SPIN STRUCTURE OF THE PROTON IN THE STANDARD MODEL

(1)

HAL Id: jpa-00224530

https://hal.archives-ouvertes.fr/jpa-00224530

Submitted on 1 Jan 1985

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

SPIN STRUCTURE OF THE PROTON IN THE STANDARD MODEL

P. Chiappetta, J. Soffer

To cite this version:

P. Chiappetta, J. Soffer. SPIN STRUCTURE OF THE PROTON IN THE STANDARD MODEL.

Journal de Physique Colloques, 1985, 46 (C2), pp.C2-201-C2-206. �10.1051/jphyscol:1985219�. �jpa- 00224530�

(2)

SPIN STRUCTURE O F THE PROTON IN T H E STANDARD MODEL

P. Chiappetta and J. Soffer

Centre de Physique Theorique, CNRS, Luminy, Case 907, 13288 Marseille Cedex 3, France

Résumé - Nous discutons tout d'abord au moyen du modèle des partons la structure interne d'un nucléon dans un état de spin déterminé puis donnons une étude détaillée des violations d'échelle des fonctions de structure dépendantes du spin en utilisant une résolution directe des équations d'Altarelli-Parisi. Nous donnons alors des prédictions pour les asymétries spin-spin dans les réactions hadroniques et pour les asymétries à un seul spin dans la production des bosons faibles.

Abstract - We first discuss in terms of the parton model the internal structure of a nucleon in a definite spin state and give a detailed study of scaling violations for the spin dependent structure functions by the direct resolution of the Altarelli-Parisi equations. Then we make predictions for double spin asymmetries in hadronic reactions and for single asymmetries in weak boson production.

Unpolarized deep inelastic scattering (DIS) experiments have yield us to a precise knowledge on how the nucleon momentum is shared between quarks and gluons. The scaling violations predicted from perturbative QCD are in fair agreement with data, and this is considered as a success of the theory. Similarly, for the polarized case, we can learn from DIS the spin content of the proton and scaling violations should also test perturbative QCI). So, the first part of this talk will be devoted to a discuss- ion of partonic spin dependent structure functions (section I) and a careful study of scaling violations (section II). In section III practical ways to detect these

evolved structure functions in hadronic collisions are stressed with particular emphasis to single asymmetries in weak boson production which are also sensitive to the electroweak part of the Standard Model.

I - PARTONIC SPIN DEPENDENT STRUCTURE FUNCTIONS

The first model which was used to describe spin dependent structure functions is the so-called SU(6) model / l / based on the SU(6) wave function. If & q denotes the differ- ence between the quark helicity parallel to the parent proton and the quark helicity antiparallel one has :

A uT( x ) - |%( x ) u )

Mr^{( x )} = " \ V^{X )}

This simple choice does not satisfy the Bjorken sum rule jlj

{ l G4

\ [ A u ( x ) +Au*(x) -Ad(x) - A d ( x ) J dx = f- (2) '0 V

where G, /G„ is the ratio of the axial vector to the vector coupling in neutron p decay.

After a modification to obey eq.(2) one gets the conservative SU(6) model : A u (x) = .44 u (x)

t v v (3) Ady(x) = -.35 dy(x)

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1985219

(3)

C2-202 JOURNAL DE PHYSIQUE

The valence quarks carrying only 53% of the proton spin, one has to generate sea quarks and/or gluon polarization in order to fulfil1 the important constraint :

1

2 = 2 i o x x + A

J

+ ^dx^AG(X) (4)

This can be achieved via the Close Sivers model /3/ of gluon bremsstrahlung and quark pair creation. Unfortunately, as exhibited in Fig. 1, the SLAC-YALE data /4/

on polarized electroproduction show that the quark asymmetry defined as :

F

^elAqi(x)

A1(x) = (5)

Z ei qi(x) i

is larger than predicted by the conservative SU(6) model for X) .4. This means that the valence quarks must carry a larger fraction of the proton spin at larger X.

Carlitz and Kaur /S/ have made the following suggestion :

where cos 2 8 ; l[ + H. M ] -l is called the spin dilution factor which is ,L

.

^..

important at small X. Using Field-Feynman valence distributions /6/ they obtained H = 0.052.

L& us now descrive our model /7/ which is inspired from Carlitz-Kaur but with spe- cific differences. We use for polarized valence quarks the Carlitz-Kaur model with the parametrization of Gliick-Hoffman-Reya /8/ for unpolarized valence quarks at Q, 2 = 5 Gev2, which gives a satisfactory description of DIS. Taking into account the QED correction to the Bjorken sum rule H. becomes equal to ,114. We construct the sea and glue spin dependent distributions from the unpolarized sea and glue structure functions extracted from DIS following the bremsstrahlung model. We will use

Sea quarks carry only 5% of the proton spin and the glue 228. Our parametrization is in agreement with the SLAC-YALE data (see Fig. 1). Let us emphasize that the low x region is crucial for a precise determination of the sea quark polarization.,This question will certainly be answered next year / 9 / by the EMC collaboration. We are now ready to study the evolution of the polarized distributions.

Fig. 1 - The quark asymmetry AI on a proton target as a function of X. Full. curve : our prediction. Dashed curve : conservative SU(6) prediction.

(4)

ing .logarithmic approximation for Nf = 3)

with bFv(x,t) = xA\(~,t)

bWx,t) = x[Auv(x,t) + Adv(x,t) + ~s(x,t)l

~cb(x,t) = x h ~ ( x , t )

These equations have been solved by moment inversion /11/ (suited for large X),

linear approximation /12/ (valid for very small t) or expansion in Chebyshev poly- nomials /l/. We will follow the direct resolution procedure introduced by Cabellini- Meunier /13/ for the unpolarized case and we give the method for the non-singlet case. According to the definition of the + distribution, eq.(8a) becomes :

The method consists in an expansion of the expression into curly brackets as a Taylor series. Keeping only the first tern one gets the simple exponential solution :

2 A$+)

~ ~ ( x , t ~ = d ~ g ( ~ , ~ ) exp Q t[l:az(s~(- -1) + 21n(l-x) + +

'1

₂ ^{( l i )}

This method can easily be extended to the singlet case.

Let us now describe our numerical. results-withn = 0.2 GeV. As shown in Fig. 2a, the behaviour of the antiquark distributionb~ = x A ~ / 6 is very similar to that of the unpolarize~distribution exhibiting an increase with Q2 at low X. As we can see from Fig. 2 b , h ~ is characterized by a more pronounced increase at very small ^Xwith Q2

.

This behaviour, in the limit X-+O, is due to our choice of xhC(x) (see eq. 7 ) which gives rise to a term proportional to In X in the expression in curly brackets.

Several predictions for spin asymmetries, which will be the subject of the next topic, become handy thanks to an analytic parametrization /7/ of the spin dependent structure functions valid for .03 4 ^X^4.9^and⁵g <so00 Gev2.

(5)

C2-204 JOURNAL DE PHYSIQUE

F i g . 2a - The a n t i q u a r k s p i n d i s t r i b u - F i g . 2b - The same a s F i g L 2 a f o r t h e t i o n h Q a s a f u n c t i o n of X f o r l o u r g l u o n s p i n d i s t r i b u t i o n AG.

s c a l e s Q ~ = 5, 50, 500, 5000 GeV .

I11 - PRACTICAL WAYS TO DETECT SCALING VIOLATIONS

I n o r d e r t o t e s t o u r e v o l u t i o n of t h e p o l a r i z e d d i s t r i b u t i o n s we w i l l now g i v e some p r e d i c t i o n s i n t h e framework of t h e hard s c a t t e r i n g model based on p e r t u r b a t i v e QCD.

L e t u s f i r s t s t u d y t h e double h e l i c i t y asymmetry f o r Lepton p a i r p r o d u c t i o n of mass Q from p o l a r i z e d p r o t o n - p o l a r i z e d p r o t o n c o l l . i s i o n s . I n t h e l e a d i n g a p p r o x i m a t i o n we have /14/ :

I f t h e s e a i n u n p o l a r i z e d ALLis z e r o . F o r l a r g e Q v a l u e s seal-ing v i o L a t i o n s d e c r e a s e t h e asymmetry g i v i n g a c o r r e c t i o n of a b o u t 30% f o r Q = 14 GeV.

Next l e t u s c o n s i d e r t h e t r a n s m i t t e d asymmetry i n prompt photon p r o d u c t i o n i n $p c o l - 1 . i s i o n s a t l a r g e t r a n s v e r s e momentum p& . T h i s r e a c t i o n i s dominated by quark-gluon s c a t t e r i n g /IS/. The n e g a t i v e XF r e g i o n i s e s s e n t i a l l y d e s c r i b e d by &GIG and s c a l i n g v i o l a t i o n s of AG (U l e a d t o d e v i a t i o n s of a f a c t o r S a t XF = -0.8 and 2 a t XF = -.4.

L e t u s f i n a l l y c o n s i d e r t h e s i n g l e t a s y m m e t r i e s i n weak boson p r o d u c t i o n a t t h e c o l - l i d e r w i t h l o n g i t u d i n a l l y p o l a r i z e d p r o t o n s . P r e v i o u s works /16,17/ were done with t h e fol.lowing a s s u m p t i o n s : f i r s t , c a l c u l a t i o n s have been made t h r o u g h t h e D r e l l - Yan p i c t u r e w i t h o u t t a k i n g i n t o a c c o u n t s o f t g l u o n r a d i a t i o n which h a s been shown /18/ c r u c i a l t o g e t agreement w i t h UA1 and U A 2 u n p o l a r i z e d d a t a . Second, t h e y i g n o r e d s c a l i n g v i o l a t i o n s f o r t h e p o l a r i z e d v a l e n c e q u a r k s and used t h e SU(6) model w i t h o u t t h e Bjorken sum r u l e , which i s i n d i s a g r e e m e n t w i t h p o l a r i z e d e l e c t r o p r o d u c t i o n d a t a . Our purpose /19/ i s t o r e v i s e t h e s e p i o n e e r i n g e v a l u a t i o n s by a d a p t i n g t o s p i n

(6)

Dashed curve : result of ref. /17/.

W .

F l p . 4 - The s p m asymmetry AL ^In$p collisions versus the kL of the lepton. Full curve : our prediction j Dashed curve : S U ( ~ ) prediction vlth Bjorken sum rule.

(7)

C2-206 JOURNAL DE PHYSIQUE

asymmetries our description of unpolarized weak boson production /l8/ and also by- using our set of spin dependent structure functions. Due to the axial couplings in the SU(2) x U(l) theory one expects non-zero single helicity asymmetries. We first consider the production of a lepton pair of mass Q at zero rapidity, i.e. the reaction pp — » (y, Z ). + X. — * t+t+ X.

The single spin asymmetry is function of the polarized quark structure functions, the axial weak coupling of the quark and the interference between the photon and the ZQ. As exhibited in Fig. 3, one gets a sizeable effect maximal at the zQ mass which differs from SU(6) limit /l7/ at small Q values. The magnitude of A. decreases with \(s. We now turn to the determination of the spin asymmetry associated to the k^ spectrum of the positive charged lepton from W+ decay at 0 £ = 90°. In Fig. 4 we make a comparison at Y"s* = 540 GeV between our choice of spin dependent structure functions and SU(6) with Bjorken sum rule. The results are very different both in shape and magnitude. The polarization of the sea quarks does not play a major role.

The effect of increasing |s decreases the magnitude of the asymmetry.

To conclude, polarized electroproduction should provide us with a crucial inform- ation about the spin content of the constituents of the proton. Double spin asymmetries in hadronic collisions should explore the effects of scaling violations.

Single asymmetries in weak boson production, particularly large at the energy of the CERN pp collider, are the unique way to determine the sign of the axial coupling in order to fully test the standard model /20/.

REFERENCES

/1/ BABCOCK J., MONSAY E., and SIVERS D., Phys.Rev. D19 (1979), 1483- 121 BJORKEN J.D., Phys. Rev. 148 (1966), 1467 ; Dl (1970), 1376.

/ 3 / CLOSE F. and SIVERS D., Phys. Rev. Lett. 39 11977), 1116.

/4/ BAUM G. et al., Phys. Rev. Lett. 51_ (198377 1135- /5/ CARLITZ R. and KAUR J., Phys. Rev. Lett. 38 (1977), 673- /6/ FIELD R. and FEYNMAN R., Phys. Rev. IH5 (1977), 2590.

/7/ CHIAPPETTA P. and SOFFER J., Marseille Preprint CPT-84/P.I615, to appear in Phys. Rev. D.

/8/ GLUCK M., HOFFMANN E. and REYA E., Z. fur Phys. C13 (1982), 119.

/9/ GABATHULER E., Contribution to this Symposium.

/lO/ ALTARELLI G. and PARISI G., Nucl. Phys. B126 (1977), 298.

/ll/ DARRIGOL 0. and HAY0T F., Nucl. Phys. B141~Tl978), 391.

/12/ RICHTER-WAS E., Krakow Preprint TPJU-24/83 (1983).

/13/ GABELLINI Y. and MEUNIER J.L., Phys. Lett. I13B (1982), 320.

/14/ HIDAKA K., Phys. Rev. D21 (1980), 1316.

/15/ CRAIGIE N.S., HIDAKA K., JACOB M., PENZO A. and SOFFER J., Nucl. Phys. B204 (1982), 365-

/16/ KINNUNEN R. and LINDFORS J., Nucl. Phys. BI89 (1981), 63.

/l7/ AURENCHE P. and LINDFORS J., Nucl. Phys. Bl85 (l98l), 301.

/18/ CHIAPPETTA P., GRECO M. and SOFFER J., Preprint INFN-Frascati 8 4 / H (P), to appear in Z. fur Phys. and references therein.

/19/ CHIAPPETTA P. and SOFFER J., Marseille Preprint CPT-84/P.I650, to appear in Phys. Lett. B.

/20/ TRUEMAN T.L. and SAUVAGE G., Contributions to this Symposium (see Round Table on:Polarized Protons for the CERN pp Collider ? ) .