ELASTIC SCATTERING AND LOW MULTIPLICITIES

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ELASTIC SCATTERING AND LOW MULTIPLICITIES

Ugo Amaldi

To cite this version:

Ugo Amaldi. ELASTIC SCATTERING AND LOW MULTIPLICITIES. Journal de Physique Collo- ques, 1973, 34 (C1), pp.C1-241-C1-259. �10.1051/jphyscol:1973128�. �jpa-00215208�

JOURNAL DE PHYSIQUE Colloque CI, supplgment au nO1O, Tome 34, Octobre 1973, pagecl-241

ELASTIC SCATTERING AND LOW MULTIPLICITIES ugo AMALDI(*)

CERN, Gensve

1. - INTRODUCTION. - The c o n t e n t s of t h e 116 papers which have been submitted t o t h e s e s s i o n I am repor- t i n g on d e f i n e t h e p r e c i s e meaning of t h e o t h e r w i s e r a t h e r vague t i t l e of t h i s c o n t r i b u t i o n . The s u b j e c t s d i s c u s s e d i n t h i s s e s s i o n a r e mainly two-body and quasi-two-body p r o c e s s e s , s t u d i e d from a n "exclusive' p o i n t of view, i n c l u d i n g t h e measurements of t h e most

I t .

~ n c l u s i v e " q u a n t i t i e s , t o t a l c r o s s - s e c t i o n s . The l a - b o r a t o r y energy of t h e p r o j e c t i l e s used i n t h e expe- r i m e n t s goes from 1 GeV t o 1500 GeV. I n t h i s r e p o r t I cannot p r e s e n t s u c h a l a r g e amount of d a t a . However t h e s e s s i o n was s o organized t h a t many t o p i c s a r e very w e l l covered by t h e r e p o r t s prepared by t h e "mini- rapporteurs". I s h a l l t h e r e f o r e touch on most of t h e main s u b j e c t s d i s c u s s e d i n t h e s e s s i o n , b u t with a very d i f f e r e n t a c c e n t , a c c o r d i n g t o whether t h e sub- j e c t i s t r e a t e d by a mini-rapporteur o r n o t . The con- t e n t of t h i s r e p o r t i s a s f o l l o w s .

2.- N o n - d i f f r a c t i v e p r o c e s s e s

2 . 1 . - Charge exchange a t h i g h energy 2.2. - ^{K O} r e g e n e r a t i o n

2 . 3 . - Energy dependence of q u a s i two-body and few-body p r o c e s s e s

2 . 4 . - Understanding quasi-two-body p r o c e s s e s 2.5. - E x o t i c exchanges

3 . - D i f f r a c t i v e p r o c e s s e s

3 . 1 . - E x c l u s i v e d i f f r a c t i o n d i s s o c i a t i o n 3.2. - E l a s t i c s c a t t e r i n g

3 . 3 . - R e a l p a r t s of t h e forward n u c l e a r ampli- t u d e s

3.4.- T o t a l c r o s s - s e c t i o n s

3.5.- Proton-proton a b s o r p t i o n i n t h e ISR ener- gy r a n g e

(*)on l e a v e of absence from P h y s i c s L a b o r a t o r y , I s t i - t u t o S u p e r i o r e d i ani it:, and from Sezione ~ a n i t i , I s t i t u t o Nazionale d i F i s i c a Nucleare, Roma.

S i n c e t h e m i n i - r e p o r t s a p p e a r i n g i n t h e p r o c e e - d i n g s of t h e Conference cover t h e s u b j e c t s l i s t e d above from s e c t i o n 2.1. t o s e c t i o n 3.1. i n c l u d e d , i n t h e f i r s t p a r t of t h i s c o n t r i b u t i o n I s h a l l f r e - q u e n t l y r e f e r t o t h e accompanying r e p o r t s l i m i t i n g myselT t o g e n e r a l o b s e r v a t i o n s and t o p o i n t i n g o u t some r e c e n t experimental r e s u l t s which a r e , i n my opinion, p a r t i c u l a r l y i n t e r e s t i n g . The s u b j e c t s from s e c t i o n 3.2. onwards a r e t r e a t e d i n more d e t a i l .

2. - NON DIFFRACTIVE PROCESSES

2.1.- CHARGE EXCHANGE AT HICJl ENERGY.- Charge ex- change r e a c t i o n s a r e p a r t i c u l a r l y simple from t h e p o i n t of view of t h e quantum numbers exchanged by t h e i n t e r a c t i n g hadrons and a r e t h u s w e l l s u i t e d f o r s t u - dying r e a c t i o n mechanism. While f o r r e c e n t p o l a r i z a - t i o n measurements i n chapge exchange r e a c t i o n s I r e - f e r t o t h e r e p o r t of W. Beusch, I b r i e f l y d i s c u s s new r e s u l t s p r e s e n t e d by a IHEP group working a t S e r - pukhov on t h e r e a c t i o n s :

The forward d i f f e r e n t i a l c r o s s - s e c t i o n s have been measured i n a n e g a t i v e secondary beam of t h e 7 0 GeV Serpukhov a c c e l e r a t o r [I ,2,3,4]. The l i q u i d hydrogen t a r g e t was surrounded by a system of guard c o u n t e r s a l t e r n a t e d with l e a d c o n v e r t e r s , t o s u p p r e s s i n e l a s - t i c p r o c e s s e s and s e l e c t only e v e n t s i n which pho- t o n s ( i n r e a c t i o n s ( 1 ) and ( 2 ) ) and a n t i - n e u t r o n s ( i n r e a c t i o n ( 4 ) ) a r e produced forward. These f o r - ward produced n e u t r a l p a r t i c l e s were d e t e c t e d i n a n o p t i c a l s p a r k spectrometer. I n c a s e of r e a c t i o n i 3 ) t h e t r a j e c t o r i e s of t h e p i o n p a i r s from t h e decay

zi

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1973128

C1-242 U. AMALDI

a r e summarized i n t h e f i r s t f o u r f i g u r e s . I n f i g u r e above 6 GeV/c) g i v e s t h e e f f e c t i v e t r a j e c t o r y p l o t t e d 1 t h e d i f f e r e n t i a l c r o s s - s e c t i o n f o r t h e p i o n charge i n f i g u r e 3 [2].

exchange c r o s s - s e c t i o n ( 1 ) i s p l o t t e d v e r s u s t h e l a - b o r a t o r y momentum, t o g e t h e r w i t h p r e v i o u s r e s u l t s ,

Fig.2. - E f f e c t i v e t r a j e c t o r y o b t a i n e d from t h e d a t a of Fig.].

F i g . 1 . - D i f f e r e n t i a l c r o s s - s e c t i o n f o r t h e charge exchange r e a c t i o n f p -, e n a s measured by V.N.

Bolotov e t a l . [ I ] f o r v a r i o u s v a l u e s of t h e momentum t r a n s f e r t .

The c r o s s - s e c t i o n a t any f i x e d v a l u e of t h e momentum t r a n s f e r t i s w e l l r e p r e s e n t e d by a power law,

==

d t . By f i t t i n g t h e d a t a i n t h e mo- mentum range 6 _i p _i 50 GeV/c , t h e a u t h o r s o b t a i - ned t h e v a l u e s of q t ) p l o t t e d i n f i g u r e 2 . The d a t a s t r o n g l y i n d i c a t e t h a t t h e " e f f e c t i v e " t r a j e c t o r y of t h e exchanged p a r t i c l e , only t h e p i n t h e s i m p l e s t model, i s l i n e a r and h a s s l o p e a ' r ( 0 . 9 7 f 0 . 0 4 ) GeV 2

.

The t r a j e c t o r y c r o s s e s z e r o a t a(o) = ^0.56+A.02

.

A d i f f e r e n t v a l u e f o r t h e i n t e r c e p t i s o b t a i n e d from t h e d i f f e r e n c e between t h e t o t a l <p and xfp c r o s s - s e c t i o n s [ 5 ] by a p p l y i n g t h e o p t i c a l theorem :

a(O) = 0.67i0.04

.

s e d i n tile p a s t . A few of t h e s e have been con- s i d e r e d i n a paper suomitted t o t h e Conf e r e l c e [6].

A s i m i l s r a n a l y s i s a p p l i e d t o t h e d a t ? obtsj.zed by measuring r e a c t i o n ( 2 ) ( t o g e t h e r u i K l w e v i o u s d a t a

F i g . 3 . - E f f e c t i v e t r a j e c t o r y o b t a i n e d by f i t t i n g t h e d a t a of t h e r e a c t i o n K-p -t -qOn i n t h e momentum i n t e r v a l 6 - 5 0 GeV/c [ 2 ]

.

I n t h e s i n g l e p o l e approximation of t h e Regge model t h i s i s t h e A 2 - t r a j e c t o r y . The d a t a i n d i c a t e t h a t it i s s t r o n g l y non-linear below t = -0.5 ~ e ? and c r o s - s e s z e r o around -1 ~ e ? , where t h e minimum of t h e d i f f e r e n t i a l c r o s s - s e c t i o n occurs. T h i s problem must be i n v e s t i g a t e d f u r t h e r .

I n f i g u r e 4 a t h e energy dependence of t h e K - c h a r - ge exchange d i f f e r e n t i a l c r o s s - s e c t i o n a t t z O i s p l o t t e d v e r s u s t h e l a b o r a t o r y momentum [3 1. T h i s c r o s s - s e c t i o n i s r e l a t e d t o t h e d i f f e r e n c e AT of t h e t o t a l c r o s s - s e c t i ~ n s K - ~ and K-n , and from t h e d a t a one o b t l i n s : AG < (9.1+_0.9) p -0.70t0.04 mb . ^(The

e q u a l i t y h o l d s i f t h e forward r e a l p a r t i s n e g l i g i b l e , a s i s i n d i c a t e d by low energy d a t a ) . The e f f e c t i v e t r a j e c t o r y , t o which both p and A2 should c o n t r i b u t e , can be computed from t h e d i f f e r e n t i a l c r o s s - s e c t i o n d a t a i n t h e r a n g e 5 < p < 35 GeV/c and comes o u t

ELASTIC SCATTERING AND LOiV MULTIPLICITIES

t o be a ( t ) = (0.28+-0.04)+ (0.44+-0.16)t

.

Fig.4.- ( a ) Forward d i f f e r e n t i a l c r o s s - s e c t i o n f o r t h e r e a c t i o n K p -t IC0n [3).

( b ) D i f f e r e n t i a l c r o s s - s e c t i o n of t h e r e a c - t i o n p+p + n+n a t 35 GeV/c [4]. A maximum i s c l e a r - l y a p p a r e n t around ( t 1 ^{5 2 G ~}

.

F i g u r e 4b shows t h e a n g u l a r d i s t r i b u t i o n of r e a c - t i o n ( 4 ) o b t a i n e d a t 3 5 GeV/c [4]. The forward narrow peak i s , as usually, a t t r i b u t e d t o p i o n exchange. Note however t h a t a t t h e s e high e n e r g i e s a c l e a r secondary maximum appears. The energy dependence of t h e d i f f e - r e n t i a l c r o s s - s e c t i o n i n d i c a t e s t h a t p and A2 exchan- g e s do n o t g i v e l a r g e c o n t r i b u t i o n s .

For t h e f i r s t time p o l a r i z a t i o n measurements i n K - p

and pp charge exchange have been r e p o r t e d a t t h i s Conference. They a r e d i s c u s s e d i n t h e r e p o r t by \V.

Beusch.

2.2. - ^{K O} REGENERATION. - New p r e l i m i n a r y d a t a on

K O - K0 r e g e n e r a t i o n i n deuterium have been p r e s e n t e d a t

L S

t h i s Conference by two groups. 'Ke University of Massachusetts- Mc G i l l - N o r t h w e s t e r n - P i t t s b u r g h C o l l a b o r a t i o n wor- k i n g a t t h e AGS h a s o b t a i n e d r e s u l t s i n t h e momentwn r a n g e 4 < p < 1 0 GeV/c [7 1. A t Serpukhov t h e B e r l i n - Budapest - Dubna- Prague- Serpukhov- S o f i a Collabora- t i o n [ 8 ] has c o l l e c t e d d a t a i n t h e momentum i n t e r v a l 20 < p < 50 GeV/c . (These experiments a r e b r i e f l y d e s c r i b e d i n t h e r e p o r t by R. Diebold). I n f i g u r e 5 some of t h e r e s u l t s of t h e two experiments a r e p l o t t e d

t o g e t h e r . The q u a n t i t y If-?l/k is t h e madulus of t h e r e g e n e r a t i o n amplitude d i v i d e d by t h e momentum. The two experiments a r e i n good agreement. The Serpukhov experiment g i v e s a good d e t e r m i n a t i o n of t h e phase of t h e r e g e n e r a t i o n amplitude, += -135Oi 4O , which t u r n s o u t t o b e energy independent. Using t h e v a l u e

@=-135' i t i s p o s s i b l e t o r e l a t e , through t h e o p t i - c a l theorem, t h e q u a n t i t y If-? \/k t o t h e d i f f e r e n c e

Fig.5.- P r e l i m i n a r y d a t a p r e s e n t e d a t t h e Conference on K O -t :K r e g e n e r a t i o n i n deuterium. The l i n e s a r e o b t a i n e d from t h e d i f f e r e n c e of t o t a l c r o s s - s e c t i o n s L

ct(K-d) - ct (K+d) a s e x p l a i n e d i n t h e t e x t .

of t o t a l c r o s s - s e c t i o n ct(KOd)

-

.

deuteron has i s o s p i n 0 , i s o s p i n i n v a r i a n c e a l l o w s -,~euteriurn

'. .

one t o w r i t e

The dashed l i n e s i n t h e f i g u r e a r e computed u s i n g t h i s e q u a t i o n and t a k i n g approximately i n t o account t h e e r r o r s on t h e q u a n t i t i e s a p p e a r i n g i n t h e r i g h t - hand s i d e . The agreement i s good. I n c o n c l u s i o n t h e - s e p r e l i m i n a r y d a t a a g r e e w i t h t h e s i m p l e w p o l e exchailge model, i n both t h e phase and energy-depen- dence, a s i n t h e c a s e of r e g e n e r a t i o n i n hydrogen

[lo I.

.

.

\

.

0.4 -

0.3 -

2.3.- ENERGY DEPENDENCE OF QUASI-TIYO-BODY AND FEW- BODY PROCESSES.- Recent i n f o r n a t i o n on n o n - d i t f r a c -

t i v e p r o c e s s e s o b t a i n e d w i t h bubble chambers and w i t h s p e c t r o m e t e r s a r e reviewed i n t h e r e p o r t s by G. O t t e r and R. Diebold r e s p e c t i v e l y . The t h e o r e t i - c a l a s p e c t s a r e d i s c u s s e d by G.A. Ringland and by M. Aguilar-Benitez. I n p r e v i o u s conferences a f u l l r a p p o r t e u r t a l k was devoted t o t h e l a r g e f i e l d of r e a c t i o n mechanism.Since t h i s i s n o t t h e c a s e t h i s

y e w , i n t h i s s e c t i o n I s h a l l l i n i t myself t o sone c o n s i d e r a t i o . l s r e l a t e d t o t h e energy dependence of quasi-two-body and few-body e x c l u s i v e re5,ctiops r e - f e r r i n g t o t h e nccoapanying r e p o r t s f o r t h e d e t a i l e d d i s c u s s i o n .

T c b l e I i s a c o n p i l a t i o n of t h e r e s u l t s p r e s e n t e d c t t h e Conference. A s u s u a l , t h e c r o s s - s e c t i o n of each p r o c e s s i s p a r a m e t r i z e d i n t h e form

Cr s+r l/pn (6

0.2

-

'.,

Cl-244 U. AMALDI

and t h e n-value i s f i t t e d t o t h e d a t a i n a given numbers exchanged i n t h e t-channel. I n t e r e s t i n g r e - momentum range. The i n f o r m a t i o n c o n t a i n e d i n t h e t a - s u l t s on t h e sarne t y p e of c o r r e l a t i o n , b u t observed b l e i s i n agreement with what h a s been known f o r ma- i n e x c l u s i v e few-body p r o c e s s e s , have been p r e s e n t e d ny y e a r s : t h e n-value i s c o r r e l a t e d w i t h t h e quantum by t h e Aachen- Berlin-CERN-London ( 1 . C . ) - v i e n n l -

T a b l e I

Compilation of t h e d a t a p r e s e n t e d a t t h e Conference on t h e energy dependence of quasi-two-body n o n - d i f f r a c t i v e p r o c e s s e s . The momentum-range used i n t h e f i t i s i n d i c a t e d t o g e t h e r with t h e approximate v a l u e of t h e forward s l o p e [ I I I.

R e a c t i o n Dominant Momentum Average s l o p e P a p e r

exchange r a n g e n b ( G ~ v " )

number

(GeV/c and remarks

- 0

x p - t x n I' 5 - 50 1.12 2 .03 b - 9 , forw. d i p 3 57

Gp ⁺ xOAf+ fJ 2 - 1 3 1.6 1 b = l O , f o r w . d i p 180

7 i p ⁺ $n 6 - 5 0 1 . 3 5 i . 0 4 358

$P 3 $A++

*2 2 - 1 9 1 . 5 7 f . 1 5 , forw. d i p 180

K + ~ -t K*OA++ x 4 . 6 - ^{1 6 1.68 +- .08} fozw. peak, f l a t > .5 256

p n -+ A++&- x 3 - 9 0 1 . 4 5 2 . 2 2 forw. peak 326

- ⁺ z++ ++

P P A n 3 - 6 1.09 f .10 b - 12 , f l a t t e n s 254

n-P * P-P *, X 4 - 4 0 1.87 .09 b - 8 44

n+n w p B , ( p ) 2 . 5 - 1 3 2.4 b = 3 , small forw. d i p 247

K+N -t p ~ * O ( 8 9 0 ) A, c 3 - 5 3.2 +_ .5 backward K* peak 292

C o l l a b o r a t i o n [12]. They s t u d i e d f ive-body f i n a l s t a - t e s produced i n K-p i n t e r a c t i o n s a t 6 , 1 0 and 1 6 GeV/c

Each event was c l a s s i f i e d a c c o r d i n g t o which p a r t i - c l e s go "forward" and which "backward" i n t h e c e n t e r - of-mass- system. T h e r e e x i s t 3 0 d i f f e r e n t combina- t i o n s f o r t h e r e a c t i o n s under study. They were named

" s e c t o r s " . The number of e v e n t s i n each s e c t o r was d i v i d e d by t h e r e l e v a n t phase s p a c e t o remove kinema- t i c e f f e c t s . I t was found t h a t t h e d i s t r i h t i o n ofpopu-

l a t i o n s among t h e s e c t o r s c a n be understood by t h e hy- p o t h e s i s t h a t "backward" and "forward" moving p a r t i - c l e s a r e produced a t t h e two o p p o s i t e v e r t i c e s of a simple exchange diagram. For i n s t a n c e , t h e s e c t o r s i n which vacuum quantum nymberscail be exchanged a r e i n -

deed more h e a v i l y populated t h a n s e c t o r s i n which only s t r a n g e bosons can be exchanged. The c r o s s - s e c t i o n s f o r each t y p e of exchange have t h e momentum

dependence shown i n f i g u r e 6.

a POMERON c SrO MESON

A BARYON

.

I I I I I I I I 1 I I I

6 10 16

q0,, ^G"+

Fig.6.- Energy dependence of t h e c r o s s - s e c t i o n s f o r t h e five-body r e a c t i o n s of e q . ( 7 ) a n a l y s e d w i t h t h e

"binary l o n g i t u d i n a l phase space a n a l y s i s f ' d e s c r i b e d i n t h e t e x t . I n drawing t h e f i g u r e f i v e " s e c t o r s "

have been chosen which correspond t o d i f f e r e n t ex- changed quantum numbers ( p a p e r n080).

ELASTIC SCATTERING AND LOW MULTIPLICITIES C1-245

I n T a b l e 11 t h e average n-values o b t a i n e d from t h i s a n a l y s i s a r e compared w i t h t h e average n-value from two-body r e a c t i o n s , w i t h t h e i n t e r e s t i n g c o n c l u s i o n t h a t t h e energy dependence of t h e c r o s s - s e c t i o n s i s very s i m i l a r when t h e exchange of t h e same quantum numbers i s allowed.

T a b l e I1

C o r r e l a t i o n between quantum number exchanges and n- v a l u e s i n a five-body p r o c e s s and i n quasi-two-body r e a c t i o n s [12]

Type of Average v a l u e of Average v a l u e of exchange n from t h e analy- n from 2-body

s i s of - t h e r e a c - r e a c t i o n s t i o n K p ^-t NKnnn

Pomeron 0. 2 0.2

Meson 1.3 2.

S t r a n g e Meson 2.2 2.5

Baryon 3 . 3 4

T h i s a n a l y s i s s u p p o r t s t h e i d e a t h a t i n t h i s energy range t h e dynanics of few-body, quasi-two-body and two-body p r o c e s s e s a r e very s i m i l a r . Moreover, i n s p i - t e of t h e r e l a t i v e l y small r a p i d i t y range a v a i l a b l e a t t h e s e e n e r g i e s , t h e p a r t i c l e s p r o d u c e d i n t h i s few-body p r o c e s s a t each of t h e two v e r t i c e s of an exchange dia- gram do n o t g e t confused, but c o s t l y keep t h e d i r e c - t i o n of t h e i n c o n i n g p a r t i c l e , s o t h a t hadrons produ- ced i n t h e " u ~ p e r " and "lower" v e r t i c e s mainly appear a s forward and backward moving p a r t i c l e s . Probably t h e s e q u a l i t a t i v e f e a t u r e s r r e p a r t i a l l y due t o t h e c l u s t e r i n g of t h e produced p a r t i c l e s i n r e s o n a a c e s , but s t i l l t h e y r e v e a l i n t e r e s t i n g a s p e c t s of t h e under- l y i n g dynamics.

2.4.- UNDERSTANDING QUASI-TWO-BODY PROCESSES.- The p r e s e n t s t a t u s of t h i s problem i s reviewed i n t h e r e - p o r t by G.A. Ringland. S i n c e t h e exchange of Regge p o l e s a l o n e does n o t e x p l a i n some very b a s i c f e a t u r e s of t h e d a t a , c o r r e c t i o n s have t o be i n t r o d u c e d t o mo- d i f y t h e simple p i c t u r e . Many ways of i n t r o d u c i n g t h e s e ( a b s o r p t i o n ) m o d i f i c a t i o n s have been devised,

b u t none seem t o be a s y e t g e n e r a l l y accepted, s o t h a t a t p r e s e n t t h e o p i n i o n s of t h e e x p e r t s on t h e s t a t u s o f

t h e f i e l d a r e q u i t e v a r i e d [13]. A major d i f f i c u l t y connected with t h e s e m o d i f i c z t i o n s , which s r e expected on t h e o r e t i c a l grounds, i s t h a t t h e y c?-use t h e d i f - f r a c t i o n peaks t o s h r i n k l e s s r a p i d l y w i t h energy t h a n i s observed experime:ltally ( s e e Ringland r e p o r t ) . Given t h i s s i t u a t i o n , i t i s n a t u r a l t h a t t h e models develop i n c l o s e connection w i t h t h e a v a i l a b i l i t y of new d e t a i l e d experimental i n f o r m a t i o n , l o s i n g

a p a r t of t h e i r p r e d i c t i v e power. A t t h e same time t h e q u a l i t y of t h e d a t a has g r e a t l y improved and more and more experiments a r e s u f f i c i e n t l y complete

t o g i v e i n f o r m a t i o n d i r e c t l y on t h e amplitudes and t h e i r i n t e r f e r e n c e s .

To i l l u s t r a t e t h e s e p o i n t s I have chosen two exam- p l e s . F i g u r e 7 c o n t a i n s some of t h e r e s u l t s [14] ob- t a i n e d w i t h t h e Argonne E f f e c t i v e Mass Spectrometer on t h e r e a c t i o n s

1

0

600 700 800 900

M n L MeV

Fig.7.- pw i n t e r f e r e n c e e f f e c t s a s measured by t h e Argonne E f f e c t i v e Mass Spectrometer. The cross-sec- t i o n combination p l o t t e d on t h e v e r t i c a l a x i s i s such a s t o s e l e c t n a t u r a l - p a r i t y exchange. The h o r i - z o n t a l a x i s i s t h e mass of t h e nn system.

The i n t e r f e r e n c e between p- and w p r o d u c t i o n i s very c l e a r l y seen t o change s i g n i n p a s s i n g from one t o t h e o t h e r r e a c t i o n , and from t h i s i t i s p o s s i b l e t o e x t r a c t t h e r e l a t i v e phase of t h e p- and w-produc- t i o n amplitudes. The i m p l i c a t i o n s f o r exchange mecha- nisms a r e d i s c u s s e d i n t h e r e p o r t by R. Diebold.

Mere it i s enough t o s t r e s s t h e p r e s e n t t r e n d : mea- surements of i n t e r f e r e n c e terms a r e becoming s t a n - d a r d and, t o g e t h e r w i t h amplitude a n a l y s i s , t h i s r e s u l t s i n s t r i n g e n t t e s t s f o r t h e dynamical models.

To i l l u s t r a t e t h e way i n which models adapt t o t h e changing experimental s i t u a t i o n l e t us c o n s i d e r t h e extreme c a s e of a r e a c t i o n which i s t h e o r e t i c a l l y d i f f i c u l t t o understand : backward pion-nucleon s c a t - t e r i n g , which proceeds through baryon exchange. F i - gure 8 a shows t h e p o l a r i z a t i o n p r e d i c t e d by v a r i o u s models b e f o r e t h e llleasurement by L. Dick e t a l . [15]

a t 6 GeV/c. A f t e r t h e measurement t h e m o d e l s have been adapted t o t h e experimental i n f o r m a t i o n and a r e now i n reasonably good agreement with more r e c e n t d a t a

[16] o b t a i n e d a t 4 GeV/c (Fig.8b).

x+p,px+ ( 4 G e V / C )

Fig.8.- P o l a r i z a t i o n i n backward pion-nucleon s c a t - t e r i n g . Model p r e d i c t i o n s ( a ) b e f o r e t h e experiments, (b) a f t e r t h e experiments. Note t h a t some of t h e c u r - ves of f i g u r e b a r e amplitude a n a l y s e s which make u s e of t h e d a t a . The p o i n t s r e p r e s e n t t h i s y e a r ' s d a t a from t h e CERN- T r i e s t e C o l l a b o r a t i o n [16].

2.5.- EXOTIC EXCHANGES.- Recent r e s u l t s on e x o t i c exchanges a r e d i s c u s s e d i n t h e r e p o r t by C.W. Akerlof and c a n be summarized a s follows. The p r e s e n t d a t a show t h a t t h e c r o s s - s e c t i o n s of e x o t i c baryon exchan- ge r e a c t i o n s f a l l very r a p i d l y w i t h energy up t o a- bout 5 GeV/c. New d a t a p r e s e n t e d a t t h i s Conference [17] i n d i c a t e t h a t t h e d i f f e r e n t i a l c r o s s - s e c t i o n of t h e e x o t i c meson exchange r e a c t i o n x-p + K'C- shows a marked change of behaviour f o r momenta l a r g e r than 3 - 4 GeV/c ( t h e n-value d e c r e a s e s from about 10 t o about 2 ) . T h i s could be due t o t h e domination at h i g h energy e i t h e r of double p a r t i c l e exchange o r of t h e exchange of a n e x o t i c meson s t a t e with two u n i t s of charge. T h i s e f f e c t i s not seen i n t h e r e a c t i o n K-P + X+C' [17,18], probably because i n t h i s p r o c e s s t h e domination of s-channel resonances s t r e t c h e s out t o h i g h e r energy.

3 . - DIFFRACTIVE PROCESSES.

3.1.- EXCLUSIVE DIFFRACTION DISSOCIATION.- The t h e - o r e t i c a l and experimental a s p e c t s of t h i s s u b j e c t a r e reviewed i n t h e r e p o r t s by K. Zalewski and H. L u b a t t i r e s p e c t i v e l y . I s h a l l mention o n l y t h r e e r e c e n t expe- r i m e n t a l o b s e r v a t i o n s which i n d i c a t e t h a t t h e pheno- menon of s i n g l e d i f f r a c t i v e d i s s o c i a t i o n s t i l l ap- p e a r s w i t h t h e same well-known c h a r a c t e r i s t i c s : ( i ) when t h e ensrgy i s i n c r e a s e d , ( i i ) when enhancements of l a r g e r mass a r e produced and ( i i i ) when t h e d i s s o - c i a t i o n of s t r a n g e hadrons i s s t u d i e d .

( i ) F i g u r e 9 b snows t h e energy dependence of t h e

- - - +

c r o s s - s e c t i o n f o r t h e r e a c t i o n n p -t x 1~. x p . ^The

205 GeV p o i n t h a s been o b t a i n e d a t NAL [19].

Fig.9.- ( a ) Compilation of t o t a l x-p e l a s t i c c r o s s - s e c t i o n d a t a . High energy d a t a have been o b t a i n e d a t Serpukhov [21] and a t NAL [20]. ( b ) T o t a l c r o s s - s e c t i o n f o r t h e r e a c t i o n x-P ^-+ 7 ~ - 7 ~ - % + ~

.

I t i s c l e a r l y s e e n t h a t between 20 GeV and 200 GeV t h e c r o s s - s e c t i o n f a l l s slowly, a s expected f o r a d i f f r a c t i v e p r o c e s s , but t h e d e c r e a s e i s s l i g h t l y s t e e p e r t h a n what i s observed f o r t h e e l a s t i c c r o s s - s e c t i o n ( F i g . 9 a ) .

( i i ) F i g u r e 10 shows a new enhancement observed by t h e S e a t t l e - B e r k e l e y C o l l a b o r a t i o n [22] i n t h e s t u - dy of t h e r e a c t i o n r-d + {r-x'd . The t h r e e s t a n - dard d e v i a t i o n bump a t 1.96 GeV ( c a l l e d A ) h a s bee2

4

shown t o be a s s o c i a t e d w i t h g x f i n a l s t a t e s , much a s t h e A i s a s s o c i a t e d t o px , t h e A t o f n and t h e ^Q

1 3

t o ~ ~ ( 8 9 0 ) K The a s s o c i a t i o n of a w e l l e s t a b l i s h e d resonance w i t h a p i o n i n d i f f r a c t i o n d i s s o c i a t i o n a p p e a r s once more a s a g e n e r a l f e a t u r e .

( i i i ) P r e l i m i n a r y r e s u l t s have been r e c e n t l y ob- t a i n e d on t h e r e a c t i o n

C - + n u c l e u s -t B*- + a n y t h i n g J.

no;

ELASTIC SCATTERING AND LOW MULTIPLICITIES

i s t h e accuracy of t h e experiments.

Fig.10.: Mass-of t h e t h r e z pion system i n t h e r e a c - t i o n x d ⁺ x x x+d (paper 11'376). The enhancement

" A ~ " i s a s s o c i a t e d with g n f i n a l s t a t e s , but t h e ob- s e r v e d number of g-mesons i s n o t s u f f i c i e n t t o ex- p l a i n t h e f u l l observed bump.

I20

IGO

t Z

EO-

UI t- Z W > 6C- W LL 0

5 ^40-

m Z

The experiment was performed a t t h e AGS with a 24.6 GeV/c C - beam [23]. I n t h e d a t a t h e r e i s no evidence

f o r narrow bumps in the Lo 7; mass spectrum, while a wide en- hancemeat i s observed a t the threshold of the A ?l system. ?his e f f e c t c a n be q u a l i t a t i v e l y reproduced by assuming t h a t i t i s due t o a Deck e f f e c t . ( T h i s may be an a c c i - d e n t because t h e Deck mechanism h a s d i f f i c u l t i e s i n e x p l a i n i n g many of t h e well-known d i f f r a c t i o n pheno- mena.) However, independent r ~ f t h e dynamical assump- t i o n s , t h e s e p r e l i m i n a r y d a t a suggest t h a t s t r a n g e baryons a l s o t e n d t o d i s s o c i a t e i n t h r e s h o l d enhan- cements.

A l a s t remark about f a c t o r i z a t i o n i n d i f f r a c t i o n

+

s c a t t e r i n g . I s o s p i n a n a l y s e s of t h e r e a c t i o n x-p ⁺ IC (N IC) a t 8 and 16 GeV/c (Aachen - B e r l i n - Bonn - CERN -

Notre D a m e - P e n n s y l v a n i a - T o h o k u C o l l a b o r a t i o n , paper n0237) and of r e a c t i o n s p p -t N(Nx) a t 12 and24GeV/c ( Bonn-Ham'ourg -Mtimhen Collatorat~on, paper n0267, and Weizmann- Technion C o l l a b o r a t i o n , paper n0326) a l l o w t h e d e t e r -

mination of t h e c r o s s - s e c t i o n s d x+ n(N ~ x) ] and

~ N + NN(Nx) ] due t o i s o s p i n z e r o exchange w i t h pro- d u c t t o n of t h e (Nx) system i n t h e i s o s p i n 1/2 s t a t e . The f a c t o r due t o t h e v e r t e x I C + n and N + N c z n c e l s i n t h e r a t i o of t h e s e c r o s s - s e c t i o n s t 9 t h e e l a s t i c c r o s s - s e c t i o n s HICN + n N > and C(PYN + NN) and v a l u e s independent of t h e n a t u r e of t h e incoming p a r t i c l e and of i t s energy a r e expected i f f a c t o r i z a t i o n ap- p l i e s . The t a b l e a p p e a r i n g i n L u b a t t i ' s r e p o r t shows t h a t t h i s i s indeed t h e c e s e w i t h i n r\r20%, which

3.2. - ELASTIC SCATTERING

3 Z

I

0.4 0.8 1.2 1.6 2.0 2.4 2.8

h l ( 3 a ) GeV

I A I I I I I '

1.10 a-d- a + ~ - a - d

3.2.1.- D i f f r a c t i o n Region ( I t \ < 0.5 Ge?).- T h r e e main problems e x i s t i n forward e l a s t i c s c a t t e - r i n g . They r e f e r t o ( i ) t h e shape of t h e d i f f r a c t i o n peak ; ( i i ) t h e energy dependence of t h e forward s l o p e and ( i i i ) t h e p o s i t i o n and energy dependence of t h e c r o s s - o v e r p o i n t , i. e. of t h e momentum t r a n s - f e r / ^tc \ a t which t h e d i f f e r e n t i a l c r o s s - s e c t i o n f o r t h e s c a t t e r i n g of n e g a t i v e p a r t i c l e s on p r o t o n s e- q u a l s t h e v a l u e f o r p o s i t i v e p a r t i c l e s [lo].

The d i f f r a c t i v e peak i n proton-proton s c a t t e r i n g d e f i n i b e l y shows, i n t h e ISR energy r a n g e , a change of s l o p e around It / = 0.15 Ge? [24,10j. A t a much lower energy ( 3 5 p < 6 GeV/c) c a r e f u l measurements performed w i t h t h e Argonne e f f e c t i v e mass spectrome- t e r [25] on t h e e l a s t i c p r o c e s s e s xip and Kip f o r

I t \ > 0.03 G ~ do not r e v e a l any e f f e c t of t h i s V ~ s o r t . The same c o n c l u s i o n has been reached by Dzierba e t a l . [26] who measured xmp e l a s t i c s c a t t e r i n g a t 14 GeV/c i n t h e range of momentum t r a n s f e r s 0.05 ( t 5 0.78 Gev2 . Combining t h e s e r e s u l t s with t h e da- t a of Foley e t a l . [26] f o r It\ 5 0.05 G ~ Vt h e r e ~ i s however an i n d i c a t i o n of a change of t h e s l o p e of about 2 G ~ v - ~ around / t ( = 0.05 Ge? [27].

Two groups working a t Serpukhov have p r e s e n t e d new measurements of t h e forward s l o p e i n {p e l a s t i c s c a t t e r i n g . The r e s u l t s appear i n f i g u r e 11.

- I SEATTLE- ^{IS GeV/c} BER KELEY

MASS ( ~ + a - a - ) 1836 EVENTS

F i g . 11. - Forward s l o p e of 7~-p e l a s t i c s c a t t e r i n g . The new p o i n t s have been obtained by a Serpukhov

[21] ~ n d by t h e IHEP - ^{J I N R} - UCLA C o l l a b o r a t i o n 281 I n r e f . [21] t h e e x p r e s s i o n dC/dt a e x p ( - b t )

T O U "

i s f i t t e d t o t h e d a t a i n t h e momentum t r a n s f e r r a n g e 0.07 6 \ t \ 6 0.4 Gev2

.

Jv\

1

7

-

o LASINSKI el AL X CERN-IHEP

m IHEP- JINR-UCLA (1973) A IHEP (1973)

C1-248 U. AMALDI

By themselves t h e s e r e s u l t s i n d i c a t e t h a t t h e np

d i f f e r e n t i a l c r o s s - s e c t i o n does not s h r i n k a p p r e c i a - b l y i n t h e momentum r a n g e 3 0 - 5 0 GeV/c. However i f one combines them w i t h lower energy d a t a t h e r e i s a c l e a r i n d i c a t i o n of s h r i n k a g e .

Forward s l o p e s i n neutron-proton s c a t t e r i n g have been p u b l i s h e d t h i s y e a r by Beznogikh e t a1. [30]. I n t h e experiment a deuterium gas j e t i s used a s t a r g e t f o r t h e p r o t o n s c i r c u l a t i n g i n t h e Serpukhov a c c e l e - r a t o r . The r e s u l t s appear i n f i g u r e 12. Within l a r g e e r r o r s , i n t h e momentum r a n g e s t u d i e d t h e neutron- p r o t o n s l o p e e q u a l s t h a t measured i n proton-proton s c a t t e r i n g .

10 100 s ( G ~ v * ) F i n a l r e s u l t s of t h e NAL j e t experiment by t h e USSR-

c

10 100 riment s o l i d s t a t e c o u n t e r s d e t e c t e d l a r g e a n g l e pro- t o n s r e c o i l i n g from a hydrogen j e t t a r g e t t r a v e r s e d

Tab

scattering [30]. The dashed line represents the beha- and t h e i n c i d e n t p r o t o n energy v a r i e d between 8 and v i o u r of t h e proton-proton s l o p e . 400 GeV. The r e s u l t s a r e shown i n f i g u r e 13 t o g e t h e r

Fig.13.- Compilation of measurements of t h e "forward" ( I t / ^c 0.12 Ge?) s l o p e of t h e proton-proton e l a s t i c s c a t t e r i n g c r o s s - s e c t i o n [24,31,32]. I n comparing t h e v a r i o u s experiments i t s h o u l d Be remembered t h a t , w h i l s t t h e ISR e r r o r s a l r e a d y c o n t a i n t h e s y s t e m a t i c uncertainties, Bartenev e t a l . quote a s y s t e m a t i c norma- l i z a t i o n u n c e r t a i n t y equal a t a l l e n e r g i e s Ab=+a,2 G e r 2 a n d Beznogikh e t a l . have A b z t 0 . 3 G ~ V - ? T h e dashed l i n e b z 8 . 3 2 + 2 a ' I n s f i t s t h e d a t a above s ~ 7Gev2 ( e x c e p t f o r the high energy Sergukhov p o i n t s ) with 5

a ' = 0.275 G ~ v - ~ . The e s t i m a t e d e r r o r i s Aa'= +_0.02 G ~ v - ~ .

ELASTIC SCATTERING AND LOW MULTIPLICITIES

w i t h p r e v i o u s measurements,mainly o b t a i n e d a t Ser- pukhov and a t t h e ISR. Above s = 75 G ~ t h e d a t a V ~ c a n b e w e l l f i t t e d with l i n e a r dependence i n I n s

.

However i t must be noted t h a t below s e 3 0 f3ev2 t h e forward s l o p e d r o p s very r a p i d l y , hence a s i g n i f i - c a n t change i n t h e behaviour occurs between 3 0 2nd 5 0 GeV 2

.

A c c u r a t e i n f o r m a t i o n on t h e cross-over phenomenon i s a v a i l a b l e a t r e l a t i v e l y low e n e r g i e s and comes mainly from t h e f i n a l a n a l y s i s of t h e d a t a of t h e Argonne E f f e c t i v e Mass Spectrometer [25 ] and from a K'P experiment performed a t SLAC [33 1. A s i n d i c a t e d by t h e r e s u l t of t h e p r e l i m i n a r y a n a l y s i s [lo], f o r each of t h e t h r e e e l a s t i c s c a t t e r i n g p r o c e s s e s < p , + xfp and p'p t h e cross-over p o i n t t does not vary

i n t h e momentum range 3 5 p ( 6 GeV/c. The d i f f e - r e n c e of t h e p a r t i c l e and a n t i p a r t i c l e d i f f e r e n t i a l c r o s s - s e c t i o n s i s mainly determined by t h e imaginary p a r t of t h e non-clip a m p l i t u d e w i t h c h a r g e con:dga- t i o n C = -1 i n t h e t-channel. The constancy w i t h e n e r - gy of t h e c r o s s - o v e r p o i n t t h e n i m p l i e s t h a t t h e e f - f e c t i v e r a d i u s of t h e s o u r c e of t h i s a m p l i t u d e , which i s e s s e n t i a l l y p e r i p h e r a l , does n o t vary with energy.

3.2.2.- I n t e r m e d i a t e and l a r g e momentum t r a n s f e r s . - T h i s y e a r t h e Cornell-BNL-Northeastern Collabora- t i o n [34] and t h e CERN - E c o l e P o l y t e c h n i q u e - Orsay -

Stockholm C o l l a b o r a t i o n [35] have completed t h e expe-

C

r i m e n t s on 7c-p and Kip e l a s t i c s c a t t e r i n g . Some of t h e d a t a a r e p r e s e n t e d i n f i g u r e s 14 and 15.

The $p c r o s s - s e c t i o n s show t h e well-known d i p s and s t r u c t u r e s a t It ( = 0.8 , 2 . 5 , 5 G ~ V ' and i n t h e back- ward d i r e c t i o n . The f l u c t u a t i o n s i n l a r g e a n g l e s c a t - t e r i n g a t 5 GeV/c and t h e r a p i d energy v a r i a t i o n of t h e forward and backward cross-sections a s a f u n c t i o n of energy have been i n t e r p r e t e d a s evidence f o r E r i c - s o n f l u c t u a t i o n s (36 3.

The K + - ~ d i f f e r e n t i a l c r o s s - s e c t i o n of f i g u r e 15 has much l e s s s t r u c t u r e , a s expected f o r a n e x o t ~ c channel.

The backward peak of t h e r e a c t i o n K+p ⁺ p ~ + s h r i n k s w i t h energy i n agreement w i t h what i s expected f o r t h e exchange of t h e A, $ t r a j e c t o r y , which i s b e l i e - ved t o be t h e dominant baryon exchange i n t h i s pro- c e s s [35].

I n t h e range 5 - 10 GeV/c both t h e x'p and t h e ~ ' p e l a s t i c c r o s s - s e c t i o r s at 9 0 ° i n t h e c e n t e r of mass d e c r e a s e approximately a s s -(8*1)

[35]. These power laws can be understood i n t h e framework of models which c o n s i d e r l a r g e a n g l e s c a t t e r i n g a s due t o t h e i n t e r a c t i o n of t h e p o i n t - l i k e c o n s t i t u e n t s of t h e ha- drons [37] .

F i g . 14.- The full, a n g u l a r d i s t r i b u t i o n of n p e l a s t i c t s c a t t e r i n g a t 10 GeV (CERN-Ecole P o l y t e c h n i q u e - O r - s a y - Stockholm C o l l a b o r a t i o n [35]). The d a t a of t h e Cornell-BNL-Northeastern C o l l a b o r a t i o n at 13.8 GeV/c

\34 1 cover t h z range ( t 1 5 4 . 5 G ~ V ' f o r n and t / ⁵ 3.8 GeV f o r nt and a r e i n good agreement with t h e p o i n t s shown i n t h e f i g u r e .

K + ~ - K + ~

1

m10 GeV 013.8 GeV I

Fig.l5..- K+P e l a s t i c s c a t t e r i n g . The b l a c k s q u a r e s a t 10 GeV/c a r e due t o t h e CERN- Ecole P o l y t e c h n i q u e - Orsay - Stockholm C o l l a b o r a t i o n [35] w h i l e t h e open

s q u a r e s r e p r e s e n t t h e d a t a of t h e BNL-Cornell- N o r t h e a s t e r n C o l l a b o r a t i o n [34] a t 13.8 GeV,

C1-250 U. AMALDI

Neutron-proton e l a s t i c s c a t t e r i n g h a s been measu- r e d by t h e CERN - K a r l s r u h e C o l l a b o r a t i o n from 1 0 t o 24 GeV/c and i n t h e range 0.06 It 1 3 G ~ [38]. V ~ I n t h i s It \-range t h e neutron-proton c r o s s - s e c t i o n h a s been found t o be very s i m i l a r t o t h e correspon- d i n g proton-proton c r o s s - s e c t i o n , i n agreement with p r e v i o u s r e s u l t s a t 24 GeV/c [38].

The f i n a l r e s u l t s of t h e ISR experiment of t h e

Aachen- CERN - G e n o v a - H a r v a r d - T o r i n o (ACGHT) C o l l a - b o r a t i o n a r e shown i n f i g u r e 16. I n t h i s experiment t h e momenta of t h e e l a s t i c a l l y s c a t t e r e d p r o t o n s a r e measured by m a g n e t c s t r i c t i v e chambers through t h e i r d e f l e c t i o n i n magnetic f i e l d . I t i s t h u s p o s s i b l e t o d e t e c t proton-proton e l a s t i c e v e n t s a l s o a t l a r g e momentum t r a n s f e r s , i n s p i t e of the l a r g e background of i n e l a s t i c events.

Fig.16.- Angular d i s t r i b u t i o n of proton-proton e l a s t i c s c a t t e r i n g a t t h e f o u r t y p i c a l center-of-mass e n e r g i e s of t h e I S R . S i n c e t h e a p p a r a t u s covers a f i x e d angle i n t h e c.m. system ( 2 0 - 1 0 0 mrad), t h e measured range of momentum t r a n s f e r s i n c r e a s e s w i t h t h e beam momenta.

The d i f f e r e n t i a l c r o s s - s e c t i o n shows a c l e a r mini-

mum a t It 1 ^Z 1.4 G ~ V ' s u g g e s t i n g a d i f f r a c t i o n pheno- l ' menon a s s i m p l e s t i n t e r p r e t a t i o n . These d a t a w i l l b e Po

f u r t h e r d i s c u s s e d i n s e c t i o n 3.5. .

3.2.3.- P o l a r i z a t i o n i n e l a s t i c s c a t t e r i n g . - Recent measurements of t h e p o l a r i z a t i o n and of t h e s p i n r o t a - t i o n parameter i n e l a s t i c s c a t t e r i n g a r e reviewed i n 16'

t h e r e p o r t by W. Beusch. I n f i g u r e 17 p o l a r i z a t i o n d a t a a t f i x e d t i n K-p and x-p e l a s t i c s c a t t e r i n g a r e p l o t t e d v e r s u s s .

'"0 40 ; o ' r b W d o d ;o ;o ;o 'rbo,

s (GOV? s(GeV)

6-10 -16 (GeV/c) - CERN-ORSAY- PlSA Fig.17.- Compilation of d a t a on t h e average p o l a r i z a - LO ( GeV/c) - IHEP -1TEF- JINR-SACLAY t i o n i n K - ~ and n p e l a s t i c s c a t t e r i n g f o r some se-

l e c t e d v a l u e s of t h e momentum t r a n s f e r . The new d a t a a t 40 GeV/c a r e due t o IHEP - ^ITEF - ^{J I N R} - S a c l a y C o l l a - b o r a t i o n [39].

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