THE EMC EFFECT FOR SPIN DEPENDENT STRUCTURE FUNCTIONS

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THE EMC EFFECT FOR SPIN DEPENDENT STRUCTURE FUNCTIONS

J. Szwed

To cite this version:

J. Szwed. THE EMC EFFECT FOR SPIN DEPENDENT STRUCTURE FUNCTIONS. Journal de

Physique Colloques, 1985, 46 (C2), pp.C2-269-C2-274. �10.1051/jphyscol:1985230�. �jpa-00224541�

THE EMC EFFECT FOR SPIN DEPENDENT STRUCTURE FUNCTIONS

J. Szwed

Jagellonian University, Cracow, Poland

Résumé - Je rappelle brièvement les explications actuelles de l'effet EMC en décrivant en détails le modèle avec les degrés de liberté du i et du Ï . Je suggère la mesure du rapport R^fx) = g^xVgÇfx) des fonctions de struc- ture dépendant du spin pour un nucléon et pour un noyau, qui peut cons- tituer un test pour plusieurs modèles. Dans le modèle ù - ir, on donne des prédictions pour ce rapport dans le cas des noyaux simples.

Abstract - I review shortly present explanations of the EMC effect, describing in more detail the model with A and w degrees of freedom. I suggest to measure the ratio R

(x) =

= g*(x)/g^(x) of the spin dependent structure functions in nucleus and nucleon, which may be a test for many models, and give predictions of the A-ar model for some simple nuclei.

1. Introduction

Since the measurement of the ratio

R(x) =-4-|

of the nucleon structure function inside large nucleus to that inside deuterium [1] many models attempted to explain the deviation of this quantity from unity. Since the Fermi motion turned out not to be able to account for the effect (called usually the EMC effect) it was in- terpreted as a significant change of the quark distribution inside nucleon due to nuclear interactions - a change which remains signi- ficant even at high momentum transfer Q .

The scheme shared by most of the models makes use of the decompo- sition of the nucleus structure function into a set of structure functions which seem to be better understood. To be more precise, whereas the nucleon structure function F2(x) corresponds to the diagram

Sf(x)

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1985230

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t h e nucleus s t r u c t ure function i s proportional t o t h e diagram

and can be w r i t t e n

where f ? (y) i s t h e d e n s i t y of 'question markss i n s i d e t h e nucleus and F2(z) i s t h e quark density i n s i d e the 'question marks'. Models ? d i f f e r among themselves by t h e d e f i n i t i o n s of 'question marks8. Let me review a couple of p o s s i b i l i t i e s :

? = I. A s already s a i d t h i s model is wrong which was a s u r p r i s e f o r most of t h e high energy p h y s i c i s t s when t h e EMC measurement has come.

Cv

? = N. The s i g n means a d i s t o r t e d nucleon. I n moat approaches t h i s f a c t can be t r a n s l a t e d t o a n e f f e c t i v e nucleon of l a r g e r r a d i u s 121. I n t h i s c l a s s a very i n t e r e s t i n g suggestion of r e s c a l i n g [31 connects ElvrC e f f e c t with t h e QCD s c a l i n g v i o l a - tions.

? = N + (6q) + (9q) + ... ⁺ ( 3 ~ q ) . Usually t h e nucleon with some admixture of 6q s t a t e s i s assumed C41, although 3A quark bag i s a l s o considered [53. One may a l s o approximate t h i s s e r i e s by a bag w i t h a n average number of quarks 163.

? = N +?r + A. I n t h i s model 17-91 no new degrees of freedom are in- troduced as compared t o t h e standard nuclear physics, which i a d e f i n i t e l y an advantage. I describe t h i s model i n more d e t a i l .

2. The N-A--h model [ 9 1

The complicated s t r u c t u r e r e s u l t i n g from nuclear i n t e r a c t i o n s i s

ap$roximated i n t h i s model by the presence, i n addition t o f r e e nu-

The f r e e nucleon s t r u c t u r e f u n c t i o n s a r e measured i n deep i n e l a s t i c s c a t t e r i n g off proton and deuteron t a r g e t s . Parametrization of these d a t a [ l o ] g i v e s us F2(x) N i n Eq. (2). The d i s t r i b u t i o n of nucleons i n s i d e nucleus A i s given by t h e Fermi motion so f N (y) is a l s o known.

The A i s o b a r s t r u c t u r e function which i s not measured d i r e c t l y i a constructed from t h e nucleon one [7], remembering t h a t t h e s e baryona d i f f e r only by t h e s p i n and i s o s p i n configuration of t h e valence quarks. The d i s t r i b u t i o n of A i s o b a r s can be again approximated by t h e Fermi motion. The knowledge of t h e

s t r u c t u r e f u n c t i o n comes from t h e massive ( b e l l - Y a n ) muon p a i r production where t h e cross- -section is d i r e c t l y proportional t o F 1 (x). F i n a l l y t h e pion d i s t r i - but i o n fT(z) i s taken from nuclear m a t t e r c a l c u l a t i o n [ 11 I which uses t h e many-body Schrodinger equation with t h e p o t e n t i a l r e s u l t i n g from

& A - T i n t e r a c t i o n s . The last c a l c u l u s g i v e s i n p a r t i c u l a r t h e amount of A ' s and nas a a a function of A.

Fig. 1. The EMC r a t i o

R(x) f o r i r o n t o g e t h e r

with t h e N-A-x model

curve.

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The scheme sketched above i s q u i t e r e s t r i c t i v e and l e a v e s no un- known parameters. The r e s u l t i n g curve f o r t h e r a t i o R(x) i s shown i n Pig. 1. The Q ~ - and A-dependence w a s a l s o checked t o work equally well when compared t o t h e data.

3. The 'polarizedc EMC r a t i o

I n analogy t o t h e standard EMC e f f e c t one may c o n s i d e r t h e r a t i o

of t h e polarized nucleon s t r u c t u r e f u n c t i o n s g, (x) i n s i d e a nucleus t o t h a t of a f r e e nucleon. This r a t i o can be measured i n deep i n - e l a s t i c p ( e ) s c a t t e r i n g with p o l a r i s e d beam and nuclear/nucleon t a r g e t . To remind:

(E (E') - t h e l e p t o n i n c i d e n t ( f i n a l ) l a b energy, ^{~ ( 8 )} - s o l i d ( s c a t t e r i n g ) l e p t o n angle 1.

I n t h e s c a l i n g l i m i t

(ei - ^{quark charge, q} - quark d e n s i t y with h e l i c i t y p a r a l l e l (ant i p a r a l l e l ) t o N) .

To g e t t h e i d e a what i s t h e s i z e of t h e 'polarized' EMC e f f e c t we performed t h e c a l c u l a t i o n using t h e A-n model. The c o n s t r u c t i o n of t h e quark d e n s i t y d i f f e r e n c i e s Aq f o r t h e A i s o b a r and t h e pion goes i n analogy t o t h e nucleon case. With t h e SU(6) symmetric structure f u n c t i o n s one g e t s

SU(6)

t h e nucleon: Au,, = nr 2 ^{Ad =} - k, ^{A sea = 0.}

t h e A isobar: A g = n, 1 ^{Adv =} k, ^{A sea = 0,}

t h e pion: Aq = 0.

Analogical expressions i n t h e Carlite-Kaur model [ 12 1 read : t h e Carlitz-Kaur model

2 1

t h e nucleon: A% = (yr - ^{-d )cos 2Q, A% =} - p v c o s ^20, A s e a = 0, 3 v

1 1

t h e A isobar: A% = ~ y r c o s 28, AdV =

29, A s e a = 0.

t h e pion: Aq ⁼ 0

a r e f i x e d , i n analogy t o t h e unpolarized c a s e by t h e choice of t h e nucleus, We present two examples

Fig. 2s Z - ^{odd, N} - ^{even, A = Z + N * 5}

Fig. 2b Z - ^{odd, N} - ^{even, A = Z + N}

²⁷

Fig. 2a. !he s p i n dependent r a t i o R ( x ) f o r A = ^{5 as predicted}

by t h e NAE model. Solid l i n e - t h e Carlitz-Kaur model, Broken l i n e - ^{t h e SU(6) model.}

Fig. 2b. Aa i n Fig. 2a but f o r A = 27.

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( t h e approximate e q u a l i t i e s mean t h a t t h e c u r v e s d e s c r i b e n u c l e i w i t h A c l o s e t o 5 and 27).

I n t h e c a l c u l a t i o n of gt a simple v e r s i o n of t h e n u c l e a r s h e l l model w a s assumed i n which even numbers of neutrons and p r o t o n s couple t o s p i n s 0 and t h e a d d i t i o n a l proton g i v e s r i s e t o t h e s p i n of t h e nucleus and consequently t o t h e s t r u c t u r e f u n c t i o n g l A (x).

One s e e s t h a t t h e p o l a r i z e d EMC e f f e c t shows up v e r y c l e a r l y , at l a r g e x even s t r o n g e r than i n t h e unpolarized case. This conclusion does not depend on t h e p a r t i c u l a r model chosen f o r Aq (SU(6) o r Carlitz-Kaur). I n our opinion t h e r a t i o R t (x) may be a t e s t f o r many

of t h e proposed modela. I n some of them t h e s p i n s t r u c t u r e h a s t o be introduced ab i n i t i o . This i s t o be c o n t r a s t e d w i t h t h e above pre- s e n t e d c a l c u l a t i o n where no new assumptions have entered.

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