THEORY OF SPIN EFFECTS AT HIGH ENERGY : WORKSHOP SUMMARY

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THEORY OF SPIN EFFECTS AT HIGH ENERGY : WORKSHOP SUMMARY

E. Leader

To cite this version:

E. Leader. THEORY OF SPIN EFFECTS AT HIGH ENERGY : WORKSHOP SUMMARY. Journal de Physique Colloques, 1985, 46 (C2), pp.C2-185-C2-194. �10.1051/jphyscol:1985217�. �jpa-00224528�

JOURNAL DE PHYSIQUE

Colloque C2, supplément au n°2, Tome 46, février 1985 page C2-185

THEORY OF SPIN EFFECTS AT HIGH ENERGY : WORKSHOP SUMMARY

E. Leader

Birkbeek College, London WC1E 7HX, U.K.

RESUME : Il existe un désaccord entre la théorie et l'expérience dans plusieurs réactions pour lesquelles des paramètres de spin ont été mesurés. Nous portons notre attention sur ceux-ci et sur certaines tentatives pour trouver une expli- cation théorique.

ABSTRACT : There is a disagreement between theory and experiment for several reac- tions in which spin dependent parameters are measured. We focus our attention on these and upon some theoretical attempts to explain them.

1 - Introduction

A basic aim in elementary particle physics is a knowledge of the dynamics of the basic constituents that make up the hadrons. This knowledge can be approached pheno- menologically on the one hand by studying processes in which the constituents inter- act violently with each other (reactions with large momentum transfer) and on the other hand by exploring how, structurally, the hadrons are built-up from their cons- tituents. In both these approaches the behaviour with respect to the spin degree of freedom is of crucial importance. It is a fundamental element in the structure of the inter-constituent forces, and a knowledge of the distribution of parton spins in a hadron of given helicity is ultimately as important as a knowledge of the dis- tribution of parton momenta.

For reactions at large p^, where perturbative QCD should be valid, there are clearcut and definitive predictions for the spin behaviour U , but experimentally we are in the tantalizing and frustrating situation of being just abouc, but perhaps not quite, in the region where the perturbative results should hold. Frustrating also because trends in the data (inclusive /\ polarization, asymmetry in T T * production, spin cor- relation in large angle pp collisions), if they persist at larger p , will be in disagreement with the predictions of QCD.

Several papers attempt to understand the present experimental regions of small and

"medium" p, by a judicious blending of diffractive and QCD mechanisms or by totally different approaches, such as the "massive quark model" (MQM) which is intended as a rival to QCD.

They all have the merit of making rather precise experimental predictions which should be testable quite soon. There have also been contributions which extend the classic large pA perturbative QCD calculations to new processes or to a more detai- led study of some of the already well known reactions (elastic forjn factors, deep inelastic scattering, photoproduction of vector mesons).

A paper which, at first sight, seems unconnected with the above dynamical questions, suggests a relationship between present day polarization measurements in <*~p-»Tf°n and the ultimate asymptotic behaviour of scattering amplitudes. The latter is of course linked to the underlying dynamics, though in a highly non-perturbative fa- shion, and the testable consequences of these ideas are important.

The general approach to learning about dynamics through polarization experiments was discussed by Goldstein, and a useful method for determining the P and CP of heavy mesons and for testing for violations of these symmetries, was explained by Nelson.

Both these presentations are written up elsewhere in these proceedings and we shall not discuss them further here.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1985217

2 - The b a t t l e f o r non-zero p o l a r i z a t i o n

One of t h e most i n t r i g u i n g dynamical q u e s t i o n s a t p r e s e n t i s how.to persuade an acceptable theory t o produce r e s p e c t a b l e p o l a r i z a t i o n s a t high e n e r g i e s . A respec- t a b l e p o l a r i z a t i o n r e q u i r e s n o t j u s t t h e e x i s t e n c e of a s i g n i f i c a n t h e l i c i t y - f l i p amplitude b u t a l s o t h a t it must be considerably o u t of phase with t h e helicity-non- f l i p amplitude. Theories l i k e QCD, with v e c t o r coupling and massless quarks y i e l d zero f o r t h e h e l i c i t y - f l i p amplitudes r e l e v a n t t o t h e p o l a r i z a t i o n i n hadron-hadron s c a t t e r i n g . Giving t h e quarks a mass m w i l l produce a f l i p amplitude, b u t i n order

q

t o generate a phase one must go t o higher o r d e r than t h e Born terms i n p e r t u r b a t i o n theory. The r e s u l t i s t h a t t y p i c a l l y one f i n d s f o r t h e amplitude

*non-f l i p

which then i s very small and which* 0 a s s i n c r e a s e s .

A t small t o r Q 2 t h e p e r t u r b a t i v e arguments a r e not convincing, but nor a r e t h e non- p e r t u r b a t i v e c a l c u l a t i o n s , so no fmdamenta2 progress been achieved. However v a r i o u s attempts have been made, some q u i t e ad-hoc, o t h e r more i n t e r e s t i n g , t o introduce a h e l i c i t y - f l i p amplitude phenomenologically .

Goloskokov, Kuleshov and S e l j u g i n ') use a n e i k o n a l formalism f o r nucleon-nucleon s c a t t e r i n g i n which a c e r t a i n % -matrix s t r u c t u r e i s postukted f o r t h e Born term. I t y i e l d s f o r t h e r e l e v a n t h e l i c i t y amplitude T++;+-U Born

F

I ^I

The non-flip amplitude i s then c o n t r o l l e d by a p r o f i l e f u n c t i o n {I - e x { l o ( s , b ~ ] i n which t h e energy-dependent m a t t e r d e n s i t y y i e l d i n g t h e e i k o n a l h a s t h e unusual form ( S , ) - ( S , , ^{where D} a r i s e s from t h e non-flip Born term. There a r e then two regions, "high energyv where D>> and, a s i s u s u a l , non-flip domi- n a t e s , and "super high" beyond ISR) where D(< and t h e f l i p dominates. The l a t t e r h e l p s them t o f i t t h e shoulder i n d s l d t f o r a t 540 GeV/= where most o t h e r e i k o n a l models a r e i n d i f f i c u l t y . The e i k o n a l i z e d h e l i c i t y - f l i p amplitude depends upon a p r o f i l e f u n c t i o n which i s p r o p o r t i o n a l t o aftlab, and f a i r f i t s t o t h e pp PO- l a r i z a t i o n P f o r 150 - 300 GeV/, a r e obtained. However l i k e most e i k o n a l models P -

has a l a r g e r "spike" i n t h e region of t h e d i p i n d b / d t than t h e d a t a show. The whole approach i s mainly phenomenological and should be regarded a s an attempt t o l e a r n about t h e h e l i c i t y - f l i p amplitude from t h e data. The i n t e r p r e t a t i o n can be t e s t e d : t h e p o l a r i z a t i o n changes r a p i d l y i n t h e region 2 3 0 GeV/ and develops a l a r g e p o s i t i v e spike (40 %) a t t = -1.5 GeVIc (See Fig. l next page). Spin c o r r e l a t i o n pa- rameters should be c a l c u l a t e d from t h e model.

S t a r t i n g from a v e r y d i f f e r e n t p o i n t of view, and with an i n t e r e s t i n g p h y s i c a l moti- v a t i o n , Bourrely 3 ) a r r i v e s a t e i k o n a l formulae t h a t look, surp,risingly l i k e those of Goloskokov e t a l . A nucleon i n a d e f i n i t e s p i n s t a t e i s p i c t u r e d a s a r o t a t i n g matter d i s t r i b u t i o n and s i n c e hadron-hadron cross-sections a r e energy dependent t h e i n t e r a c t i o n s t r e n g t h of a p r o j e c t i l e , c o l l i d i n g with a given region of t h e t a r g e t nucleon, depends upon whether t h a t region i s approaching o r receding from t h e pro- j e c t i l e i . e . it depends upon t h e v e l o c i t y o f t h e matter d i s t r i b u t i o n a s a f u n c t i o n of impact parameter. The e i k o n a l i s e a n e l i c i t y - f l i p amplitude i s c o n t r o l l e d by a p r o f i l e f u n c t i o n which is p r o p o r t i o n a l t o a l n s ) ^X V ( b ) : t h e v e l o c i t y f u n c t i o n W (b) being a r b i t r a r y . With a reasonable choice f o r t h i s f u n c t i o n (a gaussian,

s l i g h t l y modulated) t h e pp p o l a r i z a t i o n P f o r 100 L p~ 6 300 GeVIc i s adequately

Fig. (1) : Comparison of Goloskokov (Q = 30 and 200 GeV) and Bourrely (6 ^{= 500 GeV)}

pp p o l a r i z a t i o n s .

f i t t e d . P r e d i c t i o n s f o r P a r e given a t (? = 0.5, 1 , 10 and 20 TeV f o r ( t l & 7 GeV 2 .

Where they can be compared i . e . f o r It\& 2 G ~ v ' , t h e r e i s some s i m i l a r i t y between our rely's 0.5 TeV and Goloskokov e t als' 200 GeV p r e d i c t i o n s (Fig. l).

For I t l > 2 and a t highel: e n e r g i e s Bourrely p r e d i c t s s i z e a b l e p o l a r i z a t i o n s . It should be noted, however, t h a t t h e model i s n o t very s a t i s f a c t o r y s i n c e t h e projectile i s e f f e c t i v e l y t r e a t e d a s i f i t had zero s p i n . Thus t h e r e a r e no p r e d i c t i o n s f o r t h e s p i n - c o r r e l a t i o n parameter l i k e ANN e t c . . .

A d i f f e r e n t approach i s adopted by Troshin and Tyurin 4, who make t h e i r phenomenolo- g i c a l a n s a t z a t t h e quark l e v e l . Each quark i s supposed t o s c a t t e r independently i n some mean f i e l d a t impact parameter b. The product of t h e quark amplitudes provides an e f f e c t i v e Born term which is then u n i t a r i z e d . The quark f l i p and non-flip b-space amplitudes a r e given t h e form gi(s)exp [-X m b + iji (S)) with gnon-f lip4 */mq

.- l ¶

non-f lip, and f4 , f n , a r b i t r a r y f u n c t i o n s . No r e a l j u s t i f i c a t i o n i s gf lip = ''>m g

o f f e r e d f o r t h e s e forms though i t is claimed t h a t they a r e l i n k e d t o t h e number o f q; p a i r s which p l a y a r81e i n providing t h e mean f i e l d . F i n a l l y a 'simple, but myste- r i o u s formula P(s,. = sin[ff,$)- loni;iiJ ^{X F (e)} emerges i n which none of t h e parameters X , ^m appear. Maximising t h e r e s u l t by t a k i n g s i n c l = 1 gives P = 11 %

4

a t pL = 28 GeVIc, p$ = 6 (G~v/,)', s l i g h t l y below t h e experimental v a l u e ; but t h e formula f a i l s t o t a l l y i f t h e AGS value of 51 % f 17 % a t p: = 6.56 ( G ~ v / , ) i s Cor- 2 r e c t . ANN and ALL a t 90' a r e p r e d i c t e d t o a s c i l l a t e about t h e v a l u e s f 113 which they r e s p e c t i v e l y Bpproach asymptotically. The model i s n o t very p e r s u a s i v e and without patching up w i l l n o t f i t t h e P data.

We have already mentioned that perturbative QCD with massless quarks yields zero po- larization. An alternative dynamical scheme, the massive quark model (MQM) is used by Nardulli, Preparata& Soffer to study large angle hadron-hadron scattering at high energies. As in QCD the hadrons are composed of "quarks" (and "di-quarks") but here the constituents are massive and they interact via an infinite sequence (lying on a Regge trajectory) of vector meson exchanges, pseudo-scalar meson exchanges

(which provide a significant helicity-flip amplitude) and, where appropriate,s-chati- nel baryon exchanges. The vertex functions for a hadron to emit an active quark in any spin-flavour state and to re-absorb an active quark in any spin-flavour state

n spectator ^ H

Fig. (2) : Hadron vertex function in MQM.

are given by analytic expressions which are based upon ,SU(6) wave functions and the assumption that the spin (not helicity) of the spectator quark or di-quart is con- served. One ends up with analytic expressions for all the helicity amplitudes in meson-baryon and baryon-baryon scattering in terms of just 5 parameters, the overall normalizations in MB and BB reactions, two masses characterizing qq and q-diquark scattering, and, in MB, a parameter X specifying the relative contributions of meson and baryon exchange. The amplitudes for BB are real while those for MB are complex as a consequence of the s-channel baryon exchange. The formulae are valid at large angles and high energies. Note that although a rich helicity structure is predicted, the polarization in BB is zero because the amplitudes are real. We shall return to this question later.

Detailed predictions are given for /dt for many BB and MB reactions, the forms being

i*fB _ * lafs G ») ~\

dt T ^ I

T as s-* co , 6 fixed. (2)

&!? lBJL H <•) J

dt - ^ ^s9

One interesting prediction is that iTp-* K Z should vanish, a result which is not expected in perturbative QCD.

Other interesting predictions are : i) in pp-» pp at 90°

Afljj-* 0.97 A ^ - * -0.02 As g- » - 0.01 as s-»•* , and ii) at 90°

do- (npLx1 . . — » 0.48

dF y^—_{• ^ dt} ^PP

(Experimentally, up to the present, we have Am = 0.59 - 0.09 at p = 12.75 GeV/

and t h e c r o s s - s e c t i o n r a t i o i s 0.50 f 0.22 a t pL = 12 GeVIc)

The p o l a r i z a t i o n i n MB r e a c t i o n s depends c r i t i c a l l y on t h e v a l u e o f h i.e. upon t h e

+ +

r e l a t i v e s t r e n g t h of meson and baryon exchange i n general. However f o r K p + K p and

<p + KOA t h e p o l a r i z a t i o n i s p r e d i c t e d t o be zero.

An attempt 6 , has been made t o o b t a i n t h e v a l u e of h using preliminary d a t a on t h e

- -

h e l i c i t y d e n s i t y m a t r i x of t h e 9-meson i n I V p -rg p a t pL = 12 GeVlc. The d a t a sug- g e s t t h a t f l l -fl-l i s considerably l a r g e r than bothfll +fl-l a n d f o o and t h i s i m p l i e s 3.

Note t h a t p e r t u r b a t i v e QCD would p r e d i c t Q1-l = 0 i n c o n t r a d i c t i o n with t h e above, b u t i t i s n o t obvious t h a t e i t h e r theory can l e g i t i m a t e l y be used a t so low an ener- gy. I n any case i t w i l l be most i n t e r e s t i n g t o s e e r e s u l t s f o r t h e p o l a r i z a t i o n i n MB r e a c t i o n s now t h a t one has some i d e a o f t h e s i z e o f h .

We mentioned e a r l i e r t h a t t h e MQM provides l o t s of h e l i c i t y - f l i p i n BB s c a t t e r i n g , but zero p o l a r i z a t i n because t h e amplitudes a r e r e a l . A d a r i n g suggestion of Bourrely and S o f f e r ) S i s t o m a r r y . t h e i r model f o r d i f f r a c t i o n s c a t t e r i n g , (with i t s dominant imaginary non-flip amplitude), t o the l a r g e angle MQM model.

O f course t h i s means t r u s t i n g t h e e i k o n a l c a l c u l a t i o n of t h e d i f f r a c t i v e amplitude out t o huge v a l u e s of t !

With t h e MQM f i r s t normalized t o give t h e c o r r e c t pp deldt a t 90°, _by i t s e l f , it i s found, miraculously, t h a t t h e a n a l y z i n power i n t h e combined model i s huge, (50 % !) a t pL = 28 GeVle and a.M.= ^{45' i.e.P! =} 6 . 5 6 .

Do n o t f o r g e t t h e s u r p r i s i n g r e c e n t r e s u l t from BNL t h a t A = 51 2 17 % f o r t h i s energy & a n g l e ! Moreover A i s p r e d i c t e d t o grow s t i l l f u r t h e r , a s seen i n Fig. 3 .

ec.m.

Fig. (3) : Asymetry i n pp a t pL = 28 and 50 GeVIc i n t h e Bourrely-Soffer model.

I s t h i s remarkable agreement j u s t f o r t u i t o u s ? The p r e d i c t i o n w i l l s u r e l y f a i l a t t h e nearby value p$ = 5.95 where P = 16 2 5.7 %.

It w i l l be v i t a l l y important t o c a l c u l a t e t h e o t h e r s p i n parameters f o r pp s c a t t e - ring.

Also, f o r c o n s i s t e n c y , t h e same marriage must be a p p l i e d i n t h e meson-baryon domain.

It seems t o me u n l i k e l y t h a t t h e d e t a i l e d form of t h e e i k o n a l treatment, with i t s r o t a t i n g m a t t e r d i s t r i b u t i o n , i s c o r r e c t ( s e e comments e a r l i e r ) .

However t h e consequence of t a k i n g any type of e i k o n a l model s e r i o u s l y a t l a r g e a n g l e s i s dramatic. For nucleon-nucleon s c a t t e r i n g one i s bound t o f i n d

% ( S , O ) - + = 4nt2 a s ^{S - + @}

a t f i x e d 8, where n i s t h e power governing the decrease with q 2 of t h e two-dimensio-

2 2 1 2

n a l F o u r i e r transform F(q ) of t h e matter d e n s i t y g (b) . i . e . F(q ) + --T, a s q- 6 . (9

Since t y p i c a l l y one has n = 1 and thus

2 BB ^{h )} f (0) (modulo logs)

d t 10

i t a p p e a r s ( c . f . equ ( 2 ) ) t h a t t h e e i k o n a l c o n t r i b u t i o n w i l l u l t i m a t e l y dominate d 7 d t a s S-.& a t f i x e d a n g l e j a very s t r a n g e r e s u l t bearing i n mind t h a t i t was t h e MQM t h a t was supposed t o d e s c r i b e t h a t p a r t i c u l a r kinematic r e g i o n ! One w i l l await f u r t h e r r e s u l t s with g r e a t i n t e r e s t .

3 - ^A connection between p o l a r i z a t i o n and asymptotic theorems

There i s one r e a c t i o n , w-p- won where t h e s i z e a b l e measured p o l a r i z a t i o n a t f a i r l y small values of t may be t e l l i n g us something about t h e u l t i m a t e asymptotic beha- viour of s c a t t e r i n g amplitudes i n t h e d i f f r a c t i v e region. Given t h a t t h e crossing- even amplitude appears t o be growing ( a t t = o) l i k e s l n 2 s i . e . a s f a s t a s i t i s permitted t o by v e r y general theorems, it i s f a s c i n a t i n g t o ask8) whether a l s o t h e crossing-odd amplitude could be doing t h e same, i . e . whether a t t = o one could have a s s - r

and

F- (S) s [In s 2 - i ~ l n s l

(In analogy t o t h e pomeron i n F+ one r e f e r s t o an odderon i n P-)

Of course t h e r e l a t i v e magnitude of F- must be very small, a t l e a s t up t o SPS ener- g i e s , otherwise i t would have r e s u l t e d i n s i g n i f i c a n t d i f f e r e n c e s between p a r t i c l e - p a r t i c l e and p a r t i c l e - a n t i p a r t i c l e c r o s s - s e c t i o n s . A t t h e ISR and beyond t h e r e are h i n t s of s i g n i f i c a n t d i f f e r e n c e s , and t h e s e w i l l be c l a r i f i e d i n due course. I n t h e meantime, Gauron, Leader and ~ i c o l e s c u ~ ) n o t e t h a t because one i s l i m i t e d t o an odd- under-crossing amplitude i n * n o n and because t h e p o l a r i z a t i o n i s so s e n s i t i v e

t o phase d i f f e r e n c e s one might be a b l e t o g l e a n some information on F- from t h e change of shape w i t h energy of t h e measured p o l a r i z a t i o n . The f i t t o t h e p o l a r i z a - t i o n ( s e e Fig. 4) and t o Q ($p)- @(<p) from 8+340 GeVIc, does indeed suggest t h e e x i s t e n c e of an odderon-like term i n F-.

Fig. (4) : P o l a r i z a t i o n i n dp-, #n and p r e d i c t i o n s of Gauron e t a1 f o r higher e n e r g i e s .

The i n t e r p r e t a t i o n should be t e s t e d . The p r e d i c t e d p o l a r i z a t i o n s up t o pL = 100GeV/c a r e shown i n Fig. 4 . It should be a p p r e c i a t e d t h a t t h e asymptotic behaviour of F- a t t = o i s not some e s o t e r i c matter t o t a l l y divorced from t h e key questions of s t r o n g i n t e r a c t i o n dynamics. Indeed i t has been suggestedlO) t h a t non-perturbative QCD f o r b i d s a n odderon, so i t i s important t h a t t h e consequences of these i d e a s should be t e s t e d experimentally.

4 - 'Testing QCD a t l a r g e Q2 i n i n c l u s i v e r e a c t i o n s a ) Using an e'e- machine

We have a l r e a d y mentioned t h a t QCD has d i f f i c u l t y i n producing h e l i c i t y - f l i p ampli- tudes and i n g i v i n g them non-zero phases. Layssac, P i r e and ~ a l s t o n l l ) suggest t h a t t h e r e a c t i o n 'd 3- e ^t Z j e t s , u t i l i s i n g a l o n g i t u d i n a l l y p o l a r i z e d e l e c t r o n beam, can be used t o check t h e higher order QCD i n t e r a c t i o n s which would y i e l d an asimu- t h a l asymmetry i n t h e j e t angular d i s t r i b u t i o n .

U. .. -

The e s s e n t i a l p a r t o n i c sub-process i s 'd t-4 1% and they have c a l c u l a t e d t h e asymmetry a r i s i n g from t h e diagram i n Fig. 5.

Fig. (5) : QCD diagram f o r 3 e + ^{e t} Z j e t s .

It i s argued t h a t a " j e t " can be d i s t i n g u i s h e d from a "jyt" and an i n t e g r a t e d ( l e f t v s r i g h t hemisphere) azimuthal asymmetry of* 10 % i s p r e d i c t e d . This seems a n i c e

- and challenging experiment f o r an ete- machine.

b) Using t h e Drell-Yan and r e l a t e d processes

The c a l c u l a t i o n of and t e s t i n g of s c a l i n g v i o l a t i o n s i n deep i n c l a s t i c s c a t t e r i n g i s one of t h e c o r n e r s t o n e s of most peoples' f a i t h in QCD. (Though, i n r e a l i t y , t h e evidence

i s n o t r e a l l y compelling). Deep i n e l a s t i c l e p t o n s c a t t e r i n g i s a l s o t h e main source of o u r knowledge of t h e s t r u c t u r e of hadrons i n terms of t h e i r c o n s t i t u e n t quarks &

gluons, and i n p a r t i c u l a r of t h e momentum-fraction dependence of t h e hadronic wave- function.

I n a s i m i l a r f a s h i o n deep i n e l a s t i c l e p t o n s c a t t e r i n g with p o l a r i z e d l e p t o n s and p o l a r i z e d protons i s t h e p r i n c i p a l source of t h e e q u a l l y important knowledge of how

t h e p a r t o n s p i n s a r e d i s t r i b u t e d i n s i d e a hadron. The SLAC-YALE experiment 12) has a l r e a d y shown t h a t ~ ~ ( b ) a n d simple g e n e r a l i s a t i o n s there-of do n o t c o r r e c t l y des- c r i b e t h e s p i n dependence. Chiappetta and S o f f e r 13) have re-examined t h i s q u e s t i o n using more modern d i s t r i b u t i o n f u n c t i o n s f o r t h e valence quarks and allowing a pola- r i z e d s e a (which i s l i n k e d t o t h e gluons being p o l a r i z e d ) which p l a y s an important r81e a t small ^X values. F i t t i n g t h e SLAC-YALE d a t a and t h e Bjorken sun-rule (inclu- ding i t s lowest o r d e r QCD c o r r e c t i o n term) a t Q' = 5 ( G ~ v / , ) ' f i x e s t h e ~ a r a m e t r i - z a t i o n of t h e spin-dependent d i s t r i b u t i o n f u n c t i o n s a t = 5. I t i s found t h a t t h e s e a c a r r i e s 5 % and t h e gluons 22 % of t h e p r o t o n ' s spin. However t h e r e i s almost no SLAC-YALE d a t a below X = 0.2 s o one awaits with g r e a t i n t e r e s t t h e r e s u l t s of t h e p r e s e n t l y running p o l a r i z e d t a r g e t EMC experiment which w i l l cover t h e r e g i o n 0.04 S X S 0.2 c a r e f u l l y .

The form of t h e s p i n d i s t r i b u t i o n f u n c t i o n s i s of b a s i c importance, b u t a l s o t h e i r Q Z -evolution w i l l , u l t i m a t e l y , be s u b j e c t t o experimental t e s t . A u s e f u l a n a l y t i c parametrization i s given which roughly s a t i s f i e s t h e A l t e r e l l i - P a r i s i equations f o r 5 6 ^Q 2 5000 ( G ~ v / ~ )

'

This r a p i d i n c r e a s e can be t r a c e d t o t h e behaviour a s X + o of t h e i n p u t ( a t Q 2 =5) used f o r t h e gluon d i s t r i b u t i o n . It would thus be of v a l u e t o measure t h e small-X gluon and sea-quark p o l a r i z a t i o n s a t l a r g e Q 2 . For t h e s e a t h e b e s t way would be t o look a t t h e s p i n - c o r r e l a t i o n parameter ALL i n t h e Drell-Yan r e a c t i o n u s i n g a p o l a r i z e d proton beam on a p o l a r i e e d proton t a r g e t . %L w i l l be zero i f t h e s e a i s unpolarized. With t h e a u t h o r ' s ~ a r a m e t r i z a t i o n one expects *L,-- 15 % f o r ~~a ZOO, with t h e s c a l i n g v i o l a t i o n s being r e s p o n s i b l e f o r about 30 % of t h i s value.

For t h e gluons a good t e s t would be i n t h e r e a c t i o n PP*-, (prompt#) + X, a t l a r g e pT, i n which t h e p o l a r i z a t i o n of t h e i s monitored. The p a r t o n i c sub-processes a r e

i f

tf ^-b V G and Gt* rt . The t r a n s m i t t e d asymmetry %L i s s e n s i t i v e t o t h e gluon pola- r i z a t i o n a t small X , f o r n e g a t i v e values o f xF of t h e photon. Asymmetries f o r nega- t i v e % a r e c a l c u l a t e d t o be of t h e o r d e r o f 5 - 15 X (depending on xT 'PT/@ and t h e s e v a l u e s r e f l e c t l a r g e enhancements ( f a c t o r s of 2 t o 5) a s a consequence of t h e s c a l i n g v i o l a t i o n s .

c) Using photoproduction of v e c t o r mesons

The amplitudes f o r a p a r t o n of given h e l i c i t y t o fragment i n t o a hadron of h e l i - c i t y h a r e t h e analogue of t h e spin-dependent s t r u c t u r e f u n c t i o n s , and a r e , ultima-

t e l y , j u s t a s fundamental. Anselmino and K r o l l 14) p o i n t o u t t h a t t h e r e a c t i o n

d + p + V + X, where V i s a v e c t o r meson, and where t h e 8 and t h e p may o r may not be p o l a r i z e d , can y i e l d u s e f u l information of t h e spin-dependent fragmentation func- t i o n s , provided t h a t one measures t h e density-matrix on t h e V. The p a r t o n i c sub- processes a r e 8 G ^J < ^{and 8} t h e time reversed v e r s i o n s of those t h a t

S t r i c t l y , t h e f i n a l h e l i c i t y d e n s i t y m a t r i x occur i n p p - + V ~ d i k u s s e d ato'F'i"'

should depend upon a fragmentation d e n s i t y mt&

Dk'

h hh

with p r o b a b i l i t i e s i . e. Dhh,' ( z ) i s r e p l a c e d by a i t s diagonal elemetlts D (z) 3 D (2)

XX A X\

which simply g i v e t h e p r o b a b i l i t y f o r a p a r t o n of h e l i c i t y h t o fragment %nto t h e hadron of h e l i c i t y h. Almost nothing i s known about t h e s e spin-dependent fragmenta- t i o n f u n c t i o n s , but f o r t h e valence quarks a t l e a s t one can use SU(G) wave f u n c t i o n s a s a rough guide, and one f i n d s

where D v (z) i s t h e unpolarized -, V fragmentation f u n c t i o n . Equ (5) leads t o

e 't

= l f h h (unpolarized and p)

Q ^hh

which d i f f e r s c o n s i d e r a b l y from o t h e r suggestions i n t h e l i t e r a t u r e e.g. Donoghue has Qoo = 1 , Q 1 = Q = 0 whereas Field-Feynman have t o o = O j 3 ^{11 =} 3 ^{- 1 - 1 ' * 2}

(see r e f . 14 f o r d e t a i l s ) . An experimental t e s t i s o b l i g a t o r y !

More d e t a i l e d t e s t s of t h e s t r u c t u r e of D ~ ~ ' ( z ) can be made i f e i t h e r p o l a r i z e d \J

A V

o r p o l a r i z e d p a r e used. It i s suggested t h a t t h e p r o b a b i l i s t i c i n t e r p r e t a t i o n f o r gluons might be v a l i d i n terms of l i n e a r p o l a r i z a t i o n s , r a t h e r than h e l i c i t y s t a t e s . The gluons would then i n t r o d u c e non-diagonal elements i n t h e h e l i c i t y l a b e l s . A l l t h i s can be t e s t e d , and should be, because t h e measurement of l a r g e non-diagonal elements i n Q hh, (V) w i l l be a s e v e r e embarrasement t o QCD and t h e p a r t o n model.

5 - Summary

The measurement of spin-dependent parameters, p o l a r i z a t i o n s , c o r r e l a t i o n s , density- m a t r i c e s i s a huge Pandora1s Box. I f i t can be c a r r i e d o u t i n a kinematic r e g i o n where p e r t u r b a t i v e QCD i s supposed t o be v a l i d i t i s going t o shake QCD t o i t s very foundations. I cannot b e l i e v e t h a t Nature i s going t o r e s p e c t t h e t i g h t , narrow, p r e d i c t i o n s t h a t it makes. At t h e same time some of t h e i n t e r e s t i n g though aesthe- t i c a l l y l e s s p l e a s i n g a l t e r n a t i v e s t o QCD w i l l a l s o be forced t o f a c e t h e i r d e s t i n y .

References

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2) S.V. Goloskokov, S.P. Kuleshov and O.V. S e l j u g i n : Spin and E l a s t i c Hadron S c a t t e r i n g a t Superhigh Energies, t h i s volume,

3 ) C . Bourrely: E l a s t i c Proton-Proton P o l a r i z a t i o n i n t h e TeV Energy Domain, t h i s volume,

4) S.M. Troshin and N . E . Tyurin: Spin E f f e c t s i n Hadron S c a t t e r i n g a t Large Angles and Quark I n t e r a c t i o n Dynamics, t h i s volume,

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8) L. Lukaszuk and B. Nicolescu, Phys. Rev. Dll, 2461 (1975),

9) P. Gauron, E. Leader and B. Nicolescu: Polarization in ir~p-Hr°n and the Asymptotic Theorems, Phys. Rev. Lett. 52, I952 (1984).

10) See Ref. 9 for further references.

11) J. Layssac, B. Pire and J.R. Ralston: Spin Asymmetry in ye'-i-e + 2 jets; a Laboratory for Final State Interactions, this volume,

12) G. Baum et al., Phys. Rev. Lett., 5_1, 1135 (1983),

13) P. Chiappetta and J. Soffer: QCD Scaling Violations for Spin Dependent Structure Functions, Preprint CPT-84/P. 1615 (Phys. Rev. I), to appear).

14) M. Anselmino and P. Kroll: Polarization in Large P<j Photoproduction of Vector Mesons, this volume,