ELASTIC pp POLARIZATION AT LARGE ANGLES

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ELASTIC pp POLARIZATION AT LARGE ANGLES

C. Bourrely, J. Soffer

To cite this version:

C. Bourrely, J. Soffer. ELASTIC pp POLARIZATION AT LARGE ANGLES. Journal de Physique

Colloques, 1985, 46 (C2), pp.C2-217-C2-220. �10.1051/jphyscol:1985222�. �jpa-00224533�

JOURNAL DE PHYSIQUE

Colloque C2, supplément au n°2, Tome 46, février 1985 page C2-217

ELASTIC pp POLARIZATION AT LARGE ANGLES

C. Bourrely and J . Soffer

Centre de Physique Théorique*, CNRS, Luminy, Case 907, 13288 Marseille Cedex 9, France

Résumé - Nous proposons un mécanisme simple pour engendrer une grande po- larisation élastique pp à haute énergie et aux grands angles de diffu- sion. Nos prédictions présentent un grand intérêt pour le programme expé- rimental en cours de réalisation au Brookhaven National Laboratory ainsi que pour les futures expériences de diffusion élastique aux grands angles.

Abstract - We propose a simple mechanism to generate a s i z e a b l e analyzing power in high energy pp e l a s t i c s c a t t e r i n g a t large a n g l e s . Our p r e d i c - t i o n s are of g r e a t i n t e r e s t for the experimental programme i n progress a t Brookhaven National Laboratory and for future experiments on e l a s t i c s c a t - t e r i n g a t l a r g e a n g l e s .

Spin dependence of two-body processes a t high e n e r g i e s i s known to probe hadronic i n t e r a c t i o n s at a r a t h e r refined l e v e l and allows us to ask d e t a i l e d q u e s t i o n s about hadron s t r u c t u r e , which cannot be answered from the knowledge of unpolarized cross s e c t i o n s only. Over the l a s t ten years or s o , a l a r g e s e l e c t i o n of spin measurements for t h i s c l a s s of r e a c t i o n s have been performed. They cover mainly the region of small momentum t r a n s f e r and the corresponding " s o f t " physics has been discussed i n a comprehensive review of p o l a r i z a t i o n phenomena in hadronic r e a c t i o n s / 1 / . C l e a r - ly t o t e s t our understanding of color quark dynamics a t very s h o r t d i s t a n c e s , one must i n v e s t i g a t e l a r g e momentum t r a n s f e r processes a t high e n e r g i e s . For i n c l u s i v e r e a c t i o n s , i n the framework of p e r t u r b a t i v e QCD, the b a s i c quark asymmetries r e s u l t - ing from the h e l i c i t y conserving n a t u r e of the theory imply l a r g e double spin asym- metries a t the hadron l e v e l , but these i n t e r e s t i n g p r e d i c t i o n s /2/ have not y e t been t e s t e d for lack of experimental d a t a . On the o t h e r hand, l a r g e angle pp e l a s - t i c s c a t t e r i n g i s one of the b e s t known r e a c t i o n s and i t i s worth r e c a l l i n g the e x i s - tence of a s t r i k i n g spin dependence which has been already discovered a t the maximum ZGS energy a t Argonne. The t r a n s v e r s i t y s p i n - s p i n c o r r e l a t i o n parameter ANN was found to climb up to the l a r g e value 0.59 ± 0 . 0 9 a t © = 90° for p

=12.75GeV/c / 3 / . In terms of the five nucleon-nucleon h e l i c i t y amplitudes Y- > t h i s p h y s i c a l observable reads

^ ^ m = ^Re ^ , 4»* - 4> ³ tt ^{+ 2} ttsi ² > < ^{] )}

where

^ - i M + i l M ^ H M M W ^{2 +} * ^ i ^{2 )} - < ^{2 )}

If one t r i e s to use p e r t u r b a t i v e QCD to d e s c r i b e pp e l a s t i c s c a t t e r i n g i n t h i s energy range / 4 / , the h e l i c i t y conservation r u l e / 5 / implies t h a t the s i n g l e and dou- b l e f l i p amplitudes v a n i s h , i . e . < t

=<p, = 0 at l a r g e a n g l e s . In a d d i t i o n from symmetry arguments a t 90° we have <f>

= - < b , and from the quark i n t e r c h a n g e model

<fy

= 1^3 •

r e s u l t , one g e t s ANN (90°) = 1 / 4 / which i s d e f i n i t e l y i n d i s a - greement with the above experimental r e s u l t . Of course one can always assume the

L a b o r a t o i r e P r o p r e , Centre National de l a Recherche S c i e n t i f i q u e

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1985222

C2-218 JOURNAL DE PHYSIQUE

e x i s t e n c e of a d d i t i o n a l c o n t r i b u t i o n s r e l a t e d t o non-perturbative e f f e c t s which w i l l d i e o u t a s t h e energy i n c r e a s e s . I n t h a t ca$e one expects from t h e f u t u r e d a t a a t the AGS-BNL, a d e c r e a s i n g %(go0) towards t h e value 113.

I n t h e t h e o r e t i c a l approach of t h e massive quark model (WM) and i t s e x t e n s i o n t o t h e Quark Geometrodynamics (QGD) 161, t h e physics o f l a r g e angle two-body r e a c t i o n s has been analyzed i n d e t a i l i n a s e r i e s of papers 17, 8 , 91. By u s i n g t h e s e t of N-N amplitudes given i n Table I of r e f . / a / , one f i n d s %N(90") w i t h a l a r g e r va- l u e which should go up t o 0.97 a t asymptotic e n e r g i e s i n c o n t r a s t with the p e r t u r - b a t i v e QCD value 113 . A new p o t e n t i a l physics w i l l emerge with t h e advent of t h e p o l a r i z e d proton beam a t t h e AGS-BNL and hopefully t h i s important q u e s t i o n w i l l b e answered soon. If we now t u r n t o t h e s i m p l e s t s p i n dependent observable, t h e analyz- ing power A whose e x p r e s s i o n i s

i t w i l l v a n i s h a t l a r g e a n g l e s i n ~ e r t u r b a t i v e QCD because 95

⁰ . I n t h e MQPS QGD approach we do n o t have t h i s c o n s t r a i n t b u t a l l t h e amplitudes a r e expected t o be r e a l l i k e i n p e r t u r b a t i v e QCD and t h i s i s why we a l s o a n t i c i p a t e A = 0 a t l a r g e angles. However, i f a t high momentum t r a n s f e r t , t h e r e i s a r e w a n t of t h e imagi- nary d i f f r a c t i v e non-flip amplitude which i s known t o dominate a t small t , t h e r e w i l l be i n t e r e s t i n g i n t e r f e r e n c e e f f e c t s w i t h t h e MQM-QGD s p i n dependent r e a l ampli- tudes, which might p e r s i s t up t o very l a r g e s c a t t e r i n g angles. This i s p r e c i s e l y the mechanism we w i l l invoke t o generate a s i z e a b l e analyzing power a t l a r g e angles.

Some y e a r s ago we have presented a s a t i s f a c t o r y phenomenological a n a l y s i s o f pp e l a s t i c s c a t t e r i n g from a new impact p i c t u r e f o r low and high energy / l o / . These p r e d i c t i o n s have been extended a t t h e CERN-SPS C o l l i d e r /11/ and were found i n good agreement w i t h t h e r e c e n t d a t a . We w i l l t h e n consider t h a t t h i s impact p i c t u r e am- p l i t u d e provides a n a c c u r a t e r e p r e s e n t a t i o n of " s o f t " s c a t t e r i n g up t o reaso a b l e values of t h e momentum t r a n s f e r . For l a r g e t values, t y p i c a l l y I t ( > 5 GeV 4 a t AGS e n e r g i e s , the impact p i c t u r e was found t o p r e d i c t a d i f f e r e n t i a l c r o s s s e c t i o n below t h e d a t a which becomes n e g l i g i b l e n e a r oc,m, ^{= 90'} . C l e a r l y s i n c e t h i s i s the l a r g e angle region, we a r e missing the e f f e c t o f t h e hard s c a t t e r i n g component of t h e amplitude. Therefore we have combined t h e impact p i c t u r e amplitude with t h e IQM-QGD hard s c a t t e r i n g amplitudes des r i b e d i n r e f s . 17, 91 and properly normalized

t o t h e d i f f e r e n t i a l c r o s s s e c t i o n a t &

^90' . ^It r e s u l t s a good d e s c r i p t i o n c.m.

of d ~ l d t o u t t o l a r g e t values and f o r example a t plab = 28 GeV/c and t . m s = 4 5 0 we have d v f d t = 4x10-' mb/~ev' which i s c o n s i s t e n t with t h e expectations of r e f . / 121. Below 45' we cannot e x t r a p o l a t e s a f e l y t h e MQM-QGD amplitudes because t h e i r expressions (see r e f . 181) contain some approximations v a l i d only f o r l a r g e angle s c a t t e r i n g . I f we now c a l c u l a t e t h e analyzing power f o r above 45' from t h e

c.m.

r e s u l t i n g s e t of amplitudes we f i n d t h a t A i s v e r y l a r g e , s t a r t i n g around 50 % and decreasing slowly towards zero f o r 0 c.m. ⁼ 90' . Our p r e d i c t i o n s f o r pp a r e shown i n F i g . 1 where we have p l o t t e d A v e r s u s 6 f o r two d i f f e r e n t values o f

c.m.

plab = 28 and 50 GeV/c . We have a l s o c a l c u l a t e d a t two d i f f e r e n t e n e r g i e s which is shown i n Fig. 2. There i s a s l i g h t u n c e r t a i n t y on t h e s e r e s u l t s due t o t h e f a c t t h a t we do n o t know the e x a c t v a l u e o f d F / d t i n t h i s kinematic region. For plab = 24 GeV/c a t t h e l a r g e s t angle measured corresponding t o It(= 6.72 GeV 2 , we g e t d w l d t ⁼ I .1 x lom6 mb/GeV 2 t o be compared w i t h t h e experimental v a l u e 113'1 (8.49 * ^{0.51) mb/GeV} . Clearly a t f i x e d 0 s i n c e t h e hard s c a t t e r i n g con-

c.m.

t r i b u t i o n drops down r a p i d l y when t h e energy i n c r e a s e s from 28 GeV/c t o 50 GeVlc ,

A i s expected t o i n c r e a s e as shown i n F i g . 1 . This e f f e c t i s r a t h e r l i m i t e d because

f o r higher e n e r g i e s t h e hard s c a t t e r i n g amplitude i s s o much suppressed t h a t t h e r e

i s no reason to invoke any i n t e r f e r e n c e mechanism i n a kinematic region p r e s e n t l y

a c c e s s i b l e t o experiments t o a n t i c i p a t e l a r g e values o f A .

Fig. I - P r e d i c t i o n s f o r t h e pp analyzing power versus

0 c.m.at two d i f f e r e n t energies.

80t ^{/ ' . .} I ^{Fig. 2 - Predlctrr}

.#I

meter i n

Below plab = 50 GeV/c , the region ec.m?, ^50' has n o t y e t been i n v e s t i g a t e d expe- r i m e n t a l l y , b u t t h e r e i s a s t r o n g i n d i c a t i o n of t h i s e f f e c t from a recent r e s u l t from BNL 1141 . ^{At P l a b}

²⁸ GeV/c and : p = 6.56 ( ~ e v / c ) ~ they f i n d A

(51 *

17)% and t h i s i s perhaps t h e beginning of a new domain where l a r g e values of A re- s u l t from a maximum i n t e r f e r e n c e mechanism between s o f t and hard s c a t t e r i n g amplitu- des which a r e s t r o n g l y o u t of phase(x) . ^W have a l s o calculated ^e A f o r pn e l a s - t i c s c a t t e r i n g and the r e s u l t s a r e p r e s e n t e d i n Fig. 3. The pn G a l y z i n g power i s s i m i l a r t o t h a t of pp , except n e a r ecarn. ^{= 90' where i t} i s n o t vanishing from symmetry arguments.

We would l i k e t o i n d i c a t e t h a t a s i m i l a r c a l c u l a t i o n has been done using t h e p e r t u r - b a t i v e QCD am l i t u d e s / 4 / and one f i n d s much s m a l l e r r e s u l t s p a r t l y due t o t h e f a c t t h a t 9 ⁼ 4 ^{= 0 .} Moreover t h e c a l c u l a t i o n i s only r e l i a b l e n e a r 90' because f o r 8 ^{c.m.< 70'} t h e hard QCD cross s e c t i o n blows up very q u i c k l y and i t s extrapo- l a t i o n is t o t a l l y u n r e a l i s t i c .

( X f ~ h i s s i t u a t i o n i s s i m i l a r t o t h a t o f t h e Coulomb-nuclear i n t e r f e r e n c e a t very

small momentum t r a n s f e r 1151.

JOURNAL DE PHYSIQUE

Fig. 3 - P r e d i c t i o n s f o r t h e pn ana- l y z i n g power A v e r s u s ec

a t two d i f f e r e n t e n e r g i e s r m '

I n c o n c l u s i o n we b e l i e v e t h a t t h e e l a s t i c nucleon-nucleon a n a l y z i n g power a t l a r g e a n g l e s i s very important t o measure because i t s d e t e r m i n a t i o n i s a r e a l challenge t o o u r knowledge o f s p i n dependence a t s h o r t d i s t a n c e .

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