-

- - A Tt

+ +TC

and _ 0 A It TT It TT- TI

+ _ 0 A TE rt TE n Z

0 -2 -1 0 +1 +2 CMS LONGITUDINAL MOMENTUM, pL (GeV/c)

FIG.5.17

1-0-

laF.-

2

z LLI

5 2

TR

AN

SV

ER

SE

/4

• A

x n

V P

3 4 5 6 7

/

i /

/ /

/ / -

/ /

/ /

V

/ A

? /

0

-.4

-1.0.

AS

YM

ME

TRY

-.8

-138-

FINAL STATE MULTIPLICITY

FIG. 5.18

I ........ u --> (J)

(9

1\ r-

0.

V

0·8

0

08

0·4

0

0·8

0.4

-139 -

~~~

I

i i i

-1 0 + 1

p'" (GeV Ie) L

FIG. 5.19

, +2

1\ n\1:+n-n­and

1\ + + - 0 n n n rc-n;

- 140 -

n+

P /\ A A TC÷ TL

K.- //Tcl \Z

A

A

(ti-,„ TET,- /\

FIG. 5.20

it A A It

A Tc +

-a n - o

A

A

A

\, /0/\ / \ , ///\ A tc+ IC 7: it- it

72 n3 rit4 n5 c" /

20,

I

i 20

U1 +-' 10 c (1)

> (1)

't-

0 0 d z

10

5

-1

-1

-141 -

+ + - -A7tTtTtTt

0

0

o

1

1

1

p* (GeV/c) ~ L

FIG. 5.21

2

-142 -

A n Tu+ n- o

O it

15-

6 1

15

10

5

0 0

ID+ (GeV /c) -->

FIG. 5.22

+ 4. - _ o A TT.

it it m u

0

.3 PT

( GeV/c)

FIG. 5.23

10 A

- 144 -

CHAPTRR VI

6.1 Introduction

Events with at least two visible strange particle decays

have boPn analysed and 256 fits to hypotheses of the type

K-p ALKK + nit

have been obtained with 0 < 1“ 6. 180 events satisfied

corresponding nofit hypotheses. The average final state

5 for both fits and nofits, multiplicity was found to be

where Zo

was assumed to represent two particles. The

missing mass squared distributions forufour-constraint"

fits and for none-constraintn fits with a missing it° , K°

and lambda are Shown in fig. 6.1. The distributions are

reasonably centred about the nominal values and there is

no evidence of bias.

Various final states are discussed below and

cross-sections of resonance production are given. The

chapter concludes with coAsiderations of the production

mechanism.

6.2 The reaction ALKY

22 events of the c7lannel

K-p -0 ALK°R°

have hen identified, corresponding to a cross-section of n0

16 4 lib. The K-K effective mass distribution (fig.6.2a)

-145-

exhibits a small enhancement of 3 events at the bottom of

phase space in the region corresponding to the (p -meson. To

find the amount of cp production it was demanded that only one

kaon is observed, thus restricting it to be a K7. If we

assume that the Ko and K2 are equally probable a priori, th,:n 1

the missing K° has 3 times a higher probability of being a K. o

K2 than a K1. Assuming that these are all K, K2 decays, we

obtain a cross-section of 5 + 21-Lb for the process K-p Ac.

The production of the q) is very peripheral with all the events ,2

being produced at t (GeV/c). 0 -0

The K1 K1 effective mass distribution (both K

oIs observed)

has been searched for ft production, since we cannot have a 0

K1K2 decay mode of an object with C = -1. There is no

strong evidence for the production of this state, and an upper

limit has been estimated to be 3µ b.

The AK° effective mass distribution (fig. 6.2b) shows

no structure which may be interpreted as evidence for the

decay .x0(1815) -› A 0K0. Figs. 6.2c, d display the cosine of the centre of mass

production angle of the A and the neutral kaons. The lambda

is strongly peaked backwards in the ems while the K°Is are

produced forwards. This feature is suggestive of a

peripheral, meson exchange mechanism.

-346-

6.3 The channel Ku APKRw

30 fits have been obtained for the process K-p A. KRIE

and the cross-section for the channel is 15 + 4 µb.. Only 5 o-o

of these events are associated with a K K pair and an

assessment of T or f, production is impossible. The only

resonance wbich is apparent is a small amount of Y (1385)

production as may be seen from th;? projection of the m(A %)

versus m(KK) scatter plot, (fig.6.3), where all charge

combinations are taken. The cross-section for the reaction

K-p Y1(1385) KR is 2.0 + 1.5 µb.

6.4 Reactions K p —> A KK 2 7c

have 106 events of the type K p -->AKKicit and the

cross-section for ,his final state is 76 + 9µ b.

Effective mass distributions are lisplayed of two-body

combinations for the five-body final state in cases where

interesting structures are apparent. (fig. 6.4). The p

meson a,wears to be strongly produced, constituting about o

50% of the channel Kp v , but lz-

there is no evidence of ft production.

The (mid effective mass spectra show enhancements in

the region of the Y1(1385) for all charge states, the

production of the Y being the most prominent.

- 147 -

Table 6.1 summarises the cross-sections of resonances

produced in the channels K-p A KK + 12%, n = 0, 1, 2.

TABLE 6.1

Number of Process events Cross-section (1b)

A 9

Aft

A 9 %

A f r 7C

3 + 1.5

1 + 1 _

1 + 1

1 ± 1

5 + _

<

<

2

3

2

2 + _ Y°KK 4 4- 2 2.0 + 1.5

Ace %7t 16 + 4 18 ±4

A f t 7c % 1 + 1 < 3

A Ym (1385)1(1 22 +4.5 16 ± 4

A YNt1385)KK 18 + 5 13 + 4

A Y71385)KE 14 ± 4 7 + 3

Effective mass distributions have been investigatPd for

channels AKK + > 2% and the cases revealing some structur

are presented in fig. 6.5. K production is evident in the

negative and neutral states, both for S = 1 and S = -1. The

'e(1385) is produced in the positive and negative charge

states. There is no compelling evidence for 9 and

production or for higher mass hyoeron states.

-148-

6.5 Production mechanism

The general features of the production of lambdas and

associated particles in reactions

AKR + pions

are depicted in fig. 6.6, 7, 8, whore Peyrou plots are

displayed fo-e various particles in incroasigg final state

multiplicities in the cases whore th3 statistics are not too

limited. The properties of the leghla are reminiscent of

those in the reaction

K-p A + pions, dealt with in the previous chapter.

The transverse momentum is generally limited to low

values, and the A is produced strongly backwards in the centre

of mass system. As the multiplicity increases the A migrates

towards the forward hemisphere and at high multildicities

about 35% of theAts are produced forwards. The negative

strangeness kaons tend to follow the direction of the incident

kaon at low multiplicities and more and more of these are

produced backwards as the number of final earticles increases..

The negative pion behaves similarly to the K at low

multiplicities and the positive and neutral pions are

generally slow in the centre of mass system and are produced

in roughly equal numbers backwards and forwards. Positive

strangeness kaons are generally produced equally forwards

and backwards in all multiplicities and, in this respect, are

similar to the positive pion.

-149-

These features are in qualitative agreement with the

predictions of the multiperipheral Regge model where at

low multiplicities we expect a peripheral behaviour to

dominate, which inhibits the exchange of strangeness,

charge or baryon number. At higher multiplicities baryon

exchange mechanisms set in and the lambda occupies higher

positions along the propagator of the multiperipheral graph

and the overall behaviour becomes more ',statistical",

where this oroftction of all particles tends to become

similar.

2 m 0

IIK 16 - 8 0

m2 A

1

6 30 - 12 6

- • 04 0

. . , • 04

4 - C Channels

. . -08 '24 .40 '4 1.2 2.0

Missing K Missing A oa 0 .08 Missing it

No.

of

even

ts

20 -

10 -

4

2

4

2

-L

2 m 0

IL

1

MISSING MA SS SQUARED (GeV 2)

FIG. 6.1

tp 4 4

0

(a )

•0 1.5 0 _, m(K K)

-151- 0_0

Kp -÷ AKK

E21 K ° K° fitted decaying

2.5 3.0

NO

. OF C

OM

BIN

ATIO

NS

4

2

0

—7

1815

11

(b)

Jib 20 25 3.0 3 5 m(A K ° (Strangeness unknown)

EFFECTIVE MASS (GeV)

( d )

0 _0 20 K, K

0 1---1 11 (--F-1- -1 +1

cos e FIG. 6-2

NO

. O

F E

VEN

TS

K p --> A K 17( Tc

4

2

0 1 1 _ ri Flu r---1 1---1

1 5 2.0 2.5 3.0 m(Arc) (GeV)

-152-

* 4, Y (1385)

FIG.6-3

- 153 - f g

10 4/ 4,

K p ---> A K Kn rc

a3 K0 0 decaying

Kfitted

0-0 m ( K K )

2.2 10

Y (1385) 4'

1.6

NO

. OF C

01‘,

1 B 1

NA

T r O

N S

10 -

5

0 rr 2.6

m ( A II )

n 1.4 210

6 -

4 - m(ATt+)

-L_ 2 -

r n n 2.6

0 - r

2.0 1:4

4

6

0

2

"L- _J-

1:4 2.0 2.6 EFFECTIVE MASS (GeV)

-Lr r- r RnnP

0 m(Arc)

FIG. 6.4

rn(Krj 5=-1

K*(890)

Im(Krz.)° S=-1

K*(890)

0 rn(K S = +1

IK (890)

n 1.2 1.6 0:8 1:2 1:6

0 1-2 1 6

20, 20-

1 - G)

0

10

1-111 1

J-

OF C

OM

BIN

ATI

ON

S

O z

20

10

0 1:4

r".

_r 1 0

_ 1111-1 r „ FITI-Fl 0 1.8 2.2 1.4

EFFECTIVE MASS (GeV)

m(A ) 20

1.8 2.2

20

10

-155-

A KK

MO

ME

NT

UM

OF

A

1

AKKn

0

•

21

TR

AN

SV

ER

SE

AK R TC TC

2

1 AKK- >2TE

• . . • • •

• • ••• •

. • , • : : • • •

0 -2 0 +1

CMS. LONGITUDINAL MOMENTUM OF A (GeVic) -->

• FIG. 6.6

A K R -rc M

OM

EN

TUM

AK Rrcrt

TR

AN

SVE

RS

E

A K R> 2 is

K K

CMS. LONGITUDINAL MOMENTUM (GeV/c) --->

FIG. 6.7

it Tc

MO

MEN

TU

M

A K L7-rc Tu

(GeV/q) —_

0 1 2 -2 1 2 -2 -1 0 1 2

CMS LONGITUDINAL MOMENTUM

0

FIG. 6.8

-2

TR

AN

SVERS

E

A K 17>2n

-158-

CHAPTER VII

7.1 E production

Interactions with a decaying negative track and a seen o

emanating from the decay vertex have been accepted as

candidates. It was demanded that a kinematic fit with X2

probability greater than 1% existed for the decay hypothesis

E- Any'

Some W- decay fits have also been obtained in cases where the A° was not observed, but these events have not been used in the analysis as they are often ambiguous with 2- fits.

We have 311 events of the reaction

K-p K pion (s) Ai

For 35% of the cases there also existed a fit to the prodliction

vertex. The total cross-section for Et- production at 10 GeV/t +8 46)

was found to be 72 µb. The cross-sections for channels -6

of different final state multiplicities are given in table 7.1,

where we adopt the usual convention : e = 2 particles for the nofit channels.

47) Pig. 7.1 displays the variation of cross-section with

incident laboratory momentum for various multiplicities. The fall-off of the two-body cross-section, characterised by the

-nab Pl% empirical relation as , above the threshold region, Po

yields a value n = 2.9 ± .1 for the exponent. This is

- 359 -

typical of 6) the values associated with baryon exchange

3 processes.

TABLE 7.1

Final state multiDlicitv Cross-section (u.b)

2 <0.6

3 <2.6

.4 2.2 4. 32

5 22 + 4

6 21 + 4

7 15 ± 4

8 7 +2

9 <3 NO

There is evidence ofE (1530) production in about 15%

of the E reactions, as can he seen from fig. 7.2 where the

13-7t+ effective mass distribution is plotted for all events.

No evidence exists for two-body (or quasi two-body) reactions.

The general behaviour of the E hyperons, kaons and

pions is described by the Peyrou plots (fig. 7.3) where a

tendency is observed for the ;s to be pro'lucod forwards.

This seems to be balanced by a rather backward emission of

the kaons, while the pions are grouped at low values of

centre of mass momentum and have no preferentia3 direction.

-160-

Fig. 7.4a, which shows the centre of mass production

angle of the 2- for multiplicities of .$6 and >7 indicates

a larger proportion of forward E-Is at high multiplicities.

The mean transverse momentum of the Ens apparently decreases

with increasing multiplicity (fig. 7.4b) while the modu?_us

of the total ems momentum remains rouahly constant. The

total ems momentum consequently decreases with multiplicity,

as there is less and less available energy per particle.

It is interesting to observe that the mean transverse momentum

of the E.-for the highest multiplicity events is not

significantly higher than the corresponding <p> value for

pions. This observation is ia sharp contrast with the <11

features of p, n and A° processes where the ratio >baryon

48) <I)'T

> %

increases with multiplicity in qualitative accordance with

the predictions of phase space.

These characterisAcs are summarised in Tables 7.1 an(?.

7.2, where average ems momentum con onents are riven for

various ;?articles and final state multielicities.

In addition to the events with one kwon ill the final

state, three events of Elgl have been identifie, corresponding

to the reactions

K-p F-.° (K+)K- it+e

K-p --> Ko (K°)

K+

K-p

K° K° (K-- ) eic+

-361-

where the brackets correspond to particles with no visible

decays. The last event is also ambiguous with the hypothesis sricolco All of the threeE-Is above are produced

forward in the cms. It ray be interesting to add here an example of 2+ production observed in reaction

K-p —4, E + E' + A' + n- pi. 70.

The e was identified by its decay and the E' by a fit

to the production vertex.

7.2 49)

The discovery of the 2 hyperon gave credence to the

classification of the known -4 particles into an SU(3) 2

decuplet. Imortant indirect evidence for this scheme comes 50)

from the obeyance of the equal raw-spacing rule. This has

been confirmed to a high degree of accuracy by a recent 51)

precision measurement of the Sr mass which gave a value of 1673.3 + 1.0 MeV and a spacing of 141.5 + 2.5 MeV for the

-52) negatively charged member of the decuelet.

Pour examples of unambiguous 2- production have been

found in the 10 GeV/c experiment which constitutes about 20%

of the present world sample. In all cases the 2- was found to decay into a A°+ K, with a visible subsequent decay of

the A° in the chamber. A good kinematic fit existed for

- 162 -

the decay in all cases _aid three of t":, ,nts

observed also hal a fit at the production vortex. As an

exampl of Sr production wa show in fig. 7.5 the 1Jhotograph

of the candidat a found by t1i London (IC) group. Th Ivent

corresDonds to th chain of reactions

irp -4' geePC

, ‘rd?

This is a particularly clear cas:,, as a good hfour-constraint”

fit was obtained there was no competing fit to the decay

process. The A° fit was confirmed by a bubble count on

the positive track, but the taons worn too fast for

identification on the grounds of ionisation. Thy fact that

the 3- hypothesis is kinematically impossible with the

measured values of the decay products is illustrat,:d in

fig. 7.6 where Blaton ellipses have been drawn corrnsponding

to the decays

2-

A°1t-

The momenta of tti two decn7 products were the average values

obtained on eight measurements of the event. The

intersection of the momentum vectors lies on the ellipse

Associated with the g-and is far removed from the overlap

region of t1r) ellipses when we are likely to have a 274-

ambiguity.

- 163 -

The cross-section corresponding to the 2 events is

- _ 0

tv2.5 lib. No decays 2 E.°7E have been identified

unambiguously. However, these decay modes correspond to

topologies which are difficult to detect or offer more

possible alternative interpretations than the A°K- mode.

The i,roduction processes and some important :,laramoters

of our four events are listed in Table 7.4

Production

-. - TABLE 7.4

Decay Mass (Nell= pleb. c0s0crs

1. sr(e)(e)7( AK- 1669 + 4 .93 2.510 .783 -.855

2. 2-Kdec(KLt)7E+ AK- 1678 + 14 2.6 5.404 1.090 .301

3. 2e(e)/t-e MC 1671 ± 7 1.6 4.701 .475 .677

4. 27Kion 3on1CZ° AK- 1670 ± 2 .21 7.822 1.258 .936

ion = particle detected from ionisation

= non-decaying, fitted strange ;'article.

The average value of the mass obtained is 1670.8 + 2.5MeV/c

which is in close agreement with the value expected from the

equal mass snacing rule.

The production of the 2- hyperons a.,oars to be

predominantly forward as may be seen from the distribution of

the cosine of the droduction angle in the centre of mass

system (Fig. 7.7)53)

-164-

TABU 7.2

Multiplicity N

<'T>6 v0 .73

<1 1L511I1> .52

<pli> 1.20 m

<Pr,> .21

F.- PRODUCTION

6. 7' 8 4 5

4. .09 .56 + .07 .45 + .04 .34 ± .03 .27 +.06

+ .10 .44 + .11 .56 + .06 .77 ± .:12 .47 ±.14

+ .20 .76 + .10 .79 ± .08 .88 + .1] .57 +.11

+ .10 -.11+.11 .13+ .07 .97 + .12 .39 +.14

TABLE 7...3 .s.p.e VALUES (Ge vic

rartNiclel

w-

K+ Ko - + ic

.to

4 .73+.09 .794.35 - .38+.14 - -

5 .56+.07 .3E4.11 .42+.09 .33+.06 .54+.10 .39+.08

6 .45+.04 .35+.05 .40+01 .26+.0 .36+.05 .24+.02

7 .34+.03 - - .27+.04 .::51+.06 -

8 .27+.06 .25+.07 - .21+.03 .31+.04 -

.

Iiii

_. i

7

. .

.

.

-

.

if

I

.

2-BODY

i

4

•

i

e 1 I I 1111

- _

_ _ _ _ _

— _ - -

I

-

—...

-

1

4 •

i 1

i

1 1 1

7.

111111

...

_ ..

.. _

_

—

.

3-BODY _

...-

..-

...

...

4 -BODY

• I

_ f

_ •

_

—

-

-

—

-

I I 1 111111

_

.

.

7 .

_

-.

-.

.

5 10 1 2 5 10 1 2 5 10 K- LABORATORY MOMENTUM (GeV/c)

500

-0 100

50 z 0

U

cn 10

cn 5 0

1

0.5

0.11

CROSS-SECTIONS FOR 1:PRODUCTION IN K p INTERACTIONS

FIG. 7.1

O 0 z

/

> 0

2

20 0 c \I

V ) z 0 I— < z co 2 0 0 10 IL

7 / / / / / /

_/ / / /

1.5

[ _- -7 - decay weights excluded

/ 7 i P/7171 7, vin

_ 2.0 2.5 (7. Tc

÷ ) EFFECTIVE MASS (GeV) --->

FIG. 7.2

__ K p -- .7_.. K + pions

MO

MEN

TU

M,

TRA

NS

VERS

E

1 •

•

• • • • • • .• • • • • •• • • • • • • •• • • • • • •

• •• • • • • • • • r• •• • • • • •

• • 40 •• .41,se••• t• • •• t• ••," • •• $ • $. •

• • e• .2 • :.• ne • usu. t•• • • • • • • • ...• ••• .

it a.

-1

0

1

2

-167 - K p —› = K + pions

2 IL

p't ( CMS LONGITUDINAL MOME NTUM, GeV/c FIG. 7.3

- 168 -

(a)

N < 6

T

TOTAL

N ..›- 7

10-

0 1 -1 0 1 -1 0 1

Cos 6_-(crams)

(b) 1.0 4'

0.5

i

i f i i

4 6 6 7 8

Multiplicity -->

FIG. 7.4

-169 -

FIG 75

-172-

ACKNOWLEDGMENTS

I wish to thank Professor C. C. Butler for the opportunity of working in the High Energy Nuclear Physics

group at Imperial College, and am very grateful for the

supervision and useful guidance of Dr. S. J. Goldsack.

The assistance and inspiration provided by all

members of the Aachen - Berlin - CERN - London - Vienna

collaboration are gratefully acknowledged. In particular,

I would like to thank my colleagues N. C. Mukherjee and

D. P. Daliman for their co-operation and encouragement.

The efficient book-keeping of Miss M. Urcuhart and

diligent work by all scanners, measurers and technical

staff of the Imperial College group are acknowledged.

Finally, I express my gratitude to the Science

Research Council for providing a grant.

-173-

RPFERRNCES & FOOTNOTES

1) The members of the collaboration are:

i) Physikalisches Institut der Techndschen Hochschule,

AACHEN.

ii) Forschungsstelle fur Physik Hoher Energien der Deutschen

Akademie der Tissenschaften zu Berlin, ZIPUTHEN.

iii) CERN, European Organisation for Nuclear Research, GENEVA

iv) Physics Department, Imperial College, LONDON

v) Institut fOr Hochenergiephysik der Universittit, AIFT

2) E. Keil and W. W. Neale, International Conference on High

Energy Accelerators, Dubna 1963.

3) 1) Observation of a (Ken) resonance near 1800 YeV.

PI,y-s. Lett. 22, 357, (3966).

ii) K-p elastic scattering at 10 GeV/c, Phys. Lett.

24B, 434 (1967).

iii) Km production in 10 GeV/c K-p interactions.

Heildelberg Int. Conf. on Elementary Particles, 1967.

iv) Total and Differential cross-sections of euasi two-body reactions in 10 GeV/c Kp Interactions, do.

v) Analysis of the eT1320) and K'(1800) enhancements produced by 10 GeV/c K-p interactions, ,10.

vi) A study of transverse momentum and related variables in

8 GeV/c /1;fp and 10 GeV/c Kp interactions, flo.

-174-

vii) Lambda 13roduetion in 10 GeV/c K-p interactions,

Nuc. Phys. 15, 606 (1968)

viii) fr and anti-hyperon production in rp

interactions at 10 GeV/c, Nuc. Phys. B4, 326 (1968)

4) Chan Hong-Mo et al., CRRN report TH.866. 5) B. Kuiper and G. Plass, CERN Report 59-30. 6) ?. Keil and B. W. l'ontague, CERN Int. Report AR/Int P.

Sep/62-2.

7) M. Bell et al., Inter. Conf. on H.R. Accelerators - Dubna 8) For a detailed description of R.F. separated beams, see

F, Keil, CERN Report 66-21 9) Riddiford et al., Inter. Conf. oh H.R. kccel. and Instr.

CERN 1959. 10) Telford, App. Optics Vol. 2, No. 10, 1963. 11) The ionisation of a particle of momentum p and mass m is

expressed as I = Io(1 + (p) 2)where Io is the bubble P density corresponding to an infinitely fast track (a beam track for practical purposes). A track with I/Io r- 1 is said to be minimum ionising.

12) G. R. McLeod, CERN Report 60-11. 13) W. G. Moorhead, CERN Report 60-33. 14) See THRESH Section of CERN T.C. Prog. Library.

15) GRIND Section, CERN T.C. Prog. Library.

16) P. Fleury et al., 1962 Inter. Conf. on H.E. Phys. - CFPN

-175-

17) SLICE Section tERN T.C. Prog. Library.

18) UCRL Physics Note 389.

19) E. Malamud, CERN DD/EXP/63/15. 20) J. Zoll, CERN T.C. Prog. Library.

21) R. T. Deck, Phys. Rev. Lett. 11, 169 (1964). 22) A. H. Rosf.nfle, , UCRL - 16462.

23) G. Kellner, private communication.

24) W. Galbraith et al., Phys. Rev. 118B, 913, (1965).

25) A. H. Rosenfe74 et al., UCRL - 8031, Pt. 1, Jan. 1968.

26) M. Aderholz t al., Phys. Lett. 24B, 434 (1967).

27) R. E. Marshak, University of Rochester report UR-875-787.

28) E. Ferrari and F. Selleri, Nuovo Cim. 21, 1028 (1961).

F. Selleri, Phys Lett. 76 (1962), Nuovo Cim. Supol.

24, 453 (1962), Nuovo Cim. 214 1450 (1963).

29) C. T. Rogge, Nuovo Cim. 951 (1959), 21, 947 (1960).

30) See, for example, V. Barger and M. Olsson, Phys. Rev.

Lett. 16, 545 (1966).

31) C. Schmid, Phys. Rev. Lett. 20, 689 (1968).

32) See, for example, K. A. Ter-Matirosyan, Soviet Phys.

JET? 22, 233 (1963), and Nue. Phys. 68, 591 (1964).

F. Zachariasen and G. Zweig, Phys. Rev. 160, 1322 (1967).

Chan Hong-Mo, K. Kajantie and G. Ranft, Nuovo. Cim. 42,

157 (1967)

N. F. Bali, G. F. Chew and A. Pignotti, UCRL-27530.

J. Finkelstein and K. Kajantie, CERN preprint TH. .857 (1968).

- 176

33) See, for example, Chan Hong-Mo et al, Nuovo. Cim. 9,

157 (1967).

Chan Hong-Mo et al, Nuovo Cim. 52, 696 (1967).

S. Ratti, Heidelberg Conference (1967).

34) M. Derrick et al, Phys. Rev. Lett. 12, 266 (1967).

D. C. Colley et al., Phys. Lett. 24, 489, (1967). 35) The elastic scattering data have been obtained from:

Baker et al., Phys. Rev. 129, 2285 (1963).

Crittenden et al., Phys. Rev. Lett. 12, 429 (1963).

Focacci et al., Phys. Lott. a, 441 (1965).

Gordon et al., Phys. Lett, 21, 117 (1966).

Mott et al., Phys. Lott. 221, 171 (1966).

Foley et al., Phys. Rev. Lett. 11„ 503 (1963).

M. Aderholz et a?., Phys. Too*. 24B, 434 (1967).

Foley et al., Phys. Rev. Lett. 254 45 (1965).

The data on the other two-body processes were obtained from:

Alston et al., Int. Conf. on H. F. Phys. CERN (1962), p291

Gelsema et al., Sienna Int. Conf. (1963), p.170.

Bertanza et al., Int. Conf. on H.E. Phys.CERN (1962),p.284

Ross et al., Int. Conf. on H.E. Phys., Dana (1964),p.642.

Badier at al., do, p.650.

Hague et al., do, p.654.

36) D. R. 0. Morrison, Phys. Lett. 22,528 (3966).

37) G. Alexander et al., Phys. Rev. Lett. 124 412 (1966).

H. Lipkin and F. Scheck, Phys. Rev. Lett. 16, 71 (?966).

- 177 -

E4 M. Levin and L. L. Frankfurt, JETP Lett. 2, 65 (1965).

38) H. M. Fried and J. G. Taylor, Phys. Rev. Lett. 25.1 709(1965). 39) J. Papastainatiou, Nuovo Cim. 41A, 625 (.966).

40) The data have been obtained from:

Ross:let al., Int. Conf. on H.E. Phys. Dubna (3964),p.642

Badier et al., do, p.650.

Hague et al., do, p.654.

M. Derrick et al., Phys. Rev. Lett. 18, 266 (1967).

London et al., Proc. Int. Conf. on H. E. Phys., Berkeley

(1966).

Badier et al., Int. Conf. on Elem. Particles, Oxford (160

41) K. Gottfried and J. D. Jackson, Nuovo Cim. IA, 735 (1964).

42) L. Stodolski and J. J. Sakurai, Phys. Rev. Lett. 11,90 (1963)

43) This effect has also been noticed in 6 GeV/c Kp

interactions (Birmingham-Glasgow-London(I.C.)-Munich-

Oxford-Rutherford Lab. Collaboration, private communication).

44) 'TOM- A General Phase Space Programme", F. James,

Institut du Radium, Paris.

45) D. Cline, Talks Presented at the Symposium on Regge Poles,

(Dec. 1966), Argonne National Laboratory.

46) J. Bartsch et al., Nuc. Phys., B4, 326 (1968).

47) The cross-sections for xi production were obtained from:

J. P. Berge et al., Phys. Rev. 147, 945 (1966).

D. D. Carmony et al., Phys. Rev. Lett. 12, 482 (1964).

G. W. London et al., Phys. Rev. 143, 1034 (1966).

- 178 -

J. Badier et al., Phys. Lett. 16, 171 (1965).

M. Hague et al., Dubna Conf. (1964), p.654.

G. S. Abrams et al., Phys. Rev. Lett. 18, 620 (1967).

V. E. Barnes et al., Dubna Conf. (1964), p.662.

48) A. Biggi et al., Nuovo Cim. E., 1249 (0964), also

N. C. Mukherjee, Ph.D. Thesis (1967).

49) V. Barnes et al., Phys. Rev. Lett. 12, 204 (1964).

50) M. Gell-Man, Cal. Tech. Report CTSL-20 (1961).

S. Okubo, Prog. Theor. Phys., Kyoto 2Z, 949 (1962).

V. Barnes et al., Int. Conf. on H.R. Phys., Dubna (1964),

p. 665.

51) R. B. Palmer et al., Phys. Lett. 26B, 327 (1968).

52) The equal mass-splitting rule cannot be direety tested

because of the electromagnetic splitting between the

isotopic multiplets. Under the assumption that the

e. m. interaction is invariant under U-spin rotations and

that the medium-strong interaction has a component

proportional to the third U-spin component, it is prorlictPd

that the negatively charged members of the decuplet should

be equally spaced.

53) The data have been obtained from the compilation by

J. Allison, University of Oxford internal report.