1 Ali. N. Khorramian (IPM), Institute for studies in theoretical Physics and Mathematics Physics Department, Semnan University Workshop on Low-x physics September 2002

2 Polarized Structure Function Workshop on Low-x physics September 2002

3 Ali. N. Khorramian (IPM), Institute for studies in theoretical Physics and Mathematics Physics Department, Semnan University S. Atashbar Tehrani Physics Department, Persian Gulf University Workshop on Low-x physics September 2002

4 Outline I. Valon model II. Unpolarized and polarized valon distribution III. Polarized parton distributions IV. Proton and Neutron polarized structure functions. V. Summary & Outlook

5 E80, 130 (p) ; E142 (n) E143 (p, d) ; E154 (n) ; E155 (p, d) EMC, SMC (p, d) HERMES (p, d, n) Workshop on Low-x physics September 2002 Some experimental data for p, n, d

6 Workshop on Low-x physics September 2002 F. Arash and Ali N. Khorramian Nucl. Phys. B 99, 164 (2001)

7 Workshop on Low-x physics September 2002

8 What is the valon model? The valon model describes the hadron structure relevent for multiparticle production. The polarized valon is defined to be a dressed valence quark in QCD with the cloud of polarized gluons and sea quarks which can be resolved by high Q^2 probes. At sufficiently low value of Q^2 the internal polarized structure of a valon cannot be resolved and hence it behaves as a polarized valence quark. For example in the proton we have 2 U-valons and one D valon. Workshop on Low-x physics September 2002 I. Valon model

9 Unpolarized Valon distribution in a proton To facilitate the phenomenological analysis Hwa assumed a simple form for the exclusive valon distribution in unpolarized proton which is Where y i is the momentum fraction of the i-th valon. The single valon distributions are obtained by integration Workshop on Low-x physics September 2002 R. C. Hwa and C. B. Yang, hep-ph /

10 Unpolarized valon R. C. Hwa and M. S. Zahir, Phys. Rev. D 23, 2539 (1981); … R. C. Hwa and C. B. Yang, hep-ph / F. Arash and Ali N. Khorramian Nucl. Phys. B 99, 164 (2001) Ali N. Khorramian, F. Arash, Structure of Hadrons, Proceedings of the International Workshop XXIX on Gross Properties of Nuclei and Nuclear Excitations Hirschegg, Austria, (2001) Workshop on Low-x physics September 2002 U U D

11 Polarized Valon distribution in a proton Workshop on Low-x physics September 2002

12 Unpolarized and polarized valon distribution in a proton Workshop on Low-x physics September 2002

13 Workshop on Low-x physics September 2002

14 Workshop on Low-x physics September 2002 Polarized valon distribution in a proton

15 For calculating the LO and NLO evolutions of the spin-dependent parton distributions, we have used the well known analytic LO and NLO solution in Mellin n-moment space with the n-th moment being defined by Workshop on Low-x physics September 2002

16 Workshop on Low-x physics September 2002 III.

17 LO Workshop on Low-x physics September 2002

18 Workshop on Low-x physics September 2002

19 Workshop on Low-x physics September 2002 Moments of polarized parton distributions

20 Workshop on Low-x physics September 2002 Polarized parton distributions as a function of x

21 NLO Workshop on Low-x physics September 2002

22 Workshop on Low-x physics September 2002

23 Workshop on Low-x physics September 2002 Moments of polarized parton distributions in LO and NLO

24 Workshop on Low-x physics September 2002

25 Workshop on Low-x physics September 2002

26 Workshop on Low-x physics September 2002 IV. Proton and Neutron polarized structure functions.

27 Workshop on Low-x physics September 2002

28 Workshop on Low-x physics September 2002 Polarized structure function in LO

29 Workshop on Low-x physics September 2002 Polarized structure function in NLO

30 The compare of our predictions for polarized proton structure function from our model with the measured structure functions in experiments on proton target. Workshop on Low-x physics September 2002

31 Workshop on Low-x physics September 2002 The compare of our predictions for polarized proton structure function from our model with the measured structure functions in experiments on proton target.

32 Workshop on Low-x physics September 2002

33 Workshop on Low-x physics September 2002 Plots of neutron polarized structure function against x at Q^2= 2, 3 GeV^2

34 Plots of neutron polarized structure function against x at Q^2= 5 GeV^2 Workshop on Low-x physics September 2002

35 conclusion We have presented a model that be used for extraction polarized parton distributions. Our results for polarized proton and neutron structure functions are good agrement with available experimental data.

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