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Spin dependence of constituent quarks and structure function g1

Spin dependence of constituent quarks and structure function g1. Ali Khorramian Institute for studies in theoretical Physics and Mathematics, (IPM) Tehran, IRAN and Physics Department, Semnan University. Spin dependence of constituent quarks and structure function g 1. Outline

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Spin dependence of constituent quarks and structure function g1

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  1. Spin dependence of constituent quarks and structure function g1 Ali KhorramianInstitute for studies in theoretical Physics and Mathematics, (IPM)Tehran, IRAN and Physics Department, Semnan University

  2. Spin dependence of constituent quarks and structure function g1 Outline • Valon model in unpolarized case • Proton structure function • Convolution integral in polarized case • The improvement of polarized valons • NLO moments of PPDF’s and structure function • x-Space PPDF's and g1p(x,Q2) • Results and conclusion Spin04-Trieste-italia, October 10-16, 2004 Ali N. Khorramian

  3. POLARIZED Parton Distributions and Structure Function Spin04-Trieste-italia, October 10-16, 2004 Ali N. Khorramian

  4. Unpolarized valon distributions in a proton In the valon model we assume that a proton consists of three valons (UUD) that separately contain the three valence quarks (uud). The exclusive valon distribution function is where yiare the momentum fractions of the U valons and D valon . The normalization factor gpis determined by this constrain where B(m,n) is the beta function. The single-valon distributions are Spin04-Trieste-italia, October 10-16, 2004 Ali N. Khorramian

  5. The unpolarized valon distributions as a function of y. R. C. Hwa and C. B. Yang, Phys. Rev. C 66 (2002) Spin04-Trieste-italia, October 10-16, 2004 Ali N. Khorramian

  6. Proton structure function • valon distributions in proton • quark distributions in a valon. In an unpolarized situation we may write: This picture suggests that the structure function of a hadron involves a convolution of two distributions: Proton structure function Structure function of a v valon. It depends on Q2 and the nature of the probe. Describes the valon distribution in a proton. It in dependent of Q2. Summation is over the three valons Spin04-Trieste-italia, October 10-16, 2004 Ali N. Khorramian

  7. Polarized valon distribution Using definition of unpolarized and polarized valon distributions according to We have Unpolarized quark distribution in proton Polarized quark distribution in proton Unpolarized and polarized valon distribution Unpolarized and polarized quark distribution in a valon As we can see the polarized quark distribution can be related to polarized valon distribution in a similar way like the unpolarized one. Spin04-Trieste-italia, October 10-16, 2004 Ali N. Khorramian

  8. The improvement of polarized valons Regarding to the existence of the difficulty we suggest the following solution. First we need to improve the definition of polarized valon distribution function as in following using the above ansatz we can write the first moment of polarized u, d and  distribution functions in the improved forms as follows: The above equations can help us to consider the constraint of Polarized PDFs for the improved polarized valon model with an SU(3) Flavour symmetry assumption.These constrains have the same role as the unpolarized ones to control the amounts of the parameter values which will be appeared in polarized valon distributions. Spin04-Trieste-italia, October 10-16, 2004 Ali N. Khorramian

  9. Descriptions of W function Now, we proceed to reveal the actual y-dependence in W, functions. The chosen shape to parameterize the W in y-space is as follows The subscript j refers to U and D-valons This part adjusts valon distributionat large y values Polynomial factor accounts for the additional medium-y values This term can controls the low-y behavior valon distribution It can control the behavior of Singlet sector at very low-y values in such a way that we can extract the sea quarks contributions. For δW ’’ j(y) we choose the following form In these functions all of the parameters are unknown and we will get them from experimental data. By using experimental data and using Bernstein polynomials we do a fitting, and can get the parameters which are defined by unpolarized valon distributions U and D. Spin04-Trieste-italia, October 10-16, 2004 Ali N. Khorramian

  10. Analysis of Moments in NLO • Moments of polarized valon distributions in the proton Let us define the Mellin moments of any valon distribution δGj/p(y) as follows: Correspondingly in n-moment space we indicate the moments of polarized valon distributions Spin04-Trieste-italia, October 10-16, 2004 Ali N. Khorramian

  11. Moments of polarized parton distributions in valon The Q2 evolutions of spliting function are given by their Mellin transform which admit an expansion as follows The non-singlet (NS) part evolves according to where and the NLO running coupling is given by The evolution in the flavor singlet and gluon sector are governed by 2x2 the anomalous dimension matrix with the explicit solution given by Spin04-Trieste-italia, October 10-16, 2004 Ali N. Khorramian

  12. Spin04-Trieste-italia, October 10-16, 2004 Ali N. Khorramian

  13. NLO moments of PPDF’s and structure function By having the moments of polarized valon distributions, the determination of the moments of parton distributions in a proton can be done strictly. The distributions that we shall calculate are δuv, δdv, δ. and δg. So in moment space for g1n(Q2 ) we have some unknown parameters. Spin04-Trieste-italia, October 10-16, 2004 Ali N. Khorramian

  14. Some experimental data for p, n, d E80, 130 (p) ; E142 (n) E143 (p, d) ; E154 (n) ; E155 (p, d) EMC, SMC (p, d) HERMES (p, d, n) Spin04-Trieste-italia, October 10-16, 2004 Ali N. Khorramian

  15. Fig. 10-continued Polarized structure function for some values of Q2as a function ofx in NLOapproximation.The solid curve is our model in NLO and dashed, dashed dotand long dashedcurvesareAAC , BBandGRSV model respectively. Spin04-Trieste-italia, October 10-16, 2004 Ali N. Khorramian

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  17. The Q2 dependence of quark and gluon helicity and their orbital angular momentum.

  18. Conclusion • Here we extended the idea of the valon model to the polarized case to describe the spin dependence of hadron structure function. • In this work the polarized valon distribution is derived from the unpolarized valon distribution. In deriving polarized valon distribution some unknown parameters are introduced which should be determined by fitting to experimental data. • After calculating polarized valon distributions and all parton distributions in a valon, polarized parton density in a proton are calculable. The results are used to evaluate the spin components of the proton. • Our results for polarized structure functions are in good agreement with all available experimental data on g 1p. Spin04-Trieste-italia, October 10-16, 2004 Ali N. Khorramian

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