HIGH TRANSVERSE MOMENTUM PROCESSES

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HIGH TRANSVERSE MOMENTUM PROCESSES

J. Bjorken

To cite this version:

J. Bjorken. HIGH TRANSVERSE MOMENTUM PROCESSES. Journal de Physique Colloques, 1973, 34 (C1), pp.C1-385-C1-399. �10.1051/jphyscol:1973153�. �jpa-00215233�

JOURNAL DE PHYSIQUE Colloque Cl, suppl6ment au nOIO, Tome 34, Octobre 1973, pageC1-385

HIGH TRANSVERSE MOMENTUM PROCESSES J.D. _BJORKEN

S t a n f o r d L i n e a r A c c e l e r a t o r C e n t e r

The most common s t r o n g - i n t e r a c t i o n and even e l e c - trornagnetic phenomena a r e c h a r a c t e r i z e d by low mean t r a n s v e r s e momentum ((PL) <

*

A P I

d a r y hadrons. Yet most of t h e a v a i l a b l e phase-space i s found elsewhere. F i g u r e 1 shows two d i f f e r e n t maps o f t h e phase-space a p p r o p r i a t e t o 30+30 GeV ISR

Fig.1 a ) Peyrou p l o t f o r 3 0 + 3 0 GeV explored. b) The same, w i t h pl and r a p i d i t y y pp c o l l i s i o n s a t t h e x l o g t a n I R , w i t h a n i n d i c a t i o n of t h e t e r r i t o r y t h u s f a r

- 8

c o n d i t i o n s , along w i t h a rough s k e t c h of t h e t e r r i - t o r y now explored. These e x p l o r a t i o n s , a l o n g w i t h o t h e r s c a r r i e d out a t NAL , a r e q u i t e new, and extremely i n t e r e s t i n g . T h i s review w i l l emphasize t h e t h e o r e t i c a l p e r s p e c t i v e s , inasmuch a s t h e summary of t h e p a r a l l e l s e s s i o n s c o v e r s w e l l t h e experimen- t a l s i d e [1,2]. T h i s should not obscure t h e f a c t t h a t t h e r e a l news i s e x p e r i m e n t a l r e s u l t s not theo- r e t i c a l s p e c u l a t i o n . I w i l l cover t h e f o l l o w i n g to- p i c s :

1.- S i n g l e - p a r t i c l e i n c l u s i v e hadron s p e c t r a a t high p

1 '

2

.-

l e p t o n p a i r s , along with l i m i t s on production of 'W , ^{Z O} , and o t h e r massive o b j e c t s . 5.- M u l t i p l e c o r e s and high-p phenomena a t s t i l l

I h i g h e r e n e r g i e s .

1.- INCLUSIVE HADRON SPECTRA.

1.1.- SCALING BEHAVIOR.- The observed spectrum of x o ' s a t eY- 90° , a s measured [ I ] by t h e CERN- Columbia-Rockefeller group a t 53 GeV a t t h e ISR, p r o v i d e s t h e highest-energy, highest-pl hadron spec- trum i n e x i s t e n c e . The o b s e r v a t i o n s show immediately:

(1) The y i e l d i s much l a r g e r t h a n a n e x t r a p o l a - t i o n based on t h e Hagedorn s t a t i s t i c a l model ;

( 2 ) The y i e l d i s much l a r g e r (about 10 4 ) t h a n what i s expected from photon exchange ( F i g u r e 2 )

Fig.2

-

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1973153

C1-386 J. D. BJORKEN

d e s p i t e t h e f a c t t h a t t h e photon-exchange c o n t r i b u - I ~ : . ~ . d 3 0 / d d tgon o n l y f a l l s a s a power of

pl , roughly p;4

.

T h i s s t r o n g l y s u g g e s t s t h a t t h e o r i g i n of t h e pheno- menon i s hadronic i n nature.

The expected behaviour o f t h e hadron i n c l u s i v e d i s -

t r i b u t i o n produced by t h e photon exchange mechanism 10 - 28

i s g i v e n [21 by dimensional a n a l y s i s :

where F i s o f o r d e r a 2

.

CM 90° , t h e experiments show t h a t t h e exponent 4 should b e r e p l a c e d approximately by 8 , a s suggested theo-

r e t i c a l l y by Blankenbecler, Brodsky and Gunion [61. . 2 .4 -6 2 ~ ~ 1 6

T h i s i s shown by t h e CCR group i n t h e i r c o n t r i b u - t i o n . The b e s t t e s t s of any s c a l i n g behaviour a r e a t t h e h i g h e s t e n e r g i e s and pL , i n o r d e r t h a t any low pL o r low s backgrounds a r e not p r e s e n t , and t h e r e f o r e t h e CCR d a t a p r o v i d e s t h e b e s t t e s t . Their e s t i m a t e d e r r o r on t h e power of

p I i s s m a l l , ,< 1 and e q u a t i o n (1.1) a p p e a r s untenable. L e t u s assume t h e exponent 8 , and t h e n p l o t t h e f u n c t i o n

f o r 8 % g o o v e r s u s 2pI/& =

-

Pm, CM

i n o r d e r t o b e t t e r i n t e r p r e t t h e n a t u r e of t h i s sca- l i n g ( F i g u r e 3).

We s e e t h a t below Elab ^-J 100 GeV, t h e spectrum i s i n q u a l i t a t i v e accord with a n a b s o l u t e Feynman s c a l i n g i n pl ; t h e only change i s a h o r i z o n t a l compression of t h e d i s t r i b u t i o n a s a consequence of

%he c h o i c e of h o r i z o n t a l s c a l e 2pl / $;

.

Elab

-

.

I t n e e d s s c a r c e l y be s a i d t h a t t h e evidence presen- t e d does n o t i n i t s e l f prove t h e r e l e v a n c e o f t h i s p a r a m e t r i z a t i o n . However, I s h a l l h e r e i g n o r e a l l o t h e r s . There a r e a t t r a c t i v e t h e o r e t i c a l p r o p e r t i e s f o r t h i s form which should be f a m i l i a r t o anyone who h a s e v e r looked a t cosmic-ray p h y s i c s . Glennys F a r r a r and I c a l l i t t h e p a r e n t - c h i l d r e l a t i o n [7] :

Suppose we produce some p a r e n t ( p a r t o n , i s o b a r , e t c . of momentum p a c c o r d i n g t o a n i n c l u s i v e

s- 23.5 GeV

t'J--

\/;= 52.7 GeV

0 61 44 GeV

F= 53 Gel!

F i g . 3 - P l o t o f p8 E

-

7 2p* %

.

and 400 GeV ; C P d a t a a t 300 GeV, ( b ) CCR, BS, and SS ISR d a t a .

d i s t r i b u t i o n

E ^-do- ^N

-

(

) .

d3p P:

HIGH TRANSVERSE MOMENTUM PROCESSES C 1-387

Suppose t h e p a r e n t P decays i n t o a hadron c h i l d c o f momentum p' = xpp ( w i t h l i m i t e d pL r e l a t i v e

I '

t o t h e d i r e c t i o n of t h e p a r e n t ) according t o a Feyn- man s c a l i n g h y p o t h e s i s

( T h i s i s c e r t a i n l y t r u e f o r i s o b a r decays).

Then t h e i n c l u s i v e d i s t r i b u t i o n h a s t h e same form a s e q u a t i o n (1.2), w i t h a d i f f e r e n t f u n c t i o n f ' (which i s a c o n v o l u t i o n of f with g ) .

There i s a l s o a c o r o l l a r y . I f a local-exponent ap- proximation i s v a l i d ( i . e. f o r some range of pL we may r e p l a c e f by a c o n s t a n t and n by a n e f f e c t i v e exponent t h e n ( a t t h e same pl)

Thus t h e r e i s a u n i v e r s a l i t y of t h e s c a l i n g law, (Eq.1.2), much l i k e t h e u n i v e r s a l i t y of t h e c e n t r a l p l a t e a u - r e g i o n i n o r d i n a r y p r o c e s s e s (we mean, e.g.

i f dN/dy^, c o n s t . ( o r e a Y ) f o r a p a r e n t (such a s P,A) d ~ / d y a l s o i s c o n s t a n t ( o r e R Y ) f o r i t s

c h i l d r e n ) .

Notice a l s o t h a t i n the cascade p r o c e s s , t h e cms.

a n g l e (and t h e r e f o r e the r a p i d i t y Y l o g t a n 8/2) i s a2proximately conserved. T h e r e f o r e t h e s e considera- t i o n s a l s o s u g g e s t t h e u s e f u l n e s s of BCM o r y a s a v a r i a b l e of c h o i c e i n high-pL phenomena. Likewise p/pmax ( a t a g i v e n 9) i s a l s o a n a t u r a l v a r i a b l e . Feynman's x v a r i a b l e , x = 2 p / 6 , i s e a good

//

c h o i c e . Also 2p / & i s only a good v a r i a b l e a t

eCM = 90° ; i t should be c l e a r t h e r e c a n be no sca- I

l i n g of t h e i n v a r i a n t c r o s s s e c t i o n i n p /& over a I

r a n g e o f cms a n g l e s !

Before l e a v i n g t h e s e g e n e r a l i t i e s , we n o t e a g a i n t h a t dimensional a n a l y s i s would have p r e d i c t e d t h e exponent i n Eq.(1.2) t o be 4. To go from 4 t o 8 i m - p l i e s t h a t t h e b a s i c matrix-element f o r t h e p r o c e s s be p r o p o r t i o n a l t o m 2 , w i t h m a small ( ? ) mass ; m , < 1 GeV. (?). The o r i g i n of t h i s damping f a c t o r be-

comes a c e n t r a l t h e o r e t i c a l q u e s t i o n , t o which we r e t u r n i n s e c t i o n 3.

1.2.- PARTICLE RATIOS.-

The most important f e a t u r e of t h e d a t a on p a r t i c l e

+

-

r a t i o s i s t h a t heavy p a r t i c l e s (Km,p,p) comprise a l a r g e r f r a c t i o n of the t o t a l y i e l d . At t h e ISR, i t i s N 35% a t pI

-

a t low PL

.

The i n t e r p r e t a t i o n of t h e s e l a r g e r a t i o s depends upon what one assumes a s t h e u l t i m a t e p a r e n t of t h e hadrons we observe. I t can be e i t h e r a p a r t o n , which

"qragmentsw a s i t i s supposed t o d o i n deep-inelas- t i c lepton-induced p r o c e s s e s [ 8 ] , o r a n o r d i n a r y hadron o r i s o b a r (of l i m i t e d mass), o r perhaps a

" f i r e b a l l " [9 1

.

I f t h e p a r e n t i s a low mass hadron, one does n o t have t o go f a r t o q u a l i t a t i v e l y understand t h e f a c t t h a t t h e heavy p a r t i c l e s a r e more dominant. While i s o b a r and resonance decays t e n d t o p o p u l a t e t h e c e n t r a l p l a t e a u , w i t h a n e x c e s s of p i o n s , t h i s me- chanism is g r e a t l y diminished i n importance a t h i g h pl because of t h e s t e e p l y f a l l i n g spectrum. Glennys F a r r a r and I c a r r i e d o u t a simple c a l c u l a t i o n t o i l l u s t r a t e t h i s e f f e c t 171

.

However, i f we make t h e corresponding assumption a t high pl , e.g. a l l members of t h e 3 5 and 52 a r e produced with a p-8 I spectrum, a g a i n a c c o r d i n g t o s t a t i s t i c a l weight, and a g a i n with 3 5 / E = 2/1, we g e t

Again, anyone who h a s f a m i l i a r i t y w i t h cosmic r a y p h y s i c s should understand t h i s . For those who do n o t , i t i s a simple e x e r c i s e u t i l i z i n g Eq. (1.4) : i s o b a r s have a n o n t r i v i a l g ( x ) , while f o r t h e s t a b l e components g ( x ) = ~ ( I - x ) and the? a r e erhanced.

Those who u s e t h e h y p o t h e s i s t h a t t h e u l t i m a t e p a r e n t s ( o r g r a n d p a r e n t s ) of t h e hadron s p e c t r a t h a t we o b s e r v e a r e p a r t o n s , i n p a r t i c u l a r quarks,should a l s o f i n d t h e q u a l i t a t i v e t r e n d s , w i t h i n c r e a s i n g p 1 which a r e observed a t t h e ISR reasonable. When 2p /& i s l a r g e , i t i s r e a s o n a b l e t o suppose t h e

I

p a r t o n s a r e v a l e n c e p a r t o n s , predominantly u-quarks.

These u-quarks ( a l o n g with same d ) p r e f e r e n t i a l l y

- -

fragment i n t o p and K , not p and K

.

quark p r e f e r e n t i a l l y fragments i n t o x+ a s w e l l ; t h u s a xi/ x - r a t i o g r e a t e r t h a n u n i t y i s a l s o r e a s o n a b l e ( t h i s l a t t e r phenomenon i s observed i n

C1-388 J.D. BJORKEN

d e e p - i n e l a s t i c e l e c t r o p r o d u c t i o n ) . However i f t h i s e x i s t i n g t h e o r e t i c a l i d e a s a r e s u r e t o be r e f i n e d , i s t h e r i g h t i n t e r p r e t a t i o n , we a r e a l s o f o r c e d t o

conclude t h a t t h e r a t h e r l a r g e p/%+ r a t i o .W 30%

and K+/ % + r a t i o .u 35% observed a t t h e ISR f o r pI >z 3 GeV i m p l i e s s i m i l a r l y l a r g e r a t i o s i n e+e- c o l l i d i n g beams, which ( a c c o r d i n g t o t h e parton- model i d e a s ) produce predominantly a mono-energetic beam of u and u

-

The problem o f i n t e r p r e t a t i o n becomes much more a c u t e when t h e NAL d a t a of t h e Chicago-Princeton group i s taken i n t o account. A t such l a r g e v a l u e s of p/p- , i t becomes e v e r more probable t h a t t h e p a r t o n i s a u-quark, and t h u s a l a r g e ^K+/%- r a t i o i s expected. I t i s not observed ( 1 . 0 ,< K+/x- 6 1.2 o v e r t h e e n t i r e range of the d a t a ) . And t h e p/K+

r a t i o - 1 i m p l i e s a n e x t r a o r d i n a r y amount of baryon p r o d u c t i o n i n e+e- a n n i h i l a t i o n [lo].

1.3.- ANGULAR DISTRIBUTION OF INCLUSIVE SPECTRA.- From t h e phase-space p l o t s i n f i g u r e 1 , we s e e t h a t

t h e r e i s a g r e a t d e a l of t e r r i t o r y from e .-100mrad.

CM t o eCM ^N 45O which, a t t h e ISR, y i e l d h i g h pl s e c o n d a r i e s but which i s n o t y e t explored. F o r lGeV

< PI < 3 GeV , t h e d a t a of t h e British-Scandinavian group show no d i s c e r n i b l e d i f f e r e n c e i n t h e i n v a r i a n t c r o s s - s e c t i o n , a s f u n c t i o n of pl , f o r eCM = 60°

and eCM = 90°

.

pI h a s been e x t r a c t e d . I s h a l l not review t h e s e , inasmuch a s

modified, o r g e n e r a l i z e d c o n s i d e r a b l y by t h e time any such d a t a w i l l appear.

2.- STRUCTURE I N PHASE-SPACE OF HIGH-p EVENTS.- 1

- 2.1.- THE GEOGRAPHY OF THE FINAL-STATE HADRON POPULATIONS.- Of c l e a r i n t e r e s t and importance i s

t h e d e t e r m i n a t i o n of what i s produced i n a s s o c i a - t i o n w i t h a high-p secondary. We hzve a l r e a d y in-

1

d i c a t e d t h a t i f t h e secondary i s t h e decay product of a p a r e n t , both p a r e n t and secondary p o s s e s s ap- proximately t h e same l a b o r a t o r y a n g l e [ l l ] . ( T h i s . i s , by t h e way, a L o r e n t z corrariant s t a t e m e n t f o r a l l L o r e n t z b o o s t s e x c e p t t h o s e which make one of t h e s e c o n d a r i e s wee). I n o t h e r words a j e t may be formed. D e f i n e a j e t - a x i s by t h e d i r e c t i o n of t h e momentum o f t h e highest-pl hadron e m i t t e d i n a high- pI event. Then a n a t u r a l h y p o t h e s i s i s t h e following

( 1 ) P a r t i c l e s of h i g h p e m i t t e d i n t h e same I

hemisphere a s t h e h i g h e s t p hadron emerge i n t h e I

same d i r e c t i o n , w i t h a n g u l a r f l u c t u a t i o n A e .$ 0 . 5 / ~ ~ i n t h e c o l l i n e a r Lorentz frame i n which t h e j e t emerges a t 90° - t o t h e beam d i r e c t i o n .

T h i s h y p o t h e s i s is a n e c e s s a r y consequence of par- ton-model orthodoxy [ l o ] , b u t has a g e n e r a l i t y t h a t extends beyond it. The r e g i o n of phase space occu- pied by members of a j e t i s shown i n f i g u r e 4. We s e e t h a t t h e d i s t r i b u t i o n i n r a p i d i t y of a s s o c i a t e d hadrons should be peaked, w i t h width l e s s t h a n 2

l n i t s of r a p i d i t y .

F i g . 4

-

I r y i n g p.,.,0.3 GeV t o avoid t h i s c o n c l u s i o n ) . Con-

I

c i t y of a s s o c i a t e d hadrons on t h e o t h e r s i d e i s li- s i d e r t h e hadron of l a r g e s t pl. Following t h e pre- n e a r i n

p, , t h e r e w i l l be a t l e a s t one high-p

I ceding argument, we would be l e d t o e x p e c t a j e t i n

A ^-

hadron i n t h i s o p p o s i t e hemisphere ( a t pl >210GdV,

HIGH TRANSVERSE MOMENTUM PROCESSES C1-389

t h e o p p o s i t e hemisphere a s w e l l . T h i s has a l r e a d y been i l l u s t r a t e d i n Fig.4. The two j e t s need not emerge i n o p p o s i t e d i r e c t i o n s , i . e . w i t h A e ~ i 8 0 0 : E s t i m a t e s of t h e i r c o r r e l a t i o n e a s i l y a l l o w f o r f l u c - t u a t i o n s i n t h e i r r e l a t i v e r a p i d i t y Ay of two u n i t s . T h i s p i c t u r e i s summarized i n t h e next two hypotheses.

( 2 ) Event by e v e n t a p l a n e may be d e f i n e d by t h e beam momenta and t h e momentum of t h e hadron posse- s s i n g t h e h i g h e s t p

.

1

r y hadron momentum normal t o t h i s p l a n e pN i s a s t e e p l y f a l l i n g f u n c t i o n a s pN i n c r e a s e s .

(3) Event b) e v e n t , t h e p o p u l a t i o n of secondary hadrons i s c o n f i n e d t o t h e u s u a l low-pl r e g i o n a l o n g the beam d i r e c t i o n s and t o a t most two approximately c o p l a n a r j e t r e g i o n s , a s shown i n f i g u r e 4 , which a r e d e f i n e d by t h e h i g h e s t pL p a r t i c l e s i n o p p o s i t e hemispheres. I t i s very improbable t o f i n d hadrons l a r g e d i s t a n c e s o u t s i d e t h e s e j e t r e g i o n s o r o u t s i d e t h e u s u a l low-pl fragmentation r e g i o n s and c e n t r a l p l a t e a u .

We d o n o t mean t o imply by t h e s e hypotheses t h a t a l l shaded r e g i o n s i n f i g u r e 4 a r e w e l l populated i n a t y p i c a l high-pL event. Some j e t s may b e almost empty s e t s . D i f f e r e n t models s a y d i f f e r e n t t h l n g s . But most models of which I am aware a r e n o t i n con-

f l i c t w i t h t h e above hypotheses, and t h e hypotheses a r e t h e r e f o r e very important t o t e s t . I n f a c t , t h e only models I know t h a t a r e i n c o n f l i c t a r e s 9 a t i s - t i c a l "nova" models [12,131 f o r which t h e m u l t i p l i - c i t y i s assumed t o grow l e s s r a p i d l y t h a n l i n e a r w i t h f i r e b a l l mass. These v i o l a t e t h e c o p l a n a r i t y hypothesis ( 2 ) .

The c o p l a n a r i t y h y p o t h e s i s h a s n o t y e t been exami- ned e x p e r i m e n t a l l y . The CCR d a t a on 2 - p a r t i c l e c o r r e l a t i o n s a r e a t l e a s t q u a l i t a t i v e l y i n agreement w i t h h y p o t h e s i s ( 3 ) . I f a p a r t i c l e i s observed i n c o i n c i d e n c e w i t h t h e high pL no and i n t h e same hemisphere, i t s r a p i d i t y i s s h a r p l y c o r r e l a t e d with

t h e 2

.

Before d e s c r i b i n g what i n g e n e r a l t h e models s a y , i t i s u s e f u l t o f u r t h e r d i s s e c t t h e r e g i o n of par- t i c l e p r o d u c t i o n which we have describerr i n t o frag- m e n t a t i o n r e g i o n s and " p l a t e a u " i n o r d e r t o o r g a n i z e o u r t h i n k i n g about t h e q u i t e complicated kinematics.

I f i n d i t h e l p f u l t o f i r s t c o n s i d e r t h e photon- exchange process. A l l t h e d i f f e r e n t r e g i o n s a l r e a d y a p p e a r i n t h a t p r o c e s s and c a n be g e n e r a l i z e d over t o t h e h a d r o n i c c a s e w i t h o u t a n overcommitment t o s p e c i f i c models. Consider f i r s t e l e c t r o n - p r o t o n deep-

i n e l a s t i c s c a t t e r i n g i n t h e e l e c t r o n - p r o t o n c e n t e r of mass frame. An i n e l a s t i c c o l l i s i o n a t l a r g e w p o p u l a t e s phase space a s shown i n f i g u r e 5. Deep-

Fig.5

-

.

i n e l a s t i c cognoscentes w i l l r e c o g n i z e t h e parton- f r a g m e n t a t i o n r e g i o n ( c o n t a i n i n g t h e most e n e r g e t i c hadrons, f o r o r d i n a r y l a b o r a t o r y kinematics w i t h i n i t i a l p r o t o n a t r e s t ) , t a r g e t f r a g m e n t a t i o n re- g i o n , hole-fragmentation r e g i o n , and t h e two p l a t e a u r e g i o n s , hadronic p l a t e a u and c u r r e n t p l a t e a u [141.

T h i s p i c t u r e u s e s i d e a s of s h o r t - r a n g e c o r r e l a t i o n i n r a p i d i t y , which may be wrong-especially i n t h e c u r r e n t - f r a g m e n t a t i o n region. G e n e r a l l y expected i s t h a t t h e m u l t i p l i c i t y of hadrons i n t h e c u r r e n t - p l a t e a u is r e l a t e d t o t h e m u l t i p l i c i t y of hadrons i n t h e eie- a n n i h i l a t i o n p r o c e s s , inasmuch a s t h e h o l e and p a r t o n f r a g m e n t a t i o n r e g i o n s along w i t h t h e c u r r e n t p l a t e a u comprise t h e f r a g m e n t a t i o n r e - g i o n of t h e v i r t u a l photon. Now c o n s i d e r a proton- p r o t o n c o l l i s i o n proceeding v i a photon exchange, a s i n Fig.2. E v i d e n t l y we should i n v e r t the d i s t r i b u - t i o n of f i g u r e 5 about t h e o r i g i n t o o b t a i n t h e f r a g m e n t a t i o n of t h e left-mover. That would l e a v e a gap between t h e two r e g i o n s . However, t h e r e i s good reason t o b e l i e v e the gap i s f i l l e d by a n o r - d i n a r y Yradron p l a t e a u . I n a d d i t i o n t o t h e photon exchange, pomeron exchange l e a d i n g t o p a r t i c l e pro- d u c t i o n should be p r e s e n t and i m p o r t a n t inasmuch a s t h e impact parameter i n t h e c o l l i s i o n i s not l a r g e , That i s , t h e r e i s no reason t o throw away diagrams such a s f i g u r e 6.

The complete map of t h e p o s s i b l e populated r e g i o n s of phase space i s shown i n f i g u r e 7a. There a r e 15 d i s t i n c t regions. Impossible e n e r g i e s a r e r e q u i r e d t o s e e them a l l a t t h e same time. S a v i t [151 h a s

J.D. BJORKEN

Fig.6 - Proton-proton s c a t t e r i n g v i a photon exchange, w i t h Pomeron-exchange c o r r e c t i o n .

worked t h i s o u t i n t h e a c t u a l p r a c t i c a l c a s e of pl

/& n o t s n a l l . Then uany of t h e s e regions merge, and we a r e l e f t with only 9 mixed p l a t e a u x , as shown i n Fig.7b. In r e a l i s t i c conditions (pL<< lOGeV) t h e s e i s no c u r r e n t plateau or mixed plateaux and t h e r e g i o n s re- duce t o 5. Let no one be deceived t h a t t h e s i t u a t i o n i s n o t complex. A l l 15 r e g i o n s c a n be g e n e r a l l y iden- t i f i e d i n a v a r i e t y of models : they a r e not s p e c i f i c t o p a r t o n ideas. F o r example, j u s t t h e t h r e e g e n e r a l hypotheses made e a r l i e r r a t h e r n a t u r a l l y account f o r a l l t h e r e g i o n s except t h e hole-fragmentation regions.

To s e e t h a t they a l s o a r e g e n e r a l , s t a r t w i t h t h e c o n f i g u r a t i o n of Fig. 7 a (where e v i d e n t l y s >> p2)

1 and keep t h e hadron c o n f i g u r a t i o n s i n t h e j e t s cons- t a n t w h i l e lowering t h e i n c i d e n t beam momenta. F o r s u f f i c i e n t l y l a r g e s , v a r i a t i o n of p r o j e c t i l e e n e r g i e s i s n o t supposed t o a f f e c t what happens i n t h e c e n t r a l r e g i o n ( a t f i x e d p ). Thus no change i s

I

f o r c e d a s long a s hadron plateaux(Pomeron couplizigs) e x i s t a d j a c e n t t o t h e p r o j e c t i l e fragmentation re- gions - and a s long a s energy and momentum a r e con- served. We cannot d e c r e a s e t h e beam e n e r g i e s t o s o low a value t h a t the t o t a l four-momentum i n t h e i n i - t i a l s t a t e i s l e s s t h a n what e x i s t s i n t h e hadron j e t s a l o n e ! Some easy examination of t h e kinematics shows t h a t balance i s a t t a i n e d when t h e p r o j e c t i l e fragmentation r e g i o n s o v e r l a p t h e h o l e fragmentation regions. T h i s q u i t e g e n e r a l argument i n d i c a t e s t h a t t h e e x i s t e n c e of t h e h o l e fragmentation r e g i o n s i s n o t s p e c i f i c t o models, a t l e a s t i f i t i s assumed t h a t t h e p i c t u r e of short-range r a p i d i t y c o r r e l a t i o n s i n t h e p r o j e c t i l e and hadronic p l a t e a u regions i s n o t completely abandoned f o r t h i s c l a s s of events.

3.- MODELS. - Given t h i s geography of phase-space f o r high-p p r o c e s s e s we c a n compare t h e p r e d i c t i o n s

I

of the v a r i o u s t h e o r e t i c a l models a s t o how t h e va- r i o u s r e g i o n s a r e populated. Also, a s we proceed, we

Fig.7 - Fragmentation r e g i o n s and p l a t e a u x f o r a high-pL pp i n t e r a c t i o n .

( a ) General case.

( b ) Minimum-energy c o n f i g u r a t i o n ; a f i n i t e f r a c - t i o n of i n i t i a l - s t a t e energy h a s emerged i n the high-p j e t s .

( c ) Real l i f e t h e r e i s no c u r r e n t p l a t e a u u n t i l pL >> 10-20 GeV.

must remember t h a t a c e n t r a l dynamical problem i s t o d i s c o v e r t h e o r i g i n of t h e f a c t o r m 2 i n t h e matrix element ( o r , m4 i n t h e c r o s s - s e c t i o n ) which c h a r a c t e r i z e s t h e v i o l a t i o n of dimensional s c a l i n g .

HIGH TRANSVERSE MOMENTUM PROCESSES C1-391

The phase-space p o p u l a t i o n s f o r 6 d i f f e r e n t models a r e shown s c h e m a t i c a l l y i n f i g u r e 8.

Unadorned

vw//// / n /d Multiperipheral

MODEL

Kindergarten Partons

PHASE-SPACE POPULATION

Constituent PI v w / / / / / v / l l

Interchange ,

I

-

Covarirrnt Furton Model

OPE

F i g . 8 - Phase-space-populations (shown shaded) f o r 6 d i f f e r e n t models of h i g h - p p r o c e s s e s I

a ) M u l t i p e r i p h e r a l model b) Kindergarten p a r t o n model C ) C o n s t i t u e n t i n t e r c h a n g e model d ) C o v a r i a n t p a r t o n model e) P a r t o n - f i r e b a l l f ) One-pion exchange

3.1.

-

-

I n such models a m u l t i p e r i p h e r a l l a d d e r f i l l s t h e hadron p l a t e a u r e g i o n s i n f i g u r e 8a u n t i l t h e hole- f r a g m e n t a t i o n r e g i o n s a r e reached. Beyond, i n t h e t r a n s i t i o n , mixed p l a t e a u , and c u r r e n t p l a t e a u re- g i o n s , a l l i s l e f t empty u n t i l t h e parton-fragmenta- t i o n r e g i o n s a r e reached. I n each such r e g i o n one p a r t i c l e i s found. Or i f i s o b a r s a r e i n c l u d e d , a f i - n i t e number o f p a r t i c l e s may be found t h e r e . The power of m2 needed i n t h e amplitude c a n i n t h i s model be provided by t a k i n g t h e members of t h e l a d d e r t o be s p i n l e s s , and t h e v e r t i c e s without form-factor.

Then t h e amplitude e s s e n t i a l l y c o n t a i n s a J = 0 par- ton-parton s c a t t e r i n g p r o p o r t i o n a l t o t h e s q u a r e of

2 2

a t r i l i n e a r c o u p l i n g c o n s t a n t g , [m ]

.

3.2. - THE KINDERGARTEN PARTON MODEL [2 , 4 , 5 1 . - I n t h i s model a l l f r a g m e n t a t i o n r e g i o n s a r e assumed t o

be f u l l , w i t h roughly t h e same d e n s i t y a s expected

i n deep i n e l a s t i c p r o c e s s e s . I n p a r t i c u l a r t h e mul- t i p l i c i t y i n t h e c u r r e n t - f r a g m e n t a t i o n r e g i o n should be t h e same a s observed f o r t h e corresponding r e g i o n i n deep i n e l a s t i c e l e c t r o p r o d u c t i o n . I f a high-p

I hadron i s observed, a s i n a n i n c l u s i v e experiment, i t c a r r i e s about 7 m of t h e energy of i t s p a r e n t p a r t o n [5,71 because of the s t e e p f a l l of t h e p r i - mary spectrum with i n c r e a s i n g pL

.

Thus t h e r e should be a gap o f - l - 2 u n i t s of r a p i d i t y between t h e observed hadron and t h e r e s t of t h e po- p u l a t i o n i n t h e c u r r e n t f r a g m e n t a t i o n region. I f t h e t r i g g e r i s o n t h e t o t a l hadron energy i n a j e t , a s would be t h e c a s e were t h e hadron d e t e c t o r a c a l o r i - meter, t h e n t h i s b i a s i s removed. I n such a c a s e t h e d i s t r i b u t i o n should be s i m i l a r t o what i s found i n t h e c u r r e n t - f r a g m e n t a t i o n r e g i o n i n e l e c t r o p r o d u c - t i o n . T h e r e t h e e v i d e n c e f a v o r s ( t h a n k s t o t h e r e c e n t C o r n e l l experiment [17] on m u l t i p l i c i t i e s i n t h e deep i n e l a s t i c r e g i o n : -, 2.5 GeV, 1 < Q~ < 10 GeV 2 ) a d i s t r i b u t i o n q u i t e s i m i l a r t o what i s found i n o r d i n a r y p r o c e s s e s . I n a n experiment i n which one t r i g g e r s on a high-p p a r t i c l e i n one hemisphere and

I

then o b s e r v e s t h e hadrons emerging i n t h e o p p o s i t e hemisphere they should ( i n t h i s model) a g a i n comprise a n "unbiased jet". Thus a h i g h e r a s s o c i a t e d m u l t i - p l i c i t y i s expected i n t h e hemisphere o p p o s i t e t o the high-p t r i g g e r hadron than on t h e same s i d e .

I

The d i f f e r e n c e i n m u l t i p l i c i t i e s o n t h e two s i d e s should be roughly independent of pI a t s u f f i c i e n t l y high ( i . e. impossibly h i g h ) 5

.

[51 have c a r r i e d o u t more d e t a i l e d s t u d i e s of many of t h e s e questions.

The main d i f f i c u l t y w i t h t h e k i n d e r g a r t e n p a r t o n model i s i t s e x p e c t a t i o n of dimensional s c a l i n g f o r t h e i n c l u s i v e d i s t r i b u t i o n ( a n exponent 4 i n s t e a d of t h e observed 8-10 i n Eq.cl.4)). To o b t a i n t h e power m2 i n t h e matrix-element a p p e a r s t o r e q u i r e a g a i n J=0 p a r t o n s s c a t t e r i n g v i a J=0 exchange, while t h e d a t a ( i n p a r t i c u l a r t h e v e r y l a r g e p/K r a t i o (, 1) r e p o r t e d i n t h e NAL experiment s u g g e s t s t h a t what i s s c a t t e r e d c o n t a i n s t h e quantum numbers of t h e p r o j e c t i l e s , i n p a r t i c u l a r baryon number. W i - t h o u t major a d j u s t m e n t s , t h i s model o f hadron-hadron c o l l i s i o n s ( o r a t l e a s t t h e quark-parton-plus-gluon v e r s i o n of i t ) appears t o be simply wrong.

3.3.

-

.-

Blankenbecler, Brodsky, and Gunion [6] argued t h a t whether o r not high-p hadrons may be produced v i a

1

C1-392 J.D. B

h a r d p a r t o n - p a r t o n c o l l i s i o n s , a s assumed i n t h e p r e c e d i n g model, they can be produced by a c o n s t i - t u e n t - i n t e r c h a n g e mechanism. To me t h i s l i n e o f a r - gument h a s l e d by f a r t o t h e most comprehensive and c o n s i s t e n t d e s c r i p t i o n o f high-pl i n c l u s i v e and e x c l u s i v e p r o c e s s e s i n existence.Brodsky and F a r r a r [41] have developed a very r e l a t e d ( b u t n o t i d e n t i - c a l ) l i n e of argument which v e r y e a s i l y summarizes t h e p h y s i c s involved. F i r s t of a l l ( a s d i s c u s s e d by Brodsky and F a r r a r L 4 l l and by Matveev, Muradian, and Tavkhelidze [ l g l ) , f o r e x c l u s i v e p r o c e s s e s a t f i x e d a n g l e and high e n e r g y , t h e e l a s t i c s c a t t e r i n g of a p a r t o n from a n o t h e r p a r t o n i s assumed t o pro- ceed a c c o r d i n g t o dimensional a n a l y s i s . I f a p a r t o n s c a t t e r s e l a s t i c a l l y from a meson t h e amplitude i s damped by a power of m 2 /s where m2 i s a s m a l l mass. That i s t h e p r i c e t h a t h a s t o be paid t o keep t h e mass o f t h e f i n a l qq bound system small.(Brods-

-

ky and F a r r a r have examined c l a s s e s of diagrams i n s c a l e - i n v a r i a n t t h e o r i e s t o s u p p o r t t h i s conten- t i o n ) . For each a d d i t i o n a l bound c o n s t i t u e n t , one i n c l u d e s a n o t h e r power of m 2 /s

.

P r o c e s s Fixed-angle c r o s s - s e c t i o n

which i n f a c t i s i n good accord w i t h t h e d a t a . Given t h e r u l e , t h e s y s t e m a t i c behavior of i n c l u s i v e pro- c e s s e s made on t h e b a s i s of t h e i n t e r c h a n g e model

c a n be reduced t o dimensional a n a l y s i s ( o r automo- d e l i t y [ 1 9 ] ) . Given t h a t f o r some reason t h e qq s c a t t e r i n g term (which c o n t r o l s t h e k i n d e r g a r t e n - p a r t o n d e s c r i p t i o n ) i s a b s e n t , t h e next most impor- t a n t c o n t r i b u t i o n i s t h e s c a t t e r i n g of a meson M from a quark, e i t h e r qq -' MM o r qM + qM

.

"meson" M i s meant a c o r r e l a t e d qq p a i r i n t h e protnn's wave f u n c t i o n , which p o s s e s s e s a low inva- r i a n t mass. Because of t h e f a c t o r [m212 i n t h i s c r o s s - s e c t i o n , we g e t , a g a i n u s i n g dimensional ana-

l y s i s , n = ⁸ i n Eq. (1.4). I n a n Mq c o l l i s i o n , t h e q and M i n t h e i n i t i a l beams r e s i d e i n t h e hole-fragmentation r e g i o n s . The c o l l i s i o n t r a n s p o r t s them t o t h e parton-fragmentation r e g i o n s . The "me- sont' M d o e s

=

-

.

a p p a r e n t l y o m i t t e d by Brodsky and F a r r a r , h a s t h e same s c a l i n g behaviour ( a n exponent 8 ) a s

and consequently a t f i x e d x t h e p/"+ r a t i o would e v e n t u a l l y be expected t o tend t o a non v a n i s h i n g c o n s t a n t . With t h e v a r i e t y of mechanisms a v a i l a b l e , i t s h d l d b e p o s s i b l e t o account f o r t h e d a t a [20].

Another p o s s i b l y r e l e v a n t p i e c e of evidence comes from BNL d a t a a t 28 GeV. The BNL-VPI-Wisconsin- Purdue c o l l a b o r a t i o n u s i n g t h e ARGO s p e c t r o m e t e r [21] o b s e r v e s t h e r e a c t i o n pp -, p + hadrons, where t h e observed p h a s h i g h p

.

I

no p i o n s a s s o c i a t e d w i t h f r a g m e n t a t i o n of t h e obser- ved high-pL proton. The a s s o c i a t e d m u l t i p l i c i t y a t f i x e d m i s s i n g mass i n c r e a s e s s h a r p l y a s t h e p of

I t h e t r i g g e r p r o t o n i n c r e a s e s beyond 1 GeV/c. The f i r s t o b s e r v a t i o n i s i n accord w i t h t h e i n t e r c h a n g e p i c t u r e . The r i s e i n n - i s not ; a t f i x e d m i s s i n g

mass t h e behaviour i s supposed t o be q u a l i t a t i v e l y t h e same a s i n e l e c t r o - p r o d u c t i o n , where t h e evidence f a v o r s no i n c r e a s e i n n a t f i x e d m i s s i n g mass.

-

HIGH TRANSVERSE MOMENTUM PROCESSES Cl-393

3.4.

-

-

a s P r o f e s s o r Polkinghmne [22] h a s d e s c r i b e d t h i s viewpoint i n some d e t a i l , I s h a l l only very b r i e f l y p a r a p h r a s e h i s remarks u s i n g t h i s language.

The diagram of f i g u r e 9 a which i s d e s c r i b e d a p t l y

Fig.9

-

2 a c c o u n t s f o r one hadron-plateau and one t a r g e t f r a g - mentation region. However high-pl i s c a r r i e d i n t o t h e black box a t t h e top by two o f f - s h e l l p a r t o n s , and c o n s i d e r a b l e f l e x i b i l i t y e x i s t s i n how t o choose t h e s t r u c t u r e of t h a t amplitude. The c h o i c e d e s c r i b e d by Fig.9b c o r r e s p o n d s , i n t h e i n t e r c h a n g e terminolo- gy, t o a qq -+ MM s c a t t e r i n g which would produce a c o n f i g u r a t i o n i n phase s p a c e s i m i l a r t o t h e una-

~ r n e d m u l t i p e r i p h e r a l model i f t h e masses of t h e :sons M were t o be l i m i t e d . However, u s i n g s p e c t r a

~f masses f o r t h e two "meso& M c a n r e s u l t i n a f i l - l i n g i n of t h e c u r r e n t f r a g m e n t a t i o n r e g i o n s and a d d i t i o n of Pomeron exchange c a n f u r t h e r p o p u l a t e t h e vacant a r e a s of phase space i n t h e low-p

1 ten- t r a l r e g i o n s ( F i g . 9 ~ ) . Hence t h e model i s c a p a b l e of a v a r i e t y of responses depending upon t h e t r e n d of t h e d a t a .

3.5. - PARTON-FIREBALL HODEL [9 1. - Berger and Bran- s o n [ 9 ] e n v i s a g e a two s t e p p r o c e s s i n which two f i r e b a l l s of high-p a r e produced by a mechanism es-

I

s e n t i a l l y amounting t o a d i r e c t p a r t o n - p a r t o n i n t e - r a c t i o n . From c o n s i d e r a t i o n s s i m i l a r t o what I des- c r i b e d a s t h e p a r e n t - c h i l d r e l a t i o n , t h e f i r e b a l l produced i n a s s o c i a t i o n with a n i n c l u s i v e t r i g g e r hadron of h i g h pl has low mass ( i n o r d e r t h a t t h e i n e l a s t i c i t y i n t h e p a r t o n ^-t hadron t r a n s i t i o n be low). The f i r e b a l l on t h e o t h e r s i d e has a l a r g e mass.

This p i c t u r e i s t h e r e f o r e i n l i n e with what d a t a

e x i s t s on a s s o c i a t e d m u l t i p l i c i t y . Also, t h e predo- minance o f heavy p a r t i c l e s i n t h e spectrum a l s o might be understood inasmuch a s t h e f i r e b a l l compo- n e n t s a l l have roughly t h e same Y and hence p and K have t h e h i g h e s t momentum. The a u t h o r s gues- sed a p / ~ + r a t i o of 5 f o r NAL c o n d i t i o n s of p / p m a x ~ 1 / 2 , i n s t e a d of t h e observed 1. They f u r t h e r - more expected t h e r a t i o t o be a s h a r p l y r i s i n g func- t i o n of 2p _I /&

.

3.6.

-

.

Development of many of t h e parton-fragmentation i d e a s can be found i n t h i s paper. The p r o p e r t i e s of t h e f i n a l s t a t e s w i l l be most s i m i l a r t o t h e kindergar- t e n p a r t o n model.

3.7.- MBELLER-REGGE DIAGRAMS AND THE COLEMAN PREPA- RATA MODEL[23,24].- I n 1969, Coleman P r e p a r a t a (and i n q u i t e a s i m i l a r way, L.P. Yu) invented a p a r t b n model f o r d e e p - i n e l a s t i c s c a t t e r i n g which a c c o u n t s f o r s c a l i n g , and a l s o i s c a p a b l e of p r o v i d i n g a Muel- ler-Regge framework f o r d i s c u s s i n g i n c l u s i v e s p e c t r a , i n c l u d i n g t h e d i f f i c u l t c u r r e n t - f r a g m e n t a t i o n r e g i o n s . The diagrams a r e shown i n f i g u r e 10.

pornerons 5

"

Mlxed Pornerons Reggeons

C

-- Current Pornerons

.

i P

Fig.10

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27