PARTONS IN STRONG INTERACTIONS

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PARTONS IN STRONG INTERACTIONS

D. Horn

To cite this version:

D. Horn. PARTONS IN STRONG INTERACTIONS. Journal de Physique Colloques, 1973, 34 (C1),

pp.C1-153-C1-159. �10.1051/jphyscol:1973116�. �jpa-00215196�

PARTONS IN STRONG INTERACTIONS*

D. HORN

Physics Department , Tel Aviv University

1.- HADRONIC CURRENTS.- The great success of the partem model [l] is in its application to the struc- ture of hadrons as revealed in experiments in which they are probed by electromagnetic or weak currents.

In this section I will shortly review the key facts and their interpretation and implications. Most of these facts can be equally well accounted for by u- sing the light-cone algebra, which some people may view as more appealing since its assumptions are well defined in contradistinction to the parton model which remains somewhat vague. The questions treated in the other sections, namely the hadronic spectrum of parton reactions and the description of hadron- hadron collisions, cannot be treated by the light- cone algebra. I restrict myself therefore to the parton language.

1.1.- Scaling in deep inelastic electron scattering.

This led to the development of the parton approach.

Let us repeat here just the kinematics. Denoting the photon momentum by q and the proton momentum by p we

2 2 use » : q.p , co = 1/x - 2Mv/-q . For large v and-q

the Bjorken scaling is observed : V W -> F (x) , ep ep, >

W -> F (x) . It is interpreted in the parton model as a point interaction of the photon with a single parton which carries a fraction xp of the momentum p of.the proton.

1 . 2 . - °i/CL < 0.2 . This implies dominance of spin 1/2 partons for which 2xF = F . In t h i s case the approach to zero i s expected to be

-S ~ - J .

Interpretation : the n(p) i s dominated by the d(u) quark near x -» 1 . 1/4 i s the r a t i o of the square of the charges 1/9 : 4/9 .

1 . 4 . - The d i s t r i b u t i o n near co -• 1 , or rather

2 2 3 near co'= C O + (M / - q ) -» 1 behaves l i k e (co'-l) .

This can be r e l a t e d to the electromagnetic form f a c - -2

tor of the nucleon which behaves l i k e t ( s e e s e c - t i o n 3 ) . It i s known as the Drell-Yan r e l a t i o n .

1 . 5 . - At high co ("wee" x) one expects t o see domi- nance of the Pomeron which leads to vco -» c o n s t , and

0" <± cr . Experimentally cr /cr ~ 0 . 8 5 near co'~ 20. en ep en ep 1 . 6 . - Parton d i s t r i b u t i o n s and the presence of gluons. One may describe the s t r u c t u r e functions i n terms of s i x qoark-parton d i s t r i b u t i o n s , thus :

-

— = 2F*

(x) = £ [ u ( x ) + u ( x ) ] + i [ d ( x ) + 3 ( x ) ] x l q q

+ — [ s ( x ) + s ( x ) ]

Quantum number constraints (B,Q,S) for the proton result in

.1 1 1 dx(u-u) = 2 , | dx(d-d) = 1 , / dx(s-s) = 0 0 -0 "0 which corresponds to the net uud structure of the constituent quark model.

The momentum sum rule is : xdx(u+u+d+d+s+s) < l Experimentally

| I xdx(s+s) + / xdx(u+u+d+d) = | / dx^^+F®") s

1 . 3 . - t e t us i d e n t i f y therefore the partons with current quarks" ( t h e parton-quark model). Because of t h e charges of the quarks one f i n d s the p r e d i c t i o n 1/4 < F^/F®

^ 4 . Experimentally F*

< F*

^<> near x -» 1 i t i s smaller than 1/2 and may a c t u a l l y be 1/4.

See a l s o the review by J . C . Polkinghorne (Session 10)

o> 0.56 + 0.8

Interpretation : since we assume most of the proton momentum to be carried by the u and d quarks we con- clude that about half of the net momentum is carried by other objects,!.e. neutral gluons.

This checks with neutrino experiments. There, one 12

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1973116

Cl-154 D. HORN

From t h e s l o p e of t h e e n e r g y i n c r e a s e of

t h i s q u a n t i t y , o n e e s t i m a t e s e x p e r i m e n t a l l y ( i n t h e f ew-GeV r a n g e )

T h i s f o l l o w s by n e g l e c t i n g s,; , i . e . t a k i n g OC= 0 , Oc: is t h e Cabibbo a n g l e .

-

1.7. - E x p e r i m e n t a l l y 2N ^: gN = ^.38:.02 i n t h e r a n g e of few-GeV l a b o r a t o r y energy. Using t h e same a p p r o x i m a t i o n s a s above one f i n d s

6 /:dx [d+u+$(a+;)]

0

assuming V-A i n t e r a c t i o n s of t h e c u r r e n t w i t h t h e q u a r k s . I n t e r p r e t a t i c m of t h e e x p e r i m e n t a l r a t e of

M

1 / 3 : dominance of q u a r x s o v e r a n t i q u a r k s .

1.8.- T h i s may l e a d t o a p i c t u r e of " v a l e n c e quarks"

a n d a n SU(2) ( o r SU(3)) i n v a r i a n t qq s e a . Some pro- blem may a r i s e from t h e c h a r g e sum r u l e

which l e a d s t o a n e x p e r i m e n t a l e s t i m a t e between .18 and .22 . Hence t h e r e e x i s t s a " p o l a r i z a t i o n of t h e qq sea" f a v o u r i n g t h e dz o v e r t h e u i p a i r s i n t h e pro-

The b a s i c q u e s t i o n s a r e :

a ) A r e t h e r e wee h a d r o n s produced i n p a r t o n i c pro- c e s s e s ? I f t h e answer is no t h e n o b v i o u s l y one s h o u l d s e e h a d r o n s w i t h p a r t o n ( q u a r k ) quantum nlun- b e r s . However even i f t h e answer i s y e s one c a n con- t i n u e t o a s k :

b ) Is t h e r e a r e t e n t i o n of q u a r k quantum numbers 7 i . e . , do t h e hadrons t h a t a p p e a r i n t h e 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 c a r r y on t h e a v e r a g e t h e c h a r g e s (Q,B,S) of t h e p a r t o n ?

To be s p e c i f i c , l e t u s draw t h e p i c t u r e of t h e ex- p e c t e d s i t u a t i o n i n d e e p i n e l a s t i c s c a t t e r i n g . I n t h e l t p a r t o n b r i c k w a l l frame" we f i n d t h e momenta p r o t o n : ( p + h12 6 ; 0 , 0 . - ~ ) photon : ( 0 ; 0 , 0 , ~ F

m 2

p a r t o n i n : ( x p + - ; O , O , - ~ P ) 2XP

2

p a r t o n o u t : ( x p + h ; O , O , X P )

where p f l = ^{M Y} and hence xp = I- ₂ 0 .

U s i n g t h e l i m i t p

and d e f i n i n g t h e r a p i d i t y y = z 1 ld(E+pZ)/(E-pZ)) , we f i n d :

p r o t o n : y s - .$ ^In(-q 2 ^{) + l n x} p a r t o n i n : y

- I n ( - q 2 )

1 2

p a r t o n o u t : y S - ₂ ^{In(-q )} .

B j o r k e n [ 2 ] s u g g e s t e d t h a t t h e r e s u l t i n g d i s t r i b u - t i o n of h a d r o n s w i l l l o o k l i k e - i n f i g u r e 1 , where we s e e t h r e e f r a g m e n t a t i o n r e g i o n s - t h e p r o t o n r e - g i o n , t h e h o l e r e g i o n ( p a r t o n i n ) and t h e p a r t o n r e - g i o n ( p a r t o n o u t ) - and two i n t e r m e d i a t e r a n g e s which may d e v e l o p p l a t e a u s : one i s t h e r e g u l a r h a d m n p l a - t e a u w i t h r a n g e l n o and t h e o t h e r i s t h e new k i n d of p a r t o n p l a t e a u w i t h r a n g e I n ( - q 2 ).

t o n . T h i s is however a f i n i t e e f f e c t on a n i n f i n i t e

- -

s e a ( l i m xu = l i m xd

c o n s t . f o r x + O ) . Recent ex-

proton p e r i m e n t a l r e s u l t s a l l o w f o r t h e p o s s i b i l i t y t h a t a c -

hadron p r o t o n

t u a l l y 1/3 may be r i g h t a f t e r a l l .

...

...

1.9.- e'e- + h a d r o n s . T h i s i s viewed a s e+e-

q q - -+ hadrons. I n a c o l o u r e d q u a r k model - + I n ( - q 2 ) - Q n o -+en (-q2) + W q 2 ) ( e + e -

h a d r o n s )

(e'e-

2;)

which i s s m a l l e r t h a n t h e p r e s e n t CEA e x p e r i m e n t a l r e s u l t s and seems t o be t h e f i r s t c l o u d on t h i s o t h e r - w i s e s i m p l e a n d s u c c e s s f u l p i c t u r e .

2.- THE PARTON HADRON TRANSITION.- Some q u e s t i o n s a r i s e i f one g o e s one s t e p f u r t h e r and a s k s t h e qubs- t i o n how t h e p a r t o n s decay i n t o hadrons. T h i s was wi- d e l y d i s c u s s e d d ~ . i n g t h e l a s t y e a r and I w i l l t r y t o p r e s e n t h e r e a s h o r t review o f t h e i s s u e s and answers.

- -

Pnw (-q 2,

F i g . 1

S e v e r a l a u t h o r s r a i s e d o b j e c t i o n t o t h e p a r t o n

p l a t e a u ( a l s o known a s c u r r e n t p l a t e a u ) . Landshoff

a n d P o l k i n g h o r n e [ 3 ] c l a i m t h a t a l l t h e p a r t o n re-

s u l t s c a n be s i m p l y u n d e r s t o o d by u s i n g a c o v a r i a n t

p i c t u r e of t h e form of f i g u r e 2 i n which t h e b l o b

r e p r e s e n t s t h e a m p l i t u d e of a hadron t o e m i t and ab-

s o r b a p a r t o n . The b a s i c a s s u m p t i o n to b e made i s

t h a t t h e p a r t o n - h a d r o n a m p l i t u d e i s damped i n t h e

v i r t u a l mass o f t h e p a r t o n ( i . e . a f a s t e r damping t h a n t h a t g i v e n by t h e p a r t o n p r o p a g a t o r o n l y ) . T h i s h o l d s i n cp 3 t h e o r i e s t h a t u s u a l l y s e r v e a s models f o r R e r g e c a l c u l u s . I t i s however a s t r l n g e n t assump- t i o n . I f t r u e t h e n o n l y d i a g r a m s l i k e f i g u r e 2 l e a d

t o s c a l i n g . I n p a r t i c u l a r f i g u r e 3 , which shows a n a d d i t i o n a l Pomeron c c u p l i n g , h a s t o v a n i s h i f t h e parton-Pomeron v e r t e x i s damped i n mass. S i n c e t h i s d i a g r a m i s f o r b i d d e n i t a l s o t u r n s o u t t h a t t h e r e i s n o p a r t o n p l a t e a u and t h e r e f o r e one s h o u l d s e e o n l y t h e 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 and t h e l n w h a d r o - n i c s t r u c t u r e . (More s o p h i s t i c a t e d v e r s i o n s of t h i s model c a n a c c o u n t f o r a f i l l i n g of t h e r a p i d i t y gap by a l l o w i n g p r o d u c t i o n of h i g h m u l t i p l i c i t i e s which l e a d t o a s l o w approach t o s c a l i n g [4].

S i m i l a r r e s u l t s were o b t a i n e d f o r c l a s s e s o f d i a - grams by Kogut, S i n c l a i r and S u s s k i n d [5]. They con- s i d e r e d m u l t i p e r i p h e r a l a n d p o l y p e r i p h e r a l diagrams i n cp3 and c u t o f f quark-gluon t h e o r i e s a n d c l a i m t h a t t h o s e diagrams t h a t s c a l e do n o t show a p a r t o n p l a - t e a u .

C a s h e r , Kogut and S u s s k i n d (CKS) 161 s u g g e s t a n a l - t e r n a t i v e t h a t was m o t i v a t e d by u n p u b l i s h e d i d e a s o f B j o r k e n . I n s t e a d o f h a v i n g a m u l t i p e r i p h e r a l c h a i n , t h e y s u g g e s t u s i n g diagrams l i k e f i g u r e 4.

One may t h e n s a y t h a t t h e c r e a t i o n of t h e p a r t o n p a i r s is by n o means a s h o r t - c o r r e l a t i o n p r o c e s s . I n s p a c e t i m e i t s h o u l d b e r e g a r d e d a s a c o n t i n u o u s pro- c e s s t a k i n g p l a c e w h i l e t h e p a r t o n s a r e moving away from one a n o t h e r . F i g u r e 4 c o r r e s p o n d s t o t h e

+ -

e e + h a d r o n s problem b u t a s i m i l a r p i c t u r e c a n b e drawn i n t h e e p c a s e . Whatever t h e mechanism i s , we s h a l l e x p e c t t h e same mechanism t o show u p i n t h e e p and e+e- c a s e s , d e t e r m i n i n g t h e In(-q 2 ) beha- v i o u r . Note t h a t s u c h i n t e r a c t i o n s were n o t i n c l u d e d i n f i g u r e s 3 and 4 . I n p a r t i c u l s r t h e p o i n t - l i k e gluon-quark v e r t e x d o e s n o t l e a d t o a damping of t h e k i n d assumed by Landshoff and P o l k i n g h o r n e [13] i n t h e d i s c u s s i o n of f i g u r e 3.

L e t u s r e t u r n now t o t h e quantum number r e t e n t i o n q u e s t i o n . I t was proposed by Feynman and withdrawn by him a f t e r t h e c o u n t e r arguments by F a r r a r and Rosner 171. The r e t e n t i o n c o n j e c t u r e s a y s t h a t i n t h e ( o u t g o i n g ) 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 t h e ave- r a g e c h a r g e s (2,B,S) s h o u l d be t h o s e o f t h e p a r t o n . Simple models [7 ][8 ] of decay c h a i n s show t h a t t h i s i s n o t a n e c e s s a r y r e s u l t . Thus i n a model of qq p a i r p r o d u c t i o n i n t h e vacuus, we f i n d t h a t i n a d d i - t i o n t o t h e p a r t o n c h a r g e Q we s h o u l d 3ee t h e ave-

q

r a g e c h a r g e of t h e e x i s t i n g p a r t o n p r o p a g a t o r

where P -

qq o n l y i n a n

<Q )q = Qq

i s t h e p r o b a b i l i t y of qq p r o d u c t i o n . Thus SU symmetric s i t u a t i o n we s h o u l d e x p e c t

3

,

O t h e r w i s e t h i s s i m p l i f i e d model l e a d s Q + c ( a n d ( ~ > = Q - - c ) .

9 9 q

What a b o u t SU3 i n v a r i a n c e ? One o f t e n h e a r s t h e argument t h a t SU3 i n v a r i a n c e s h o u l d n o t be e x p e c t e d h e r e s i n c e i n t h e c e n t r a l r e g i o n o f hadron r e a c t i o n s one o b s e r v e s more p i o n s t h a n kaons. T h i s argument h a s two f l a w s : a ) t h e p a r t o n p l a t e a u may be d i f f e - r e n t i n n a t u r e from t h e hadron p l a t e a u and t h e r e f o r e o n e c a n n o t u s e i t a s a n argument ; b ) SU v i o l a t i o n

3

i n t h e meson s p e c t r u m d o e s n o t mean SU3 v i o l a t i o n on t h e p a r t o n l e v e l , s i n c e t h e t r a n s i t i o n from p a r - t o n s t o h a d r o n s depends on t h e wave f u n c t i o n s of t h e l a t t e r . To be more s p e c i f i c , s u p p o s e you p r o d u c e mainly t h e 1 - v e c t o r mesons, o r a 3 5 m u l t i p l e t of v e c t o r mesons ,and p s e u d o s c a l a r mesons, t h e n by a l l o - wing them t o decay i n t o t h e o b s e r v e d K and x mesons one o b t a i n s e a s i l y a r a t i o of d K > 4 .

A c t u a l l y i n a model of t h e t y p e of f i g u r e 4 w i t h s i n g l e t g l u o n e x c h a n g e s one would e x p e c t a n SU3 i n - v a r i a n t c z O .

Now we come t o t h e f i n a l q u e s t i o n : why a r e n o t

q u a r k s o b s e r v e d ? CKS [ 6 ] h a v e shown i n two dimen-

C1-156 D. HORN

s i o n a l m a s s l e s s QED t h a t t h e o u t g o i n g s t a t e s d o n o t t h i s momentum i s a b s o r b e d by a p a r t o n ( s e e F i g . 5 ) . i n c l u d e s t a t e s of s p i n 1/2, a l t h o u g h such f i e l d s

e x i s t i n t h e L a g r a n g i a n . T h i s i s i n t e r p r e t e d by them a s a n e f f e c t i v e s c r e e n i n g of t h e c h a r g e by a l l meson f i e l d s . CKS s p e c u l a t e t h a t such a mechanism may work i n a t h e o r y of a c o l o r SU(3) of gauge f i e l d s .

A major achievement i n t h e f i e l d - t h e o r e t i c approa- c h e s was r e c e n t l y announced by G r o s s and Wilczek [ 9 ] and P o l i t z e r [lo], who o b s e r v e d t h a t non-abelian gauge t h e o r i e s have t h e i n t e r e s t i n g p r o p e r t y t h a t t h e e f f e c t i v e c o u p l i n g c o n s t a n t s v a n i s h f o r -q 2

,

t h u s r e n d e r i n g them a s y m p t o t i c a l l y f r e e . T h i s l o o k s v e r y much l i k e t h e p a r t o n e x p e c t a t i o n w i t h t h e excep- t i o n t h a t ( v e r y s m a l l ) l o g a r i t h m i c c o r r e c t i o n s t o s c a l i n g a r e e x p e c t e d . These t h e o r i e s behave s i m p l y f o r -q2

b u t become v e r y c o m p l i c a t e d f o r s m a l l momenta, and t h e r e may e x i s t t h e e x c i t i n g p o s s i b i l i - t y t h a t t h e o n l y way t o a v o i d t h e i n f r a r e d s i n g u l a - r i t i e s i s by c o m p l e t e l y s h i e l d i n g t h e gauge c o l o r s , t h u s f o r b i d d i n g t h e e x i s t e n c e of f r e e q u a r k s and g l u o n s [I I ] .

To summarize t h i s s e c t i o n , we may answer t h e ques- t i o n r a i s e d a t t h e b e g i n n i n g t h a t some c e n t r a l r e g i o n of h a d r o n s ( p a r t o n p l a t e a u ) i s e x p e c t e d t o develop.

T h i s way a f r a c t i o n a l l y c h a r g e d q u a r k d o e s n o t have t o be produced. The c h a r a c t e r i s t i c s of t h e 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 a r e model dependent a n d l e a v e u s w i t h v e r y i n t e r e s t i n g open q u e s t i o n s .

3.- LARGE ANGLE HADRON SCATTERING.- The main bulk o f h a d r o n i c c o l l i s i o n s o c c u r s i n t h e r e g i o n of low

t r a n s v e r s e momenta. I n Feynman's l a n g u a g e i t c o r r e s - ponds t o i n t e r a c t i o n s between wee p a r t o n s o f t h e two d i f f e r e n t hadrons. I n o r d e r t o s e e some t y p e of sca- l i n g phenomena a n a l o g o u s t o c u r r e n t i n t e r a c t i o n s one would l i k e t o l o o k a t some l a r g e -q2 . Such c a s e s a r e d i s c u s s e d i n this and i n t h e n e x t s e c t i o n .

D e s c r i b i n g t h e e m i s s i o n and a b s o r p t i o n a m p l i t u d e s by two d i m e n s i o n a l G a u s s i a n s , one r e t i l i z e s t h a t t h e

-+ k ' i n t e g r a t i o n l e a d s t o

t h u s e m p h a s i z i n g t h e h a r d p a r t o n ( x n e a r 1 ) r e g i o n . The form f a c t o r i s o b t a i n e d by t h e f u r t h e r x i n t e - g r a t i o n

where we assumed a n a m p l i t u d e (1-x)' f o r F2(x) which a p p e a r s i n s i d e t h e i n t e g r a l . T h i s e s t a b l i s h e s t h e Drell-Yan r e l a t i o n . F o r t h e p r o t o n w e c h o o s e y = 3 i n o r d e r t o o b t a i n F - t -2 , which c h e c k s a l s o w i t h t h e e x p e r i m e n t a l F 2 ( x )

(1-x) 3 .

x-t 1

I f t h e s p i n o f t h i s h a r d ( x = 1 ) p a r t o n i s p a r a l l e l t o t h a t o f t h e p r o t o n , t h e l a t t e r w i l l behave a s a p o i n t p a r t i c l e m o d i f i e d by a n o v e r a l l t-dependence.

T h i s c o r r e s p o n d s t o a n a s y m p t o t i c GE = GM/(l+p ) P r e l a t i o n .

3.2.- An a l t e r n a t i v e approach i s t o assume a n a s y m p t o t i c power dependence a t b o t h l a r g e x and l a p g e t r a n s v e r s e d i r e c t i o n s . Thus B l m k e n b e c l e r , Brodsky I n s e c t i o n 1 we l o o k e d o n l y a t t h e l o n g i t u d i n a l

and Gunion [13 ](BBG) t r e a t t h e f o r m - f a c t o r problem d i s t r i b u t i o n s i n c e t h e r e was o n l y one v a r i a b l e i n

by u s i n g two t h e problem. Here we w i l l have t o d i s c u s s both l o n g i -

w i t h momenta p z ( p + t u d i n a l and t r a n s v e r s e d i r e c t i o n s i n t h e p a r t o n wave

f u n c t i o n s . Two b a s i c a p p r o a c h e s a r e found i n t h e l i - pa = ( x p + t e r a t u r e .

3.1.- A l l p a r t o n s have b a s i c a l l y o n l y a n o r i g i n a l l o n g i t u d i n a l momentum component. T h e r e i s a s t r o n g c u t o f f i n t h e t r a n s v e r s e d i r e c t i o n . . T h i s i s motiva- t e d by t h e o b s e r v a t i o n of t h e c u t o f f i n p a r t i c l e pro-

d u c t i o n a t l a r g e pT . L e t u s l o o k a t a form f a c t o r F i g . 6

in this approach [12]. We start with a proton moving and t h e y n o t e t h a t i n a B e t h e - S a l p e t e r a p p r o a c h i n

w i t h a momentum * - + - ^{in the} z-direction. I t is hit which one t r i e s t o s o l v e f o r t h e wave f u n c t i o n of

by a photon w i t h momentum k p e r p e n d i c u l a r t o z and t h e bound s t a t e p i n t e r m s of c o n s t i t u e n t s a a n d c

o n e f i n d s n a t u r a l l y an e x p r e s s i o n of t h e form

where 2 2 2

$+ ( 1 -x )ma + xmc 2 -

S($,X) = (pa+pc) -

x(1-x)

@ depends on t h e p o t e n t i a l . I n some s p e c i f i c examples

@ i s a l s o a f u n c t i o n of S and t h e s e a u t h o r s u s e t h e - r e f o r e a n a s y m p t o t i c e x p r e s s i o n YNS-" N(x) f o r t h e b e h a v i o u r of t h e f u n c t i o n a t S

( i . e . b o t h a t x + 1 and + m ) . N ( x ) i s supposed t o be smooth. No- t e t h a t h e r e t h e c o r e ( q u a r k p a i r o r a n t i q u a r k ) a n d t h e q u a r k a r e t r e a t e d s y m m e t r i c a l l y , w h e r e a s i n t h e p r e v i o u s a p p r o a c h t h e r e was a c l e a r asymmetry ( t h e p a r t o n was t r e a t e d " i n c l u s i v e l y " ) .

I n c n l c u l a t i n g t h e form f a c t o r one o b s e r v e s now t h a t a t l e a s t one of t h e p a r t i c l e s must h a v e a compo- n e n t of l a r g e

and t h e r e f o r e i t t u r n s o u t t h a t t h e form f a c t o r w i l l behave l i k e t-n. BBG show s p e c i f i c a l l y t h a t f o r a quark of s p i n 1/2 and c o r e ( q q p a i r ) of s p i n

t h e y o b t a i n

GE

t-n I n t . ^The

b e h a v i o u r of F ( x ) n e a r x + l i n t h i s model t u r n s o u t )2n-1

t o be F ~ ( 1 - x

2 s o t h a t t h e Drell-Yan r e l a t i o n i s o b t a i n e d .

L e t u s t u r n now t o f i x e d a n g l e e l a s t i c s c a t t e r i n g ( f i x e d t / s , l a r g e s ) . Using t h e f i r s t a p p r o a c h one would s a y [12][14] t h a t t h e p r o c e s s i s due t o h a r d p a r t o n c o l l i s i o n s ( F i g . 7 ) ; i n o r d e r t o t r a n s f e r t h e l a r g e t o n e h a s t o u s e

p a r t o n s and i f t h e p a r - t o n - p a r t o n s c a t t e r i n g were g l u o n exchange one would r e c o v e r t h e Abarbanel D r e l l - G i l m a n [ 1 5 ] r e a l ampli- t u d e t h a t l e a d s t o C , u F 4 ( t ) . I n a more g e n e r a l c a -

d t

s e one would a l l o w f o r a more c o m p l i c a t e d p a r t o n - p a r t o n c r o s s - s e c t i o n , h o p e f u l l y a s i m p l e f u n c t i o n of t / s .

U s i n g pp e l a s t i c d a t a f o r s < 5 0 ~ e ? o n e f i n d s [ 1 2 ] t h a t a p o s s i b l e p a r a m e t r i z a t i o n i s ( - t + 0 . 7 ) ' ~ . ~ f ( t / s ) which i s r e m i n i s c e n t of t h e f o r m - f a c t o r bohaviour a l - t h o u g h w i t h a somewhat d i f f e r e n t power. The a p p a l i n g f e a t u r e i s however t h a t f ( t / s ) n e -23 tfs , which d o e s n o t l o o k l i k e any r e a s o n a b l e c r o s s - s e c t i o n . I t seems t h a t t h e o n l y way o u t i s t o modify t h e mechanism.

Kogut and S u s s k i n d [ 1 4 ] s u g g e s t e d a n a n a l o g y w i t h

atom-atom c o l l i s i o n s , i n which t h e n u c l e i r e p r e s e n t t h e h a r d p a r t o n s and t h e e l e c t r o n s wee-partons ( x = l analogaus.to l a r g e mass, x 0 s m a l l mass). The l a r g e

t c o l l i s i o n must t h e n t a k e p l a c e between t h e n u c l e i b u t a n a d d i t i o n a l c o r r e c t i o n due t o e l e c t r o n exchan- g e s must a p p e a r . T h i s r e f l e c t s t h e motion of t h e e l e c t r o n c l o u d t h a t f o l l o w s t h e n u c l e i . I f o n e t r i e s t o implement t h i s approach i n c a l c u l a t i o n s and i n - c l u d e s wee p a r t o n e x c h a n g e s i n a d d i t i o n t o t h e h a r d p a r t o n r e a c t i o n [ 1 2 ] , t h e b e h a v i o u r of f ( t / s ) c a n be

a c c o u n t e d f o r by assuming a p a r t i c u l a r d i s t r i b u t i o n f o r t h e wee p a r t o n s . The r e s u l t i s s e n s i t i v e t o t h i s n o n - s c a l i n g assumption. Using t h i s approach o n e c a n ' t h e n a l s o f i t N* d i f f r m t i o n p r o d u c t i o n , and (pp,p) i n c l u s i v e d a t a (24 GeV, -t > 1.5 ~ e ? ) i n t h e exchan-

t 1

g e r e g i o n x - - > - . The d i f f i c u l t y of t h i s a p p r o a c h s 2

i s t h a t a s y m p t o t i c a l l y one would e x p e c t h e r e t h e s a - me l a r g e t b e h a v i o u r f o r pp and pp s c a t t e r i n g . - A t a v a i l a b l e e n e r g i e s t h e y d i f f e r c o n s i d e r a b l y .

The d i f f e r e n t a p p r o a c h of BBG [13] views t h e 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 p a r t o n exchanges. Thus i n AB ⁺ CD t h e y sum o v e r a l l diagrams of t h e t y p e of f i g u r e 8.

Each p a r t i c l e h a s a p a r t o n wave f u n c t i o n YL&S ?IL(x) -L L = A,B,C,D , and s i n c e l a r g e t means t h a t a t l e a s t t h r e e p a r t i c l e s p o s s e s s p a r t o n s w i t h l a r g e 5 ^{t h e y}

o b t a i n

where I i s some smooth f u n c t i o n of c o s e = Z . I n p a r - t i c u l a r , a t 90'

= do- ^(90')

* ^{[ M I 2 =} s-2(A+C+D) I(O)

167c s 16x 2 .

Thus i n p-p s c a t t e r i n g , s i n c e A = C z D z 2 o n e s h o u l d -1 2

e x p e c t an s d e c r e a s e . The a v a i l a b l e d a t a c o r r e s - pond b e t t e r t o s-lo b u t t h e h i g h e n e r g y t a i l 3 0 _( s 5 4 0 ~ e ? c a n b e f i t t e d w i t h s-I' .

The pp:pp q u e s t i o n , which i s a problem f o r t h e

h a r d - p a r t o n approach, i s a s u c c e s s h e r e . S i n c e t h e r e

i s a mismatch between t h e q u a r k s and a n t i q u a r k s t h e

a u t h o r s e x p e c t a r a t i o of p p : p p s l : 5 0 a t 90' ( e x -

p e r i m e n t a l l y i t i s s l :I 0 0 a t 5 CeV/c).

C1-158 D. HORN

I n x p c o l l i s i o n s BBG t r e a t t h e problem by assuming t h a t t h e x h a s a n e l e c t r m a g n e t i c form f a c t o r F d t - l Hence r p -+ x p c o r r e s p o n d s t o A = C = ¹ . ^{D = 2 and}

. Moreover by assuming a v a l e n c e q u a r k s t r u c - d t

t u r e a n d r e s o r t i n g t o t h e u s e of q u a r k ( d u a l i t y ) d i a - grams t h e y have s p e c i f i c p r e d i c t i o n s f o r t h e t depen- d e n c e and r a t i o s of c r o s s - s e c t i o n s .

A t f i x e d s t h e y o b t a i n e d a good f i t t o f p

7[p d a t a w i t h a - 2 , ^{@ = I} .

S i m i l a r s p e c i f i c p r e d i c t i o n s a r e o b t a i n e d f o r KN r e a c t i o n s and i t r e m a i n s t o be s e e n whether t h e s e va- r i o u s p r e d i c t i o n s a r e born o u t by e x p e r i m e n t a l r e s u l t s .

T h e r e remains of c o u r s e t h e c o n c e p t u a l q u e s t i o n why one does n o t i n c l u d e h e r e d i a g r a m s i n which two q u a r k s i n t e r a c t r a t h e r t h a n g e t i n t e r c h a n g e d . A f t e r a l l a

-4 2 d a

p r i o r i t h a t s a v e s a n s ( o r f ( s ) ) f a c t o r i n .

Should one t h i n k o f t h e quark-quark i n t e r a c t i o n a s s o s t r o n g l y damped i n s ?

I n a r e c e n t p a p e r Brodsky and F a r r a r [ 1 6 ] m o d i f i e d t h e BBG approach by emphasizing t h e d i f f e r e n c e b e t - ween qq and qqq s t r u c t u r e s . They o b t a i n t h e i n t e r e s - -

t i n g r e s u l t t h a t f o r c e r t a i n sets of diagrams i n a s p i n 1/2 - v e c t o r gluon t h e o r y , i n which a l l q u a r k s c a r r y f i n i t e p a r t s of t h e hadron momentum, m a t r i x e l e m e n t s have t h e s i m p l e form

where n. ( n i s t h e number of incoming ( o u t g o i n g )

f

momenta. They a r g u e t h a t i f t h e bound s t a t e wave f u n c - t i o n does n o t modify t h i s r e s u l t , and f i x e d a n g l e s c a t t e r i n g w i l l s c a l e l i k e --s2-n dm f ( i ) where n

d t

i s t h e o v e r a l l number of q u a r k s i n v o l v e d . T h i s l e a d s n a t u r a l l y t o d i f f e r e n t form f a c t o r s f o r p i o n s and p r o t o n s a s assumed i n t h e BBG approach [13], however meson-baryon and baryon-baryon r e a c t i o n s a r e e x p e c t e d now t o behave l i k e s-a and s-lo r e s p e c t i v e l y .

4. - LARGE TRANSVERSE MOMENTUM PRODUCTION. - ^Once

a g a i n one f i n d s two sets of p o s s i b l e a p p r o a c h e s t o t h i s problem, f o l l o w i n g t h e same l i n e s of r e a s o n i n g u s e d i n t h e p r e v i o u s s e c t i o n . The d e t a i l e d p r e d i c - t i o n s of t h e v a r i o u s models w i l l b e d i s c u s s e d i n t h e m i n i - r e p o r t by P o l k i n g h o r n e , t h e r e f o r e I w i l l con- c e n t r a t e j u s t on t h e main p o i n t s .

The approach of s c a t t e r i n g of h a r d p r o t o n s was f i r s t d i s c u s s e d by Berman, B j o r k e n and Kogut [17].

A r e c e n t s y s t e m a t i c s t u d y of t h i s approach was c a r - r i e d o u t by E l l i s and K i s l i n g e r [ l a ] . I n c l u s i v e pro- d u c t i o n of p a r t i c l e s i s d e s c r i b e d i n t e r m s of l o n g i - t u d i n a l p a r t o n a m p l i t u d e s , a p a r t o n - p a r t o n s c a t t e - r i n g c r o s s - s e c t i o n , and p a r t o n f r a g m e n t a t i o n i n t o h a d r o n s . The d i s c u s s i o n of s e c t i o n 2 s h o u l d a p p l y h e r e , and one e x p e c t s t o o b s e r v e a 'Iparton p l a t e a u "

which l e a d s t o a n i n c r e a s e of m u l t i p l i c i t y w i t h I n + and s h o u l d be t h e same a s t h e one e x p e c t e d t o o c c u r i n e p and e+e- r e a c t i o n s . I f t h e p a r t o n - p a r t o n r e a c t i o n s were dominated by gluon exchange, one would o b t a i n a s c a l e - i n v a r i a n t c r o s s - s e c t i o n

where = ^{2pT/& and 8} i s t h e c.m. p r o d u c t i o n a n g l e .

Recent l a r g e a n g l e p r o d u c t i o n d a t a seem t o p r e f e r s -4 . F i t t i n g t h e s e d a t a w i t h t h i s approach i m p l i e s t h a t q-q s c a t t e r i n g must be more c o m p l i c a t e d , never- t h e l e s s t h e o b s e r v e d i n c r e a s e of m u l t i p l i c i t i e s w i t h I n pT i s a p o i n t i n f a v o u r of t h i s approach.

The o t h e r c a l s s of models, e.g. t h e BBG approach [13], views meson p r o d u c t i o n a s due t o a f u s i o n of q w i t h q . Hence a n i n c r e a s e of m u l t i p l i c i t i e s d o e s n o t f o l l o w . Another d i f f e r e n c e i s t h a t i n t h e BBG model baryon p r o d u c t i o n t u r n s o u t t o s c a l e w i t h a d i f f e r e n t power t h a n meson p r o d u c t i o n , s o t h a t asymp- t o t i c a l l y o n l y mesons s h o u l d s u r v i v e .

O t h e r models t h a t c a n be c l a s s i f i e d i n t o t h i s same c a t e g o r y a r e t h o s e of Landshof f and P o l i n g h o r n e [3 1,

and Amat i , Caneschi and T e s t a [ 1 9 ] , who d e v e l o p t h e i r i n t u i t i o n f o r p a r t o n r u l e s from model t h e o r i e s l i k e m u l t i p e r i p h e r a l c h a i n s i n f i e l d t h e o r y .

I n summary, we s e e t h a t t h e a p p l i c a t i o n o f p a r t o n t h a t l a r g e momentum-transfkr r e a c t i o n s of hadrons

a p p r o a c h e s t o hadron s c a t t e r i n g i s s t i l l f a r from ha- w i l l a l s o show some f e a t u r e s of p o i n t - l i k e i n t e r -

v i n g t h e s i m p l e f e a t u r e s and s u c c e s s which was met i n a c t i o n s , b u t we have s t i l l t o w a i t f o r t h e o r i e s and

c u r r e n t i n t e r a c t i o n s ( s e e s e c t i o n 1). The hope i s e x p e r i m e n t s t o c o n v e r g e on some u n i q u e answer.

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