P INTERACTIONS USING a BUBBLE CHAMBER. By

A STUDY OF 4 Gev/c % -p INTERACTIONS USING A BUBBLE CHAMBER.

'LIU YAO SUN

A thesis presented for the degree of Doctor of Philosophy of The University of London and for the Diploma of the Imperial College,

Department of Physics, Imperial College of Science & Technology, London, S.W.7. ======June 1963. CONTENTS

Page

Abstract AS 00 SO 0* ts 1.

Preface .• ...... PO 2.

Introduction Os 400 OP ** 3.

CHAPTER I. Pion Resonances. 1.1'. The Chew-Low Extrapolation Method. 5. 1.2. The Pion-Pion Interaction and the p-particle. 8. 1.3. Other Pion Resonances. 10.

CHAPTER II. Contribution of the P -particle to g.-P Scattering. 2.1. One Pion Production. 14. 2.2. Low Energy Elastic Scattering. 16.

A PENDIX 2.A. .. 19. APPENDIX 2.B. 27.

CHAPTER III. Apyaratus and Experimental Procedure. 3.1. The Hydrogen Bubble Chamber. 33. 3.2. The Pion Beam. 34• 3.3. Method of Scanning. • • 34. 3.4. Measurement of Events. 38. 3.5. Data Processing. 40. 3.6. The Maximum Detectable Momentum. 43. 3.7. Measurement of Beam Momentum and Related Quantities. 45. CHAPTER IV. Interpretation of Events.

4.1. Interpretation of Events by -Pitting Prododure 50 412i Identification of Track by Ionization Measurement. 52 CHAPTER IV. -contd.

4.3. Scanning Efficiency and Cross-sactions 53 CHAPTER V Analysis of Four-prong Events.

111•• 5.1. The Reaction + p p + + 63. (A) Angular and Momentum Distributions. (B) Productional channels. (C) The 3 -particle channel. (D) The charged 3/2, 3/2 Isobar channel.

(E) The Direct Channel.

5.2. The Reactions t)r +p-p+r;,- + +cir 71. + - and fir + p n + (IT + + rx + qr

(A) Anestilnx. tea. momentum Distributions.

(13) Production of N (A) and ni .

5.3. Events with More than one Neutral Secondary Particles. 74 (A) Angular and Momentum Distribution.

(B) The Effective Mass Distributions.

CHAPTER VI Discussion. 6.1. The Effect of Increasing Multiplicity 114 6.1. Bipion States 114 (A) The Possible 4q7 Resonances at 395 and 520 Mev. (n) The 1=2 Resonance. (C) The Asymmetry In +ha5°-Deceiy.

6_1, Thd Nucleon-Two-Pion System. 117. 6.4. Three Pion System. 118.

ACKNOWLEDGEMENTS. Os 00

REFERENCES. • • •• •• 131.

CAPTIONS TO FIGURES, •• 135. 1.

ABSTRACT'

The interactions of 4-Gevic negative pions with protons have

been studied by exposing the 81 cm Hydrogen Bubble chamber of Saclay and Ecole polytechnique to a 91:7-beam originating from the CERN Proton

synchrotron. The results of a study of 2128 events with four charged

secondaries are presented in this thesis.

Chapter 1 contains a brief account of pion resonances, Chapter 2

discusses possible contributions of the p -particle io some 7c7- p reaction channdis. In chapters 3 and 4, apparatus and method of interpreting individual events are presented. Results of various reaction channels are presented and discussed in chapters 5 and 6. Cross-sections for these reactions including p w and N productions

are given..Possible evidence for dipion resonances at 400 and 500 Mev

••• are presented and the presence of other resonances examined. 2.

PREFACE

The work presented in this thesis was undertaken by the author, as a member of the Bubble Chamber Film Analysis Group at Imperial College, under the supervision of Professor C.C. Butler, The author joined the group in 1959. He spent a year studying the basic theory of elementary particles before taking part in film analysis for the 24 Gev/c P-P experiment in which the group was a collaborator.

After the completion of measurement and reconstruction of the P-P events, the author took responsibility for organizing the scanning, measuring of some 10 Gev/c 117-p films which were taken in CERN using the 81 cm Hydrogen Bubble Chamber of Saclay and Ecole Polytechnique. The primary beam was then found io have far too large a momentum and angular spread to make good analysis possible. Subsequently, in 1961, a decision was made to carry out a more refined experiment using a 4 Gev/c pion beam in the Bubble Chamber, in collaboration with the Achen, Munich, Hamburg, Bonn and Birmingham groups. Since November 1961, about 100,000 7i7-p pictures have.1►v produced during 3 runs, together with an equivalent number of ie-p pictures. The author took part in two of these runs. The analysis of the results of the /t-p experiment in this thesis was partly made by the author. The work on the p —particle contribution to pion-proton scattering discussed in Chapter II is based on a paper by the author and his colleague

Mr. A-U-Zaman, published in Il Nuovo Cimento, 1962. 3.

INTRODUCTION

Since the existence of the %-meson (or pion) was predicted by Yukawa in 1935 and its subsequent discovery in 1947 by Powell et al, many experiments have been carried out in order to determine the properties

of free pions and to explore their interactions with nucleons. The main

properties of free pions are now determined whereas the interactions of

pions and nucleons are still not well understood, although explored by many experiments on pion-nucleon scattering and pion photo-production: Early experiments on pion-nucleon scattering were at low energy

where inelastic scattering was either energetically forbidden or insignificant compared with the elastic channel, and so a relatively straight forward

phase-shift analysis was possible. When the primary energy exceeds 300 or 400 Mev, there is enough energy in the centre of mass system of the pion and the nucleon to produce additional particles with high probability.

These so called inelastic interactions, which have been extensively investigated both experimentally and theoretically, are an important source for our understanding of nucleon structure. Recent experiments using highly energetic pion beams (i.e. above 1 Gev) with hydrogen bubble chambers or other hydrogen targets, have shown that in most of the collisions, only a small fraction of the available energy is spent on the production of secondary particles. In other words, in the overall centre of mass system the primary particles (the pion and the proton) retain most of their energies L .

and momenta after the collision. The same is true for nucleon-nucleon

collisions. This implies that the collisions are essentially peripheral with only the meson cloud of the nucleon involved. Recent experiments have shown that in thoce collisions, resonant states between pions are formed. The quantum numbers of these states are in many cases still uncertain.

The purposes of the present experiment are to further investigate these resonances, to search for new resonances and to test various

models of the collision processes. Attention is concentrated on peripheral interactions i.e. those of low momentum transfer.

In previous experiments on pion-proton interactions the 1 #.0 2 Gev/c region has already been explored, but with a primary pion momentum of 4 Gev/c one is able to search for new pion resonances at higher masses. Furthermore,, at this primary momentum peripheral collisions are expected to be more dominant then they are in the 1r•.2 Gev/c region. On the other hand, the primary momentum was not chosen to be higher than 4 GeV° because of the limitation imposed by the error on determining the effective missing mass of neutral particles formed in the reaction. If a maximum limit on one pion mass is fixed for this error, then, with the maximum detectable momentum 300 Gev/c of the 81 cm Hydrogen Bubble Chamber, it was calculated that the primary momentum should not exceed 6 Gev/c, however, when this experiment was started the 4 Gev /c pion beam was the only available one. 5. CHAPTER

PION RESONANCES.

1.1 The Chew-Low Extrapolation Method. Direct study of pion-pion interactions is not yet possible and so the study of peripheral collisions where a free incident pion interacts with a pion in the pion cloud of the nucleon, becomes indispensible as a means of gaining an insight into the pion-pion interaction, One importance of this is that one may relate the pion-pion interaction to the nucleon electromagnetic structure through dispersion relations of the nucleon form factor, although in itself the pion-pion interaction is a subject of enormous interest. The. peripheral collision of the following reaction

117 p + p + 9`) (1.1.1) can be represented by the Feynman diagram in Figure 1.1. The theoretical differential cross section corresponding to the (1.1) first approximation theory was first calculated by Chew and Low in the following form.

2 42 - -µ2 a2 a f2 44). G700210)2) a02)a(w2) _ 2n 0?+42)2 kiL (1.1.2)

For the sake of clarity in discussion, we shall for most of the time restrict ourselves toi=p interactions. 6. where

A2 = -(pf-p)2 is the invariant square of the four momentum transfer,

w2 = (qi q2)2 is the square of the total energy of two pions in their centre of mass system, 2 f = 0.08, f being a dimensionless •it -N coupling constant,

A = Pion mass,

kiL = momentum of the incident pion in the laboratory system,

paf,k,q1 and q2 are respectively the four momenta of the target proton, the recoil proton, the incident pion, the scattered Trand the 7[

The assumptions of Chew and Low are that,

\ a2 a 2 2 0), „has a pole at A =-11 and that this pole is isolated. a(e)a(of)

f 2 2k (2)0 u 1 (0 ) approaches the physical cross--section of the free TK 2 2 pion-pion scattering as A approaches -µ .

Here we use the metric

7. 2 In the physical region, A .07, Os therefore for a chosen band of w a 2a a plot of (A2+g2)2 against A2 (hereafter referred to as., the a(A2)a(u?) Chew-Low plot) will allow one to extrapolate to the unphysical point A 2= -P2 and hence obtain 0,1m kw)./ 2% (1.2) + o Anderson et-al showed that for 7C + p-410-1C`" + p +lt the pion-pion cross-section obtained by the extrapolation method was about the same as that in the physica3 rQL,rion io41

8. lim w 2‘ , %IC (w2) 2 2 ° `A A --1 -11

where 0,00w/ 2% ) was defined as

2 a20 f - 7C7C a(0) = 27C iL

(1.1.3) 2 with A2max 02min being the maximum and the minimum values of A and being functions of w. The cross-section by either method indicated a p-state resonance at 30g2 . p -4 + p 4.'0, the p-state resonance showed up more clearly in the cross-section obtained by extrapolation than that obtained in the physical region. They further showed, in the procedure

of extrapolations, that except for the region 032 < 10p2 in le4T--,i-+10-01P, 8.

,2 a linear fit of the Chew-Low plot gave the best 1 which is an indication of the reliability of the fit. The fitted line lay above zeroforA2>A2 .(S).n All these results showed that although mi the reaction it + p + p + it° did not come entirely from the one pion exchange process, the latter played a dominant role, and that in the reaction the pole at .62 = -µ2 was reasonably isolated.

1.2 The Pion-Pion Interaction and the P -particle. As was mentioned previously, the-knowledge of the pion-pion interaction is important because it can be related to the electromagnetic structure (1.3) of the nucleon. Frazer and Fulco , in fact, suggested that in order to explain the vector nucleon form factor, there should exist a 2 strong pion-pion resonance at a total mass squared of about 11 µ 1 in the I=11 J=1* state. Bowcock et.z1.(1e4) re-examined this problem by using a subtracted dispersion relation for the vector nucleon form factor and more recent experimental results on electron-nucleon scattering, and 2 predicted that the resonance should be at 22.4 A Experiments since then have been carried out by many bubble chamber groups in order to look for this resonance. Although the work of Anderson et al.(1.2) gave support to Bowcockls prediction, the first convincing evidence was reported by Erwin et al.„(1'5) who analysed the 1.9 Gev/c 1-p interactions

I1J denote the isotopic spin and angular momentum respectively. 9. in the Adair 14—inch hydrogen bubble chamber. For the reactions

+ ic - + p n + 7C + 7c (1,2,1)

p + 7<• +7C (1.2.2)

n + 7C• + 7C (1.2.3)

2 events were chosen which had low momentum transfer, ie.IA21< 1400 Mad They found a very marked peak in the mass spectrum for the two pion system at 765 Mev (mass squared 30 p2), with a width of about 100 Mev. Since the one pion exchange process is dominant at low momentum transfer, one expects, under the assumption of charge independence, the cross sections for different dipion isospin states to be in the following ratios (with experimental results, at the extreme right column).

Reactions 1=0 1=1 1=2 expt.

1.2.1. 2 2 2/9 1.7 + 0.3

1.2.2. 0 1 1 1

1.2.3. 1 0 4/9 0.25 + 0.25

This is convincing evidence for the assignment 1=1. One also observes that (co2 ) as defined in (1.1.3) is 83 + 8 mb; less than but close to 7C7C 2 the p—state resonant value of 1210i. (ie 115 mb), where 7 := 1/q, with q being the momentum of each pion at the rest system of the dipion. Hence

10. J.1 was assigned- This 1=1, J=1 resonance at about 765 Mev has been observed and confirmed in many other experiments(1.6). It is now known as the P -particle. A suggestion that the p -particle in fact consists of two resonant states, ie. p and p , each with a width less than 15 Mev and 1 2 situated about 30 Mev apart, was made by Bulton et al(1.7), but no other experimental group has so far confirmed this.

1.3 Other Pion Resonances. After the p, the second well established pion resonant state is known as the CO. It was first reported by Maglic et al.0.8) when studying the 1.61 Gev/c proton-antiproton annihilation in a hydrogen bubble chamber. They observed, in the reaction

P + P + 9i7 + 4 + 7C + 91? (1.3.1). a resonant state of 7c° at 780 Mev with a width of about 15 Mev. This resonant state has also been observed elsewhere, (1. 9) (1.10) in particular by Pevsner et al (1. 10) studying the reaction

+ - 0 d P + P + +IC (1.3.2) for an incident 91;- momentum of 1.23 Gev/c. The fact that the w has only been seen in the neutral charge state has led to the assignment

I=0, while the Dalitz plot for the three pions points to J=1 and odd 11. parity. We note that this co particle has the 'same quantum number as.the one predicted by Nambu (1'11), and by Chew(1.12) in order to fit experimental data on the charge distribution of nucleons. However their predicted masses are somewhat lower than that of the w. In the above mentioned experiment, Pevsner et al observed, in addition to the w peak, a second at 546 Mev with a width r< 25 Nev. They interpreted this as the three-pion decay of another unstable particle, which they named the 11 meson. This'll -meson was later (1.13a) confirmed by Bastien et al , who looked for the reaction

K- + P —3 A + 11° at a threshold K--momentum of 725 Mev/c. Their results strongly suggested that the 77 was produced through an I.0 state and decayed electro-magnetically with isospin violation. This particle has been investigated extensively by many other groups, and is believed to have zero spin, odd parity and even G-parity.(1.13b)

Another unstable particle much discussed recently is the L;(1.14)(1.15) with isospin tentatively assigned to be unity. Other properties and even its existence are not yet established.

There is, up to now, only one resonance that has been reported + - above 1 Gev/c. It is an I=0 It - IC resonant state at 1250 Mev, with (1.16), a width of 100 +50 Mev probably corresponding to the one predicted by the Regge pole approach, ie. J=2 with other quantum numbers 12. equal to those of vacuum (1.17). A more recent experiment by the Milan and Paris Group (1.18) has indicated that J is in fact probably equal to two. This resonance is now referred to as the f°. 13

it o IC -

2 A

P P

Pig. 1.1

14. CHAPTER II

Contribution of the P —particle to IC--p Scattering

2.1 One Pion Production

Although many pion—pion resonant states have been reported in recent years, the P—particles remains the most conspicuous one. It is, therefore, of great interest to see how much the p—particle contributes to the process (1.2.1), if we consider the final pions as the decay products of an intermediate p—particle and examine it by means of the peripheral model.' (Figure 2.1). The simplest form of the interaction L:'grangian for the coupling between the p and the pion is

L ( Pc1() (2.1.1) pmt 2 git rst P µ

1 ,3)'p describes where erst is the Levi—civita symbol, p = kp p2 the field of the p while cF's describe the pion fields and g is a ooupling constant. The differential cross section corresponding to Figure 2,1a is ( Appendix 2.A), 2 ao 2 f2 g4 1 1 A2)2 a(w2) 3(21)2 "2,2 • / 2 2\2 2 2 lco 1-cu r 4

* Being Hermitian and satisfying the requirements of Lor,entz invariance and parity invariance.

15, A2 (41max (2 4-112-6e) - p2 d (A2) 2 '112 (A2+122)2 ,)A2 4w 3 min

with incident pion momentum in the laboratory system,

cuo = rest mass of the P.-particle,

A = pion rest mass,

w . total energy of the two final pions in their barycentric

system,

2 A = -(13f-16)2, is the invariant square of the four-momentum transfer.

r width of the /r-w resonance, which is determined by the

decay rate of the p into two pions and is given by

g2 q3 3 (2.1.3) 47t w

q being the pion momentum in the rest frame of the p f2 = 0.08

2 2 A mmax = -2m + 2EfwEiw ± 2pfwpiw , with subscripts w indicating the quantities concerned are to be evaluated in the total barycentric system W. •1/.

2 In carrying out the integration in (2.1.2) a out—off factor 8µ2 was included, since the peripheral model is expected to hold only for small ac; momentum transfer. Two curves of —aco vs. w are shown in Figure 2.3. These curves correspond to an incident pion momentum of 4 Gevic, but to different values of r . The total cross sections (with 42 <8112) are obtained by integrating overp2 and are shown in Table 2.1.

TABLE 2.1

2 r (Mev) a (mb) 4x

1/3 16 0.o9 1/2 25 0.14

1 5o 0.27

i 1.6 78 0.43 2 100 0.54

2.2 Low Energy Elastic Scattering.

In the elastic scattering there are contributions from many important sources, namely, the p —particle pole, the nucleon pole and the ( ) resonance. However, if we restrict ourselves to low energy s—wave scattering, we may expect the p —particle to give the dominant effect ie. through the exchange of ap 7,41eson between the pion and the proton,(2.2)

17.

(2.1) The interaction Lagrangian of the p and b:ho rrunleon i s

ir;(a a s. pp. apv L ig p 1.1 pN 1.1 4.14 tiv a x; ard4,4

(2.2.1)

The second term does not contribute to the s—wave scattering amplitude f0+. The amplitude due to the p exchange is therefore easily calculated and is given below. (Appendix 2.B), 2 gigue 1 Cwo +2q2 co,2 4q2 0+ im)(w+m)+(E+m)(w—m)tog 87w 2q 2q W 02

— 2 (E—m)(w+m) (2.2.2)

with q = bexycentric momentum w total barycentric energy, E = proton energy in the barycentric system, m = proton mass.

For very small value of q, fo+ reduces to

g1g 7t 2g f0+ (2.2.3) 47C wo eiPpsinq) f is actually the Born term in f where 6 is the 0+ 0 q s—wave phase shift, hence

tan So o+

= a

where as is the s-wave scattering length experimentally known to be (-0.087 ± 0.05)µ-1.

From nucleon form factor data

= 0.06g ic (2.2.6) g1 we have 2 1.8 (2.2.7)

On the other hand, from the width of the p, which is not accurately. determined, but is generally taken to be •`-'100 Mev, we deduce that

2 2 (2.2.8) 4 it 2 gE Thus we see that the two values of — are in remarkable agreement, bearing 47c in mind that figure (2.1) and figure (2.2) give at most the dominant contributions to the respective processes. This agreement give us some confidence about the quantum state of the p, ie. I=J=1, and a width r = 100 Mev. However, it does not exclude the possibility that the p consists of two sharp resonances.

19. APPENDIX 2.A.

The differontial cross section can be expressed as follows,

2 = l T 1 dp (2.A.1)

1 1 2 where F y IT! and dp are invariant quantities representing the flux, the square of the transition amplitude and the density of states of the final particles. T is defined through the S-matrix and is given by

= 1 i (2ir)4 T 64(Pf - Pi) (2.A.2) with PP f representing the total momentum four-vectors of the initial and final particles. Fcr the process in Figure 2.1a the effective part of the Lagrangian (2.1.1) is

L g7c Pu 00 (2.A.3)

- o where 0° and 0- are respectively the fields of the Pt 'X and 7C . This is obtained by using the following relations, ip

412 "

0° (2.A.4) 20. with similar relations for ths p .

As in 2.1, we shall here denote the four-momentum of the incoming -o p and the outgoing lz and p by kippiyqv c1,q2 and pf, respectively, with A being the four-momentum of the virtual meson. ff we sum over final nucleon spin states and average over initial nucleon spin states, then,

Z I G-2 * IT 12 =i spin rx(Pf )Y5 u(P. 2. )12 012+122)2

1 k k '121) v (ci1 _q2)v K2 -M2

2 1 2 = G2g4 rir ( 612)2 (K2 .._ m2)2 (kif- A )4(q1-9.2) D

2 1 -N (4 II- kiL oos.0k)2 = 6"/- (en 122)2 (K2,-.2)2

where K 4-momentum of the p 4-momentum of the final pions in the reference system qk in which the p is at rest (we shall hereafter refer

to this as the K-system).

The term 612) is the contractor of 2 field operators of K2 - M2 spin 1 particle in the momentum-space.

21. M . mass of the p

w + i --- with w being the total energy of the pp r 2 o the decay probability.

1 should 1, .T26.t be replaced by the modulus square& The term (K2..m2)2

j•e•p

1 (K2_m2)2 i K2 (02 - (K2 r2(0 02

hence

2 1 2 2 2 T1 . 16G2 g4 A k. (K2_ co2o) +.„2 _2 (i62 + 122)2 I 111 • lqk I

cos 9k • • • • ******* (2.A.5)

The density of states

> d4-1.1 d41.2 d4pf 12704 a ( p e d p = 4 (27)4 (2904 (2)

291:6 (04 1112) 0 (q1)290 o(q21 '112) 0(q2) "µ 2 ) .a(Pf)27C41

Where represents any integrations one wishes to carry out.

22, The function 0(q) is defined as

0 (q) = 1 if (1 .> 1

0 otherwise.

we obtain Integrating over io q,co1 and pfo

dp 1 d qi d q2 f a p = 8 (270') co Ef Col 2

1 (3)(p q (Ef + w + (02 - Ei f + 1 +q2i-p.-k.).

Defining , Q = + q2)

-A _N q2) t

and integrating over d Q gives .3- 3-a 1 d q d pf d p = 6 (Ef+0)1+c02 -co.-E.)1 i 8(2705 03 1w2 Ef d3--q d3?f Since 6(E +Co +co -c0 . -- E ) and ----=. are both Lorentz to 1 w2 f 1 2 1 i Ef

invariant, we may carry out the integrations separately in different 23. co-ordinate systems. Hence on carrying out the first integration in the Kr-system, we have

d3- q7 % (Ef + (A) + - E ) (.1) (.13 i 1 2

g, 2 1 d Id 2k 24c ) 2 K IC K

1 ill I d2K 2uk

where dg is an infinitesimal solid angle substandard by q K K • The second integration is best performed in the Lab. system. i.e.

d p„, d p 2 - fl, d (cosOpL) 1Pf L i E E E f fL fL

d (cosO ) = 72I PfL dEfL PL

0 pL being the angle of the recoil proton with respect to the incident pion.

24. As Q2 -(Pf -Pi)2

- 2m2 + 2mE fL

and K2 )2 (q1 q2

p. p )2 = (k.1 a.

U2 4. m2 4. 2k. 11, pfL cos - 2 (wiL +in) EfL

is the invariant mass squared of the p

with U2 = (ki+pi)2

= total energy squared in the overall centre of mass

system.

we have 1 dEfL = d (2) 2m

d (cosOpL) - 1 d (K2) . p 2k114 fL

d3' p 2 hence f d (g) d(K2) E f 4m kil

25. i.e.

1 27 2) d(K2) d p (6, 8 (2705 4nak jL

Finally2.the invariant flux F is given by

F2 = 16 (pittki v - ) pivki4)

= 16 (piki )2 - pi2 k2i

In the Lab-system this is

24- F = 4k-m/ 2 4 2 2,w ) (2.A.7)

( 2.A.5)1 (2.A.6) together with (2.A.7) give

4 g 2 ,„ 2 2 cos OK d 68 (2904 m2k2i L 1 . -A d2., d( (1,2_2\2 ÷,2_ 2 (6, 2+ 1.42)2 lc. d(42)d(K2) woi W

26. If we integrate over d. S'aic, with

d = 2 d (oos6 ) K 7C K (K2+12_ 02)2 lkiic - g 2 4K2 and bearing in mind that K2 = 0.) 2 = invariant mass squared of the p, and

G2 m2 f2 167t 2

we obtain the expression

2 2 1 f2 4 1 1 '-&-, a6 — 2 2 \2, 22' ( -(-1) - R ., ) (29e 2k a( w)(.0 3 iL (-Q uel coo co 4

2 max ( 032) w2 +112_6,2)2 2 I 6, 2 2 d 2) 4 co (A2+R2)2

2 \61 min (c02)

27. APPENDIX 2.B.

The contribution of the p particle to the ,K P elastic

scattering is through the diagram in Fig. (2.2).

The scattering amplitude can be expressed as (2.3)

T = T+ 6 + (2.B.1) Y8 'Ars where the T's are the three isotopic spin operators. It can be shown that

V 'T = 2(P1) NM. ( 2') (2.B.2)

P1 and P 3 being the isospin projection operators. As was mentioned 2 2 in section 2.2. T dominates the s-wave scattering at low energy, hence

T= 2(P1) (P) (2.B.3) Ys 'sirs 2 VI 2 1

In this appendix we shall use p,p1, k,k' to denote the initial and final nucleon and pion 4-momentum and K denotes that of the p .

1 6µv -K ---2 11 KV 01 Now7 < 1 1... >= ci1 a:(131 Au(p) (k kl)v K2 - co

28.

= g1 2 --2 1.71 (Pqr120r4412 u(p) (2.B.4) Since kv(k+10)IF (10-k)v (k+10)1) = 0 On the other hand T can be expressed as (2.1)

T = A + 2 (k + B (2.B.5) comparing (2.B.4) and (2.B.5), we have

A=0 -2 B = gig (21). (2.B.6) 2 3 2 .2 2 K

In the centre of mass system

K2 = (10 k) 2 \ 2 = (kt -k) = -2k2 (1-cos0)/ where k = centre of mass momentum

= scattering angle.

29.

Substitute this into (2.B.6) we have

2 (2.B.7) B . gig 7t(214 p.2) 2 2. 2 w- 0 + 2k kl—cos0)

If we define f1 and f2 by the following expression (0.0(0.k) 2 (6) = E < f I f i + f i I spin 2 k

with a = differential cross section

i ' i f > initial and final state vector.

we have (2.3)

(W—m)(E+m) f (2.B.8) 1 8 w W

(W+m) (Em) f B 2 8 ,301

W,E and m are respectively the total centre of mass energy the

proton energy in C.1L system and the proton mass. f1 and f2 can be expanded in terms of partial wave scattering amplitudes, i.e.

30.

f p1_1 (cos0) 1+ P1+1 (cos0) + fl-1 1=o 1=1

00 Pl cosO) cosO B(9) f2 a fl+) where 1 is the orbital angular momentum I- denotes quantities corresponding to total angular momentum j = 1 + 17; 131(cos0) is the derivative of the Lagendre polynomial of degree 1 with respect to cosO.

We are only interested in the s-waves scattering amplitude and this can be obtained by integrating (2.B.9) over cosO and using (2.B.7), (2.B.8) i.e.

(Eri-m)(w-m) 2q1g„ f = d(cos0) o+ 8 W w+2qo2 f-cos.0)

(D-m)(w+m) 2q1g1 cos0 2 2f, 8 7c W w + 2q ki -cos0)

g it 1 (E-m) (w+m)-1-(E+m) (w-m) 87tW 2q2 2 +412 L9- ( 2 ) 2(E-m)(w+m) 2.B.10). 31

MP 0

C p IIL. SIMIMMIIA

•2

(a) (a)

Fig. 2.1

at— at------

P P

Pig. 2.2 E"g '91.1 (Aeo) I' O't 6' 9' L' 9• 0

5'0

O't

c't

jg.cl (A09(03) De CHAPTER III

Apparatus and Experimental Procedure

3.1 The Hydrogen Bubble Chamber.

Details of the hydrogen bubble chamber have been described

elsewhere (3.1). It has dimensions of 81 x 40 x 31.5 cm3, and is operated 2 in a magnetic field of 20.7 kilogauss, at a hydrogen pressure of 5+ Kg/cm — 2 s and a temperature 27° K. Photographs were taken simultaneously by three

automatic motor driven cameras mounted in the same plane about one metre in

front of the chamber. The positions of the cameras form an equilateral

triangle of height 25 cm, as shown in Fig. where Ci, C2 and C 2.1, 3 represent the positions of cameras one, two and three respectively. The chamber is illuminated by three flash lamps placed at the side of the

chamber opposite to the cameras. These lamp flashes are delayed by 1 mosec.

after the entry of the pion beam. There are crosses both on the front and back glasses of the chamber to serve as fiducial marks.

For the sake of calculation, and discussion in the following sections the co—ordinate system is here chosen arbitrarily to be right—handed with origin at the inner surface of the front glass, and the X—axis lying

approximately along the direction of the pion beam in the chamber (Fig.3.1)

The photographs taken with camera one is referred to as view one, and so on. 34.

3.2 The Pion Beam(3.2)

The pion beam used in this experiment had a momentum of 4 Gev/c. The pions were produced by allowing the circulating protons to strike an internal target. The protons were of 20.14 Gev/c, accelerated in pulses, one pulse per two seconds. The target was a 3 x 4 x 38 mm3 beryllium bar, aligned along the pion beam. The lay out of the beam was as shown in

Figure 3.2. The pions were accepted into a solid angle of 5.9x10 5 sterad at an angle of 12efrom the target. They passed through a series of magnetic quadrupoles and bending magnets to arrive at the mass slit with a momentum dispersion of 1 Mev/c per centimetre. The opening of the slit was about 2 cm, hence the estimated effective momentum bite was + 1 Mev/c.

The angular spread at the mass slit was 1.3 m.rad. and 1.4 m.rad. in the horizontal and vertical planes respectively. At the entrance to the bubble chamber the spreads were 3 and 4 m.rad. respectively. The mean pion momentum was found to be 4 Gev/c21 10 Mev/c by the measurement of many beam tracks on the film (sections 3.5, 3.6). This uncertainty is comparable to the momentum spread caused by coulomb scattering of the beam in the wall of the chamber. The contamination of the beam was of 1% antiprotons and 4.7% negative muons.

3.3 Method of Scanning. In order to calculate cross sections and to allow sufficient lengths of track to be measured, only those interactions occurring in a certain 35. volume in the chamber (fiducial volume) were chosen. The momentum spread of the beam as given by the beam deSigners was much smaller than the measuring error. Also the beam had little contamination of anti— protons. Thus it was possible to choose interactions that had very short primary tracks in the chamber, since for all calculations we could assume that the primary particle was a pion and assign a value for its momentum instead of using the measured one. On the other hand, we would like the secondary tracks to be as long as permitted by the dimension of the chamber, since the measuring error is in general inversely proportional to the square of the length of track measured. However, for the primary, a sufficient length of track was needed so that it would be possible to determine whether_it was a beam track or not. (There were also tracks caused by particles coming from interactions in the metal of the chamber).

The criterion for a beam track was chosen such that it did not deviate from the mean beam direction by an angle greater than 1/100 radian.

This was about the minimum angle that could be detected on the scanning table without too much difficulty.

In view of all these criteria, the fiducial volume was chosen near the entrance of the beam to the chamber, such that all interactions in the volume had a primary track of more than 10 cm, and energetic secondary tracks of at least 20....J30 cm. The fiducial volume was skew with inclined faces defined by two parallel lines in view 2 (i.e. the central view) perpendicular to the X—axis (Fig. 3.3). The average length 3 6 . of beam tracks in the fiducial volume was calculated from the distribution in depth (z-co-ordinate) of tracks in the chamber to be

20.56 cm.

The fiduoial volume was divided into two region9,111 and R27 by a

plane defined by another line in view 2 paralled to the others. Events in

R have not been analysed, but were recorded in case better statistics 2 were needed later.

View 2 and one other view were simultaneously scanned by two persons.

An interaction was recorded as an event only if its apex was in either

R or R and its primary was a beam track. The number of beam tracks 1 2 was counted for every tenth photograph.

As the total charge of the 9;T--p system is zero, all events must have an even number of emergent prongs, half positive and half negative. The events were classified as 4-, 6-, or 8- prong events. No 10-prong events were observed. Zero-prong events were also searched for, but the detection efficiency turned out to be quite low.

In order to estimate the scanning efficiency, all films were scanned at least twice. The scanning efficiency of a certain class of event was estimated in the following way. Assuming each event has an equal probability of being found in one scan and defining efficiencies e and 1 e for the first and the second scans by 2 ni = number of events found in first scan 1 = n = Ne = number of events found in second scan 2 t n = Ne1 e = number of events found in both scans 12 2 where N is the true number of events. 37. The combined efficiency is therefore,

1)(1-e2) e +e -e e 1 - (1-e 1 2 1 2 n12 n1 n2 (n11-112-n12)

All relevant information was recorded during scanning, for example :

(1) Stopping protons. (2) Stopping pion with subsequent decay into muon followed by the muon decay into electron or positron.

(3) Neutral knock-on-event, i.e. collision between a secondary neutral particle (presumably a neutron) and a target proton.

(4) Associated electron-positron pairs. (5) Charged and neutral V -particles.

There exist well established energy-range relations for various particles. (Figure 4.3) The momentum obtained from the range measurement of a stopping track far exceeds in accuracy that which is obtained from a curvature measurement, if the mass of the particle is known. On the other hand, if the momentum is roughly known from curvature measurement, then a stopping track gives an unambiguous identification of the particle mass. 38.

Neutral-knock-on events and electron-positron pairs also help in the identification of events, Events with charged or neutral V-particles were recorded and will be analysed, but the analysis of these events is not included in this thesis.

3.4 Measurement of Events.

Two measuring machines are employed at Imperial College for this experiment. One was constructed at the College and has been in use since the beginning of the experiment(3.3)(3.4). The other is a British National measuring machine introduced at the later stage of the experiment.

Both employ the principle of Moire fringes to digitize the movement of the horizontal stage on which the films to be measured are clamped.

The moire fringe system was designed by Messrs. Ferranti Ltd., It works as follows. Light is shone through two diffraction gratings with the same line spacing, mounted one slightly above the other, with a small angle between the lines. One grating is fixed and the other attached to the stage. The transmitted light forms a series of bands at right angle to the bisector of the angle between the grating rulings. The separation of the light and dark bands depends on the angle between the lines, and can be much greater than the line spacing. When the stage grating moves by one line spacing the bands move by one band spacing.

Thus the movement of the stage is magnified, and by counting of the bands, digitized. The light from the gratings falls on four phototransistors 39. arranged such that the band phases differ by "/2. The phasing of the signals enables the sense of motion to be determined so that the scalar adds for forward motion and subtracts for backward motion. In the first machine the stage can move in two directions at right angle in the horizontal plane. Light from a mercury vapour lamp is shone upwards through the film selected for measurement. Three optical systems mounted above the films project an image on a ground glass screen at times twenty magnification. Points of interest can be brought to a fiducial point so that their co-ordinates relative to an arbitrary origin can be measured. These co-ordinates and their identification labels are punched in code form on perforated paper tape. The computer is programmed to read and translate this tape. By repeated measurement of a straight line placed first in one direction and then in the opposite, it was found that the machine introduced a curvature corresponding to a sagitta of 15 microns for a straight line of 8 cm. This is a systematic error caused by the non- linear movement of the stage. Apart from this systematic error, there is a random error of about 3 microns on bringing a point to be measured to the fiducial point. The basic principle of the British National measuring machine is the same, through in this case, the stage on which the films are clamped moves only in one direction, thus providing the movement of the image of the photograph in the corresponding direction on the screen. The 140. movement in the perpendicular diroction is obtained by moving the optical system, to which Ferranti digitizers are again attached.

3.5 Data Processing. The information necessary for a final statistical analysis of events is of two types. The first consists of geometrical information such as co—ordinates of points, angle and curvature of tracks etc.

These are generally mass independent. The second includes kinematic information such as the energy—momentum four—vector of each particle, which can be obtained only if a mass value is assigned. To obtain all this information from the data produced from the measuring machine involves a great amount of calculation even for a single event. For a meaningful analysis of the experiment, at least a few hundred events are needed. Therefore a modern electronic computer that is fast and with a big store is essential.

In this experiment computation was carried out on an IBM 7090 computer. As the IBM 7090 requires magnetic tape ill?ut whereas the measuring machines yield paper tape, the following conversion procedure was adopted. The data was first processed by the London Mercury computer using an IBM Link programme, which carried out a first order geometrical reconstruction and rejected events with faulty labels or with badly measured tracks, points, or fiducial marks. The output of this programme was also in the form of paper tape containing some geometric information (eg. transformatiun coofficients) n17:1 moaourc,(7 no-crAinales or tracks

and points, together with a list of events rejected and the nature of

faults. It was then converted into cards using an IBM 046 and then into

magnetic tape using an IBM 1401. The magnetic tape could then be run

on the IBM 7090.

The geometrical reconstruction was done by using the CERN GAP

programme which is an extension of the CERN Moorhead programme (3°5)

It gives radius of curvature, dip angle and azimuthal angle of tracks,

and positions of points, with calculated errors. This information,

plus the knowledge of the magnetic field inside the bubble chamber gives

the momentum of each track. The output of GAP, together with a variety

of hypotheses (i.e. mass assignments to all charged and possible neutral

tracks) constitute the input to a fitting programme GRIND. Provided there

is not more than one neutral particle in a particular hypothesis, all

kinematic quantities can be calculated. However these kineaatic

quantities will in general not simultaneously satisfy energy and momentum

conservation at an interaction vertex, because of measuring errors or

incorrect hypothesis. In other words, the problems of calculating the

momenta, angles and energies of all particles is over-determined under

the requirement of energy-momentum conservation. Hence it is possible

to adjust the momenta and angles so that the conservation of energy-

momentum is satisfied and the quantity

2 . 2 2 X = [ w.(x.-x.) (3.5.1) L2. is minimized, with w being the weight of the. measured quantities i x. inversely proportional to the uncertainty of x. and x. being 1 the adjusted quantity. Since )e is related to the uncertainties, it is an indication of the "goodness of fit" for a hypothesis.

Apart from the fitting procedure GRIND also uses the energy range relation to calculate the momentum of particles which stop in the chamber.

In many cases, a fitting programme cannot absolutely decide which is the most preferable hypothesis among several. Therefore, some other sources of information are needed for a complete identification of events.

An important contribution towards theUdentification of tracks is made by the study of bubble density along the tracks, as will be discussed in Section 4.2.

If the energy of a particle is low enough so that it loses all its energy and stops in the chamber without decay, then we can infer that

usdy it =fir will,\decay a muon which then decays into an electron (or positron) and a neutrino. This

/C µ —4 e gives a characteristic length of the muon track of about 1 cm. in the chamber, corresponding to a muon momentum of 30 Mev/c.

On the other hand, the other particle which can decay into muon is the kaon, which gives a muon momentum of about 235 mev/ce It is very unlikely that a pion or a kaon will decay before it stops in the chamber,

43.

-8 -10 since its life time is about, 10 sec. whereas less than 10 sec. is needed for the particle to stop in the chamber.

For the identification of neutral secondary particles, the existence of an electron—positron pair is also useful, since it excludes the neutron as the only neutral particle and implies that there are possibly one or more neutral pions. A Dalitz pair, i.e. an electron—positron pair with apex coincident with the apex of the

7C—p interaction, shows definitely the existence of a neutral pion.

Although the criteria for identifying events were the same for all groups in the collaboration, some details varied from group to group. In order to make sure that the results from all groups were correct, a test film which consisted of a sample of about 20 events was measured and analysed by each group. The results were found

to he srtisfactory.

3.6 The Maximum Detectable Momentum.

The accuracy in the determination of the. momentum of a charged particle is limited by the uncertainty in the measured value of curvature 1/p of the track in the chamber, where p is the radius of curvature, For a track of length L, the corresponding sagitta is given by

L2 (3.6,1) ap

44, and the momentum is

P 300 H p (3.6.2)

with H expressed in Gauss, p in centimetres and P in eleaon-volts.

The uncertainty in the measurement of s depends chiefly on (1)

measurement error; (2) optical distortion, liquid convection and (3)

multiple Coulomb scattering.

For highly energetic particles, coulomb scattering is negligible

as compared with other sources of error. Thus in the absence of

magnetic field the mean uncertainty Az in determining the sagitta of

tracks of such particles is caused only by measurement and instrumental

error. The momentum corresponding to a sagitta equal to this uncertainty

is called the maximum detectable momentum and is given by

2 300 H L PIEDM (3.6.3) 8 (as) In order to obtain the PAM for this experiment, the curvature

of about 180 no-field tracks were measured and reconstructed using the

CERN Moorhead Geometry Programme, The standard deviation was found to 5 be 2.4 x 10 cm 1 corresponding to a sagitta of 110 microns, Thus

the PMDM is 260 Gev/c* from (3.6.3). However, the mean is not zero,

* On the average only 55 cm of a track was measured. If the full length of tracks was measured, then the PAM would be ' 300 Gev/c. 145.

but corresponds to a sagitta of 80 microns. This is a systematic

error due to the non-linear movement of the stage of the measuring machine and the distortion of tracks in the chamber caused by the turbulent motion of hydrogen liquid. In order to find the.extent of distortion in various parts of

the chamber, the curvature distribution of the respective parts of tracks were investigated separately. It was found that in the first

half (i.e. near the entrance of the beam) of the chamber distortion

was considerably greater than that in the other half. This can be

seen from the distribution in curvature of the first halves of about a hundred no-field tracks (Figure 3.4b). The mean curvature is -

-3.4 x 10-5 cm-1 9 corresponding to a sagitta of 160 microns for a track of 60 cm.

3.7 Measurement of Beam Momentum and Related Quantities. Apart from the no-field tracks, 60 ordinary beam tracks were measured and reconstructed. From the distribution in curvature 1/p and tanm the means of these quantities were obtained.

-1 = 0.001558 I- 0.000024 cm tang = 0.00717 + 0.0080 where a is the dip angle i.e. angle between the track and the ac,-y. plane. These correspond to a mean momentum of 3.99 + 0.06 Gev/c.**

** The combined result of the collaboration is 4.00+0.01 Gev/c, after a correction for systematic distortion is made.

46.

Some other mean quantities are 9

cosP = 0.99996 A (cosp) = 0.00002 depth = -23.1 cm.

with p being the azimuthal angle9 i.e. angle between the projection of the tract on x-y plane and the x-axis. 47

Fig. 3.1

beam direction

x R 1 camera 2 Z

front glass

Fig. 3.3 Target

Proton Synchrotron

BIM Bubble chamber Fig. 3.1 t 49

330

0 one wort I (b) 20

curvature ( ca-1) x 105

Figure 3.4 50. CHARTER IV

Jrternretation of Events

The measurement and reconstruction of events were started in the early summer of 1962. The emphasis was then on 2-prong events in order to make a detailed study of the p and other 7:— 7c resonances. During October of the same year, one of the collaborating group, the Max Planck

Institute for Physics at Munich, reported the appearance of a new resonance (63) at 620 Mev in the 1=2, J=o state in their preliminary analysis of 4- prong events. Consequently the effort of the whole collaboration was turned towards the 4-prong events.

At the time when this thesis was being written there were about 5,000 events measured and identified. However, the results presented in this and the following chapters are only for the 2,300 4-prong events. The 2-prong events were not, at the time of writing, fully analysed.

4.1 Interpretation of events by Pitting Procedure.

The following hypotheses for 4-prong events were tested 4- the fitting programme GRIND.

—, 4- 0 'K +P --:', P +1E + 7C— + 7C— + ..o.p (4.1.2)

7C—+p -4 n + 7C + 70.+7C-- 7t— (4.1,3) 51. A hypothesis was reject if the 2% exceeded a cut-off value. The cut- off value for events with no neutral particles was chosen to be 20, and for events with one neutral to be 10. The difference is due to the fact that in the fitting procedure the former has four degrees of freedom whereas the latter has one. In each case the cut-off value corresponds to a probability rJ 1/100 of rejecting a correct hypothesis. In Figure 4.1 the x distributioil for different types of events are shown. Two events which are almost certainly of the type P 7C+7C-7C are outside the cut-off region. Apart from these two events, the distribution seems to be in agreement with the theoretical curve, indicating that the uncertainties assigned to the kinematic quantities in (3,5.1) are quite correct.

111— The programme also calculated the missing mass B from the measured (unfitted) kinematic quantities i.e.

= (EN2 NN - PN2)2 PN = (lo - ?i) (4.1.4) E = E EiEi N o +Mp - where a, PN are the energy and momentum carried by the neutral particles, th E.,1). are those of the i charged secondary particle and E0 P0 of the primary pion, M is the rest mass of the target proton.

The distribution of m.- ,ssing mass for events of the types (4.1.1)

(4.1.2) and (4.143) are shown in Figure (44:). The missing masses for various types of events are quite well separated, showing that the cut-off 52. 2, i x s n this experiment are reasonable, and that the measurement are sufficiently good.

Events with more than one neutral secondary cannot be kinematically fitted and are here referred to as "no fit" events, Identification as one of the following type t-

7C+ /C+ p-4 p+ 9z++ 9t0+ 7C° 1 .. • (4.1.5)

1t-+ p 4-4 n+%++ It++ 9t---4-/t--p7C° 4. • . . (4.1.6) was partially achieved by means of the missing mass deduced from the momentum of the charged secondaries.

Out of all events tested by GRIND only about 15% were unambiguously interpreted. The remainder were identified either by ionization measurement or by visual estimation, as disessed in the following section.

4.2. Identification of track by Ionization Measurement.

An important contribution towards the identification of tracks is made by the study of bubble density along the tracks. It has been reported

(4.1.) (4.2) that over a considerable range the bubble density is proportional to p-2, with being the velocity of the charged particle which gave rise to the track.

In this experiment the bubble density of all positive tracks were visually estimated during scanning, and below r,../ 700 Mev/c most pion tracks

53.

were distinguished from proton tracks. At low momentum i.e. below X100 Mev/c

both proton tracks and pion tracks are so heavily ionizing that they cannot

possibly be distinguished from each other, however, by the decay mode of the

stopping pion, an unambiguous identification is usually possible. Moreover,

energy-range relations can be used for the purpose, as is done in GRIND.

Above .A>'700 Mev/C, a proton track ionizes less than twice minimum,

whereas a pion track is at about minimum ionization, so a visual estimate

becomes very unreliable. Systematic measurement is therefore necessary.

There are three methods of measuring the distribution of bubbles,

namely, bubble counting, gap counting and the determination of the mean gap

length. Because of the difficulty in resolving overlapping bubbles, the

first method was not used in this experiment. Among the other methods,

the determination of mean gap length was preferred, because it would not be

affected by possible change in bubble diameter.

For a track of N gaps, the expected number of gaps with length greater

than x is

x N (x) = Ne g (4.2.1)

where g is the mean gap length. Provided N is large, the plot of N(x) on

a logarithmic-linear paper should be a straight line with slope 1/g.

Two microscopes were used for measuing mean gap length. In the eye-

piece of each microscope there is a graticule consisting of 5 concentric :1, - n () circles with radii 4 .0, -.21.) y _4 0, and1BX respectively, where 1-1.1 o a"-J 54. bubble diameter. Bubbles of the track were successively brought to the

centre of the circles so that the numbers of gaps with lengths greater

than predetermined distances could be recorded by a semi-automatic counter.

The mean gap length g would then be obtained either by plotting number

vs.distances on a logarithmic-linear paper, or by means of a "weighted

least squares method" (4. 3) using the London Mercury Computer. An example of the plot of number against distance is shown in Figure 4.4. The ionization density depends not only on the mass and momentum of

the charged particle, but also on the thermodynamic condition of the bubble

chamber. It is therefore necessary to compare the ionization of a track

to be studied with that of a beam track on the same photograph. The

ionization density of a beam track is known to be the minimum ionization

/ ). Hence by taking into account density 10 (with mean gap length g = 1 /Io I the dip angle, the relative ionization /II can be obtained. There are well o established relations between ionization density and momentum of charged

for a track particles in hydrogen bubble chambers. If the value of Io differs by more than 3 standard deviations from the expected value for that of, say,the pion, then the track will not be considered as a pion track

(Fig. 4.3). If the measurement lay within three standard deviations of the values expected both for a pion and a proton, then the nature of the

particle was considered as undecided.

It was found that after fitting 25% of all events were unambiguous i,e. all tracks were identified. Another 43% were unambiguous after visual 55. estimation. The rest required gap counting, which loft about 6% still ambiguous.

4.3. Scanning Efficiently and Cross-Sections. For an estimate of cross-section, the true number of events, and hence the scanning efficiency for each class of events is needed. The following are results for the 4-prong events obtained from two scans at

Imperial College.

= 239 n1

n = 251 2

= 226 n12

e1 = 93%

e2 = 94%

1T = 265

e = 99.6%

The meaning of all symbols is the same as defined in the previous chapter

These figures are for the combined results of the whole collaboration. The Imperial College group, however, left only about 1% of events ambiguous. 56.

(section 3.3).

The total cross—suction of 4—prong even-tics in 7.44 ± 0.17 rob. This value was obtained after the following corrections were applied.

(1)On the average the primary particle of each event only travelled half way through the fiducial volume. (2)The pion beam had a µ— contamination of 4.7%. The density of the liquid hydrogen, which was operated at —27°K, 5.43 atm., was taken to be 0.0625 /cc The total distance traversed

by beam particles through the fiducial volume was calculated from the average number per picture of beam tracks entering the fiducial volume,

and the total number of pictures examined.

The cross—sections for various channels of the 4—prong events are given in the following table, the errors being statistical.

TABLE 4.2

Channel (rob) + — P 7c ic 7 1.91 ± 0.8

1 7c+ Ir.-11C7c° 2.11 ± 0.9

+ - - n 7c+ IC It IC 1.10 + 0.6

+ + - - 0 n 7C qC 7C 7C 7C 1.47 + 0.7

+ — — p 7L 7C 7C 7°'° 0.85 ± 0.6

Total 4—prong events. 7.44 + 0.17 r

fit 4.1t+ 7CPIt 8 01 event

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Analysis of Four—prong Events

In this chapter a detail study of each 4—prong reaction channel will be made.

5.1. The Reaction p 7G 77 it (A)Angular and Momentum Distributions.

The ems (centre of mass system) momentum distributions of the 7C, % and the proton are respectively given in Figs 5.5, 5.6, 5.7 and the cms angular distributions in Figs. 5,8, 5.9 500. The solid curves show the phase space distributions normalized to the total histogram area. The angular distribution from the proton is strongly peaked backward whereas the lit are distributed rather isotropically. The angular distribution for the 7c consists of about 50% isotropically distributed pions, with the remaining 50% peaked forwards. The momentum distributions exhibit a slight accumulation of high momentum protons, an abundance of rather low momentum 7:fis and a phase space behaviour of the 7t~ s.

In the following sections it will be shown how these distributions can be understood in terms of three contributing production channels.

(B) Production channels.

Pion-nucleon isobars and the pion—pion resonances, for instance the p , may play important parts in the reaction

P +7t + (4.1.1.) 64. through the following channels

- % + p -4 7c + p + („it)° (5.5.1)

- ++ - A + p --> .N + A + A (5.5.2)

*0 + p N + % + 7 (5.5.3)

0 o p N + ici) (5.5.4)

With N and OW respectively denoting pion-nucleon isobars and pion-pion resonant systems. In order to find out how important these various channels are as compared with the direct channel (ie without the formation of any resonant system), the effective mass distributions + for the systems I+ P, gip, "c 1t and - - were plotted in Figs. 5.1., (3 5.2., 5.3 and 5.4. It is seen that the charged /2,3/2) isobar (Fig.5.1) * , and the p-meson (Fig.5.3) show up rather strongly, whereas at the N 3/,3/_ {hereafter denoted as N) mass in the 7t p effective mass distribution of Fig (5.2) there is no definite peak, showing that channels (5.5.3) and (5.5.4) are negligible. This is in agreement with the results obtained at Brookhaven at a blightly higher primary momentum of 4.7 Gev/c (5.1)

The effective mass of a group of particles is defined as the square root of the invariant square of the total momentum 4—vector of the particles. 65.

At 2.03 Gev/c Carmony et al (5.2) observed the charged N*, but did not find a pronounced p —peak, in contrast to the more recent data of .7tp. interactions at 2.6 Gev (5°3) in which the analogue of reaction (5.5.4) is important, The dotted lines in Figs. 5.1 5.3 are the phase space distributions normalized to the histogram area outside the peak regions (1.12 to 1.32

Gev for Fig. 5.1 and 0.66 to 0.84 Gev for 5.3). From the numbers of combinations in the peak regions above these curves one can deduce that about 33% of the reactions (4.1.1) proceed via the p channel (5.5.1) and about 25% via the charged (3/2,3/2) isobar channel (5.5.2). The + + number of events, for which none of the p 7E, IC 9t w2 effective mass values fall into the respective peak regions is 9% of all events.

(C) The P —particle channel. Fig, 5.11 represents the ems angular distribution and Fig. 5.12 the cms momentum distribution of the ic 9t system for the effective mass ranging from 0.66 to 0.84 Gev (the p—region). From Fig.5.11, one sees that the distribution is strongly peaked forwards. In order to separate + — the angular distribution of the p from that of the background it 9c + — combinations the angular distributions of the it 7 systems in the effective mass region on both sides (ie 0.4. <:M < 0.66 and

0.84 < 11,n+ < 1.10 ) of the p region were studied. The average of these distributions was then taken to be the distribution of the

66. background combinations in the p-region and was subtracted from Fig. 5.11. The remaining distribution, which should represent the angular distribution of the p -particles only, was peaked forwards even more strongly than Fig. 5.11. This fact suggests that the p-particles in reaction 5.5.1 are also produced preferentially in peripheral collisions as in 2-prong events (Sections 1.1. and 1.2), and may be described by the one pion exchange (OPE) graph :-

7c7 7E 2 A IC

p p

- The A2 distribution for all'elt combinations from the p-region of Fig. 5.3 is shown in Fig. 5.13, One notices that small momentum transfers are preferred, consistent with the suggestion of the OPE mechanism. As a further check for the OPE mechanism a Treiman - Yang test (5°4) was carried out for those combinations which fall into the p -region of fig. 5.3. The momenta of all particles of an event ware first 67. transformed to the rest system of the incident 7CC. The Treiman—Yang + angle a between the plane defined by the outgoing it and 7t, and that defined by the incoming proton and the outgoing 'X p system was calculated, Since there were two outgoing Tcts, two ass were obtained for each events. Fig. 5.14 shows the distribution of angle a for all + 7: combinations from the p —region of Fig. 5.3 for three different ranges of the momentum transfer, ie for A 2 <20, 20< A2 <60 and A2 > 60, all in the unit of m2It . These distributions should be isotropic if the OPE mechanism is predominant. It can be seen from the figures that all but high A 2 the production is consistent with the OPE mechanism.

Since the p particle is produced preferentially in the forward direction, a study of the angular distribution of its decay products will be of great interest as it is related closely to its spin (5°5) For this reason the distribution of the cosine of the decay angle of the 7t in + - the it it rest system with respect to the direction of the incident iz + (which was also transformed to the 9t rest system) was plotted,

(Fig. 5.15) restricting to A 2 < 20, The figure shows the distributions for the p region (Fig. 5.15b) as well as for the two adjoining regions

(Figs. 5.15a, 5.150). For all three regions one notices the forward backward asymmetry in favour of the going forwards, the asymmetry F-13 parameter A = being F+B 68.

A . 0.32 + 0.13 for 0.4 < M + < 0.66 ± 7C'n Gev

± 0.09 for 0.66< M+ <0.84 Gev A . 0.43 7V7Z

A . 0.24 +— 0.14 for 0.84 < M,K+7— < 9.10 Gev where F and B denote the number of 7c is going forward and backwards respectively.

The ems angular momentum distributions of Figs. 5.8, 5.9 and 5.10 can now be understood through the features of p production and p decay.

The distribution of it and lc— are peaked forwards since the p is produced in the forward direction (Fig. 5.11). However, because the p decays asymmetrically with the 7i preferentially in the forward

IVO direction, and the lc + in the opposite direction, the it ems angular distribution is thus peaked forward more strongly than the ( Figs. 5.24a,b,c and d), and the average •K ems momentum is greater than that of the 71:'+' (Figs. 5.8, 5.9).

(D) The Charged 3/2,3/2 Isobar Channel. The features of the p —production and the p —decay were describeel in the previous section. We now consider the corresponding features of the production and decay of the 3/2, 3/2 isobar e. Fig. 5.16a shows the ems angular distribution for the p systems the effective mass of which are inside the region of Fig. 5.1a (1.12 < Mpg < 1.32). 69.

Fig. 5.16b represents the cms momentum distribution for the same pic + systems. It should be pointed out that this sample of N is much less contaminated by background (N /background = 1.7 from fig 5.1a) than the sample of P—partioles from the peak region of Fig. 5.3 (P/backgvouncl

= 0.9 from Fig. 5.1c). It is seen from Fig. 5.16a that the if is produced strongly backward in the ems. This suggests that the N — production also proceeds via the OPE mechanism. ie through the following diagram :-

This suggestion is supported by the fact that small momentum transfers

(as defined by the above diagram) are preferred (Fig. 5.17). Fig. 5.18 shows the distribution of the Treiman—Yang angle a between the N—P incident and the IC — IC planes in the rest system of the incident ' for three regions of A2 le. < 20, 20 60 p, Since the two izts cannot be distinguished from each other and may therefore be interchanged, there is an ambiguity in the sign of cosa. Hence a is always taken as ranging from 00 to 900. 2 For small A the distribution (Fig. 5.18a) is very nicely isotropic, in favour of the OPE mechanism for N —production. 70. * The decay angular distribution of the proton in the N rest system with respect to the direction of the incident 9t is shown in 2 2 Fig. 5.19 for A < 30 A . There is a noticeable backward peaking, the asymmetry parameter being A = 0.20 + 0,10. Since the proton does not have much velocity in the N:* rest system and since the N moves strongly backward in the ems, the ems angular distribution of the

proton from the N is strongly peaked backward (Fig. 5.20) and therefore

contributes to the strong backward peaking of the overall proton ems angular distribution of Fig. 5.10. The ems momentum distribution of the

proton from N decay is given in Fig. 5.21. The ems angular distribution of the it from N decay (Figs. 5.22), is much more isotropic than the proton distribution, but still slightly peaked backwqrd (A . 0.42 + 0.06). This results from the slight forward decay + of the lt in the N system, and the backward motion of the N in the ems. One may deduce from Fig. 5.22 that the if from the N are responsible for the small backward peak in the overall angular distributio- of Fig. 5.8, just as the if from the pare for the slight forward peak. Fig. 5.23 shows the ems momentum distribution of the 4. from e decay. One notices a strong accumulation of it at rather low momentum.

This is just a kinematic effect of the strong occurrence of isobars, since at a primary momentum of 4 Gev/c the if coming from a p 7G system with an effective mass ranging from 1.12 to 1.32 Gev can have a maximum momentum of only 0.68 Gev/c. (see also section 6.3). 71. (E) The Direct Channel.

After having subtracted from the cms angular distributions of Figs. 5.6, 5.7 and 5,8 the distributions from the p and the isobar decay one ends up with the following situation for the direct channel. The Proton angular distribution is strongly peaked backward, the 9t distribution is JRnti.npic and the W distribution consists of about 0 isotropically distributed and 50% strongly forward peaked 77. This again suggests a peripheral type of interaction for the direct channel: the incident p and 77 keep their original direction whereas the two produced pions are distributed isotropically

52. The Reactions It + p p + 7T7 'At

AND 7< + p n + + 9C- -I- 7e-

(A) Angular and Momentum Distributions,

The cms angular distribution and the cms momentum distribution for each outgoing particle from reactions

7: + p -4 p + 7C + 7C + + (4.1.2)