SPIN EFFECTS IN HADRON SCATTERING AT LARGE ANGLES AND QUARK INTERACTION DYNAMICS

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SPIN EFFECTS IN HADRON SCATTERING AT LARGE ANGLES AND QUARK INTERACTION

DYNAMICS

S. Troshin, N. Tyurin

To cite this version:

S. Troshin, N. Tyurin. SPIN EFFECTS IN HADRON SCATTERING AT LARGE ANGLES AND QUARK INTERACTION DYNAMICS. Journal de Physique Colloques, 1985, 46 (C2), pp.C2-235- C2-238. �10.1051/jphyscol:1985225�. �jpa-00224536�

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Colloque C2, supplément au n°2, Tome 46, février 1985 page C2-235

SPIN E F F E C T S IN H A D R O N S C A T T E R I N G A T L A R G E A N G L E S A N D Q U A R K I N T E R A C T I O N D Y N A M I C S

S.M. Troshin and N.E. Tyurin

Institute for High Energy Physios, Serpukhov, U.S.S.R.

Résumé - Le comportement des paramètres An n( s , 90) et P(s,Q) pour la diffu- sion pp et 35"N dans le domaine des grands angles est considéré d'ap- rès la conception basée sur la résolution de l'équation dynamique pour l'amplitude de la diffusion dans la théorie quantique des champs Les paramètres Ann et Am peuvent osciller avec le changement de s.

Leur valeurs asymptotiques sont de 1/3 et de -1/3 respectivement. Ce comportement permet d'expliquer les valeurs expérimentales obtenues au ZGS. La polarisation P ( s , 9 ) dans le domaine des grands angles de la diffusion peut avoir une valeur considérable et ne pas dimi- nuer avec l'augmentation de s. Les relations entre s-dépendance de P(s,0 ) , An n( s , 90°) et la section différentielle sont discutées.

Abstract - Spin correlation parameter An n( s , 90°) and polarization parameter P(s,0 ) behaviour in the large angle pp- andJTN-scattering is consi- dered in the approach, based on the three-dimensional equation for the scattering amplitude in QFT. Parameters Ann and A>£ may have oscillating behaviour with s, and their asymptotic values are 1/3 and -1/3, respectively. This allows one to explain ZGS spin effects.

Polarization P ( s , 6 ) in large angle scattering may get a considerab- le value and does not decrease with s. Relations between s-dependen- cies of P ( s , Q ) , An n( s , 90°) and dg/dt (s, 90°) are discussed.

The interest in the theoretical and experimental study of spin effects in large ang- le hadron scattering is mainly related to important role of spin in a hadron and quark interaction dynamics at short distances.

QCD has serious problems in explanation of the data on spin effects. Although with known uncertainties the perturbative calculations should be applied to large angle scattering region. But they lead to zero values of polarization parameter P ( s , Q ) and spin-spin asymmetry A in all orders in oCs(Q2) due to s-channel helicity con- servation.

It might be noted that as well as QCD many theoretical models lead to equality P(s, 0 ) = 0 although their predictions for spin-spin asymmetries are found non-zero due to account of additional contributions out of perturbative frameworks of QCD. Measu- rements of spin-spin asymmetries and recent AGS results on polarization in pp-scat- tering confirm the conclusion that spin effects can not be neglected at high ener- gies.

In this situation it seems natural to pay attention to theoretical approaches which a priori do not imply s-channel helicity conservation. We use the approach based on <JFT three-dimensional dynamic equation for the scattering amplitude F=F [U].

Through this equation/1/ the amplitude is related to the generalized reaction mat- rix (U-matrix) which is relativistic generalization of the reaction matrix in quan- tum mechanics. We have in the c.m.s. for the case of two spin 1/2 hadrons (fp| =

= 1*1 = |T|):

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1985225

C2-236 JOURNAL DE PHYSIQUE

To choose t h e U-matrix we use d e f i n i t e ~ o n s i d e r a t i o n s / ~ / on quark s t r u c t u r e of had- r o n s and t h e i r i n t e r a c t i o n s which a r e s p e c i f i e d below.

We assume t h a t i n t e r a c t i o n of t h e hadronic s t r u c t u r e s ( v i r t u a l c l o u d s ) r e s u l t s in appearance of some e f f e c t i v e f i e l d Veff., and valence quarks a r e independently s c a t - t e r e d by Veff,. The U-matrix i s chosen i n t h e impact oarameter r e p r e s e n t a t i o n i n

t h e form of product: n. n-

I t i s assumed t h a t valence quarks a r e concentrated i n t h e c e n t e r of t h e i r . h a d r o n s . The f u n c t i o n s f q ( s q , b) a r e r e l a t e d t o dynamics of quark s c a t t e r i n g i n t h e f i e l d Veff. The b-deoendence of f q ( s q , b ) i s chosen i n such a way t o provide t h e r e s u l - t i n g U-matrix i n t h e form which follows from t h e known a n a l y t i c a l p r o p e r t i e s of t h e amplitude F o v e r c o s e and t h e b a s i c e q u a t i o n F = Flu]. Namely f q ( s , b) =

= gq(s)exu(-m b ) , where mq denotes t h e mass of valence q-quark. Such a form f o r quark "amplitudes" can be r e l a t e d t o q mechanism f o r quark s c a t t e r i n g when q-quark i n t e r a c t i o n r a d i u s is determined by i t s s i z e : R - r Wm-? We put g q ( s )=

= gqsA w i t h account f o r polynomial boundness of U(s, t ) and req?iregent of asympto- t i c a l growth of hadronic t o t a l c r o s s - s e c t i o n s : 6 t o t ( ~ ) - 1 0 g 2 s . For s i m p l i c i t y va- lence quark masses and quark momenta a r e considered equal.

These assumptions d e f i n e quark model f o r matrix/'/. I t should b e noted t h a t t h e y a r e n o t r e l a t e d t o any p a r t i c u l a r region of t - v a l u e s , and r e s u l t i n g U-matrix unam- biguously d e f i n e s t h e amplitude F = F[U] v i a eq. (1). The method o f c a l c u l a t i o n is founded on t h e a n a l y s i s of t h e impact parameter plane s i n g u l a r i t i e s of t h e ampli- tude i n s-channel. I t allows one t o o b t a i n e x p l i c i t l y t h e s c a t t e r i n g amplitudes f o r a l l v a l u e s of t o r e / 3 / . In t h i s way t h e s o f t and hard p a r t s of hadronic i n t e r a c -

t i o n s a r e considered Simultaneously. hll

Bq. (2) was g e n e r a l i z e d s o a s t o account f o r s p i n . The r e l a t i o n

Ah

i=l ween hadron h e l i c i t y and valence quark h e l i c i t i e s was used. We s h a l l i n t r o d u c e two f u n c t i o n s f f and f o which correspond t o h e l i c i t y f l i p and n o n - f l i p quark s c a t t e r i n g by Veff:

F a c t o r

a >

I t seems i n t e r e s t i n g t o s p e c i f y t h e i n t e r a c t i o n p i c t u r e assumed above t o introduce d e f i n i t e p h y s i c a l i n t e r p r e t a t i o n . We s h a l l assume t h a t v i r t u a l cloud a r i s i n g due t o i n t e r a c t i o n of hadronic s t r u c t u r e s c o n t a i n s n e a r l y on-shell aq-pairs. The number of quarks i n such a cloud can be estimated by q u a n t i t y Nq(s) = ( I - k ) &/mq, where k i s a p a r t of t o t a l i n i t i a l energy c a r r i e d by valence quarks. We assume f u r t h e r t h a t i n t h e c a s e of h e l i c i t y n o n - f l i p quark s c a t t e r i n g valence quarks f e e l t h e opa- c i t y of produced v i r t u a l cloud and t h e r e f o r e t h e f u n c t i o n g o ( s ) i s t o be proportio- n a l t o N ( s ) . On t h e c o n t r a r y h e l i c i t y f l i p quark s c a t t e r i n g corresoonds e f f e c t i v e l y q t o valence quark i n t e r a c t i o n with one quark from t h e cloud only. It i s n a t u r a l t o conform t o such a p i c t u r e t h e followi_ng r e l a t i o n

Eq. ( 4 ) l e a d s t o e s s e n t i a l and non-vanishing a t s + o c p o l a r i z a t i o n i n e l a s t i c s c a t - t e r i n g f o r t h e f i x e d angle region. We f i n d a non-vanishing term of p o l a r i z a t i o n pa- rameter f o r p p - s c a t t e r i n g

0

4 s i n A ( s ) s i n 2 6 (cos3

$

¹¹

P ( s , ~ ) =

-[...(a)].

(1-k)N 3cos20 +5 + s i n 3 g + ( 1 - k ) - ~ ~ - ~ s i n 2 0

In eq. ( 5 ) N s t a n d s f o r t o t a l number of valence quarks i n t h e hadrons and

A

= y f ( s ) - q o ( s ) . I t is g e n e r a l l y accepted t h a t t h e valence quarks c a r r y 1/2 of t h e t o t a l i n i t i a l energy.

Fig. 1

-

0

= 28 GeV/c f o r t h r e e d i f f e r e n t values of parameter k=0.2, k d . 5 and k d . 8

F i g u r e 1 shows t h e comparison of eq. (5) w i t h t h e d a t a l 5 / i n t h e c a s e of s i n l \ ( s ) = -,I. Solid curve corresponds t o t h e c a s e when k=1/2. The behaviour of P ( s , t ) a t p i < 4 ( ~ e ~ / c f s h o u l d be a t t r i b u t e d t o t h e f i x e d t region where h e l i c i t y amplitudes d e c r e a s e a s an exponent exp ( - ' I I / N ~ F ) and p o l a r i z a t i o n has f a m i l i a r o s c i l l a t i n g p a t t e r n .

The q u a n t i t y A ( s ) determines a l s o t h e behaviour of spin-spin asymmetries:

A

and of d i f f e r e n t i a l c r o s s - s e c t i o n 2m2

%(go0) =€jO(s)(l- (&[ I.+ {(I-B)] C O S ~ A(s)]

,

where 6 ,(s)- ( l / s ) 2 X N t 3 and t h e o s c i l l a t i n g f a c t o r i s s i n g l e d o u t I 4 / . Note t h a t a s i m i l a r conclusion about o s c i l l a t i o n s i n d i f f e r e n t i a l c r o s s - s e c t i o n was done i n r e f . / 6 / .

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Fig. 2

-

Eq. (6) allows one t o f i t f a s t i n c r e a s e of A,, observed a t t h e energy region 8- -12 GeV (Fig. 2). There a r e two p o s s i b l e modes i n s-dependence of 4, s u b j e c t t o t h e i r agreement w i t h t h e data. They correspond t o t h e c a s e s when A(s) i s a c o n s t a n t o r i t i d e n f i n i t e l y grows with energy.Respectively,either parameter & g e t s i t s maxi- mum value a t 12 GeV and then decreases monotonously t o i t s asymptotical value 1/3 o r parameter hn o s c i l l a t e s around t h e value 1/3 and decreases i n magnitude.In t h e l a t - t e r case p p - d i f f e r e n t i a l c r o s s s e c t i o n ( 7 ) has got t o o s c i l l a t e i n preasymptotic re- gion also.Asymptotic regime i n hn and d6/dt behaviour t a k e s p l a c e a t e n e r g i e s of o r d e r of 1000GeV.

It may be shown t h a t eq. (5) with minor changes i s a l s o v a l i d f o r t h e s c a t t e r i n g of spin 0 and spin 1/2 particles/7/:

m2

P ( s , ~ ) Z 2 t ? - l ( l - k ) - l s i n ~ ( s ) s i n ! 2 [ l + ( l - k ) - ~ ~ - ~ s i n ~

!]-l[l+~(+)]

e=

Thus i n t h i s paper t h e model (U-matrix quark model) has been considered which l e a d s t o e s s e n t i a l and non-vanishing a t s + b o p o l a r i z a t i o n f o r l a r g e angle e l a s t i c s c a t - t e r i n g . Experimental observation of such a behaviour w i l l confirm t h e i n t e r a c t i o n mechanism of hadron c o n s t i t u e n t s which r e s u l t e d i n eq. ( 6 ) . The model p r e d i c t s t h e p o s s i b i l i t y of o s c i l l a t i n g behaviour f o r p o l a r i z a t i o n P ( s , 8 ), and t h e parameters h n ( s , 90°) and dg/dt (go0) in oreasymptotic region.

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