ELASTIC PROTON-PROTON POLARIZATION IN THE TeV ENERGY DOMAIN

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ELASTIC PROTON-PROTON POLARIZATION IN THE TeV ENERGY DOMAIN

C. Bourrely

To cite this version:

C. Bourrely. ELASTIC PROTON-PROTON POLARIZATION IN THE TeV ENERGY DOMAIN.

Journal de Physique Colloques, 1985, 46 (C2), pp.C2-221-C2-224. �10.1051/jphyscol:1985223�. �jpa-

00224534�

JOURNAL DE PHYSIQUE

Colloque C2, supplément au n°2, Tome 46, février 1985 page C2-221

ELASTIC PROTON-PROTON POLARIZATION IN THE TeV ENERGY DOMAIN

C. Bourrely

Centre de Physique Théorique, CNRS, 13288 Marseille, France

Résumé - Nous prédisons la polarisation élastique proton-proton pour le nouveau domaine d'énergie accessible par les futurs accélérateurs. Bans le cadre d'un modèle en paramètre d'impact qui donne une bonne descrip- tion des données expérimentales pour la diffusion non polarisée pp et pp,

nous introduisons la dépendance en spin de l'amplitude de diffusion au moyen de la distribution de vitesse dans un proton. On trouve que la polarisation élastique pp devient grande à très haute énergie et aux petits angles de diffusion.

Abstract - We predict elastic proton-proton polarization for the new energy domain accessible with the future accelerators. In the framework of an impact picture model which gives a good description of the present unpolarized elastic p-p and pp experimental data at high energy, we intro- duce the spin dependence of the scattering amplitude by means of the matter velocity distribution inside a proton. It is found that the analyzing power of p-p elastic scattering becomes large at small scattering angles and very high energy.

There are two decades that the exploration of spin effects in hadronic reactions at medium energy (up to 30 GeV/c) has revealed very unexpected large effects from the measurement of different observables / l / . Although the accumulation of data poses a serious challenge to theoretical models, we know that the domain of energy under consideration involves the exchange of many resonances which in principle can be described in the framework of the Regge pole model for small scattering angles, while at large angles a hard component due to parton- parton interaction becomes dominant /2/ .

As the energy increases, the Regge contributions to the amplitudes disappear, so we can expect a negligible polarization at small scattering angle, in fact experiments reveal that the polarization remains in an energy range around a hundred of GeV/c in the laboratory / 3 / , then in order to explain the polariza- tion, "soft" interaction of partons must be taken into account, but an estimate of their contributions is a very difficult task and no reliable result is available at the moment.

However, in order to make some predictions we can refer to an impact picture model /4/ which gives a good description of the present unpolarized p-p and p-p elastic scattering at high energy / 5 / . The spin dependence of the model was introduced following the notion of matter current density proposed by Chou and Yang / 6 / , a comparison with data of the predicted analyzing power for p-p scattering in an energy domain 100-300 GeV/c shows a satisfactory agreement for a momentum transfer up to 1 GeV2 /7/.

From the present experimental situation one can ask what sort of behaviour we can expect for the p-p analyzing power when the next generation of colliders will be running in the TeV energy domain ? Of course this question is only meaningful if one supposes that accelerating a polarized beam at these energies will be feasible.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1985223

C2-222 JOURNAL DE PHYSIQUE

Before making some p r e d i c t i o n s , we summarize t h e main formulae of t h e model, f o r which a complete development i s given i n Refs. 4 , 7 . The proton-proton e l a s t i c amplitude i n impact-parameter r e p r e s e n t a t i o n r e a d s a s :

~ ( s , ? ) i s decomposed i n t o a s p i n independent p a r t flo(s,T) and a s p i n dependent p a r t s l ( s , b ) such t h a t

A

where

r e f e r t o a t a r g e t 7 1/2 along t h e z a x i s and bx i s a component of a u n i t vector.

The s p i n independent o p a c i t y f u n c t i o n i s defined by + *2

R o ( s , b )

s o ( s ) F(b

s

where S o ( s )

+L

( I n s ) ( I n u l C '

and F(b -2 ) is t h e Fourier transform of a modified parametrization of t h e proton form f a c t o r :

As a r e s u l t t h e s p i n independent amplitude i s given by

According t o t h e idea t h a t t h e m a t t e r d i s t r i b u t i o n i n s i d e a proton moves with a c e r t a i n v e l o c i t y due t o t h e presence of a c u r r e n t , then it can be shown /4/ t h a t

4 2 fil(s,b)

v F(b

Y ⁽⁶⁾

where vy i s t h e component of t h e v e l o c i t y of a small region of t h e t a r g e t i n t h e c.m. system, and we have

So t h e s p i n dependent amplitude t a k e s t h e form

while t h e t o t a l amplitude r e a d s

--?

n being a u n i t v e c t o r normal t o t h e s c a t t e r i n g plane. The analyzing power P i s then

To d e f i n e completely t h e s p i n dependent amplitude we have t o s p e c i f y v a s a func- t i o n of t h e impact parameter. In a previous paper /4/ we discussed d i & e r e n t expres- s i o n s f o r vy, one s e n s i b l e choice was a Gaussian form

2 2 -b /bo v = % b e

Y ⁽¹¹⁾

Fig.1 - Analyzing power of p-p elastic scattering for plab= 100, ZOO?

300 G ~ V / C , data from ref. 3.

Fig. 2 - Analyzing power of p-p elastic scattering

a)

0.5 TeV (dashed curve), fi

¹ TeV (solid curve)

b)

10 TeV

c)

20 TeV, with the correc-

tive term included see Eq. ( 1 2 )

(solid curve), without corrective

term (dashed curve).

c2-224 JOURNAL DE PHYSIQUE

With such a v e l o c i t y we reproduced reasonably well t h e analyzing

pwer ⁱⁿ

an energy range 100-300

and a momentum t r a n s f e r up t o 1 GeV . ^Above

t h i s momentum t r a n s f e r value our p r e d i c t i o n s do not reproduce t h e shape of t h e d a t a , which is an i n d i c a t i o n t h a t Eq. (11) i s only an approximation.

As a m a t t e r of f a c t , one can imagine t h a t a p r o j e c t i l e e l a s t i c a l l y s c a t t e r e d by a t a r g e t made of 3 quarks " f e e l s " only a g l o b a l e f f e c t when t h e momentum t r a n s f e r i s small. Now by i n c r e a s i n g t h e t r a n s f e r t h e p r o j e c t i l e probes deeper i n s i d e t h e proton s o t h a t t h e i n d i v i d u a l quarks a r e involved i n t h e s c a t t e r i n g process. A v e l o c i t y d i s t r i b u t i o n l i k e Eq. (11) which has t h e smooth behaviour of a Gaussian may correspond t o t h e o u t e r p a r t of t h e proton, while t h e v e l o c i t y i n s i d e t h e proton has probably some i r r e g u l a r i t i e s due t o t h e presence of quarks.

According t o t h i s phenomenological argument we added a c o r r e c t i o n t o t h e previous v e l o c i t y d i s t r i b u t i o n i n a way t o produce a f l u c t u a t i o n a s a f u n c t i o n of t h e impact parameter, one p o s s i b l e choice i s

2 2 -b /bo

v = ( d o b e ( 1

W1 s i n ( b / b l ) )

Y (12)

With t h i s c o r r e c t i o n included we f i n d a b e t t e r agreement with t h e d a t a , t h e r e s u l t of t h e f i t i s shown i n (Fig. 1 ) .

The parameters corresponding t o t h i s s o l u t i o n a r e l i s t e d below t o g e t h e r with those obtained f o r t h e unplarized amplitude /5/.

c = 0.167 m,

0.586 GeV a

1.953 GeV Wo

-0.06 GeV Wl

0.213

c '

0.748 m2

1.704 GeV f

7.115 GeV- ² b

6.9 G ~ v - 1 6:

1.4 G ~ V - I

An e x t r a p o l a t i o n of t h e analyzing power i n t h e TeV energy domain i s shown i n ( F i g . 2 ) . The p o l a r i z a t i o n does not vanish with i n c r e a s i n g energy, i n s t e a d we observe important o s c i l l a t i o n s between 4 0 4 0 % a t 10 and 20 TeV. The d i f f e r e n t maximums occur a t a value of t h e momentum t r a n s f e r where t h e e l a s t i c d i f f e r e n t i a l c r o s s s e c t i o n h a s a change of c u r v a t u r e . Such a p a t t e r n which bears some resem- blance t o n u c l e a r e l a s t i c r e a c t i o n s i n t h e MeV energy domain g i v e s probably a n i n d i c a t i o n of t h e composite n a t u r e of t h e proton.

References

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