Polarized Structure Function of Nucleon and Orbital Angular Momentum Firooz Arash Physics Department, Tafresh university and Fatemeh Taghavi-shahri Physics department, Iran science and Technology University Spin 2006, Kyoto, japan October 2nd - 7th 2006

Introduction Under certain conditions hadrons behave as if they were composed of 3 (2) constituent quarks. Examples: baryon magnetic moment, meson-baryon couplings and the ratio of total cross section s(pN)/ s(NN), etc. DIS  Nucleon is a complicated object Lots of q- anti q and gluons One might identify the valence quark with a constituent quark, but then the 3 quark picture would be a rough approximation: qq-bar pair and qluon has to be added to the picture. Reconsiling: consider a constituent quark as a quasi particle with a non-trivial internal structure. (The valon)

Some recent indications for the existance of valon Measurements of the Natchmann moments of proton structure function at JLab indicates : Existance of a new scaling that can be interpreted as a constituent form factor consistent with the elastic nucleon data, suggesting that The proton structure originates from elastic coupling with extended objects inside the proton. Osipenko et al. Phys Rev. D 67 (2003) 092991 One can also dress a QCD Lagrangian field to all orders in perturbation theory and construct a valon. See: M. Lavelle, Phys Lett B 371 (1996) , Phys. Rep. 279 (1997).

=> so, it seems reasonable to decompose a nucleon into its constituent quarks U and D. They would carry the internal quantum numbers of the nucleon. Study the internal structure of a valon.

Valon Representation Nucleon: composed of Three valons, Like constituent quarks in the bound state problem Valons have their own structure generated perturbatively.

The polarized structure function of hadron h can be written as: Formalism The polarized structure function of hadron h can be written as: Polarized valon dist In hadron h Working in Moment space: Moments of valon S.F. are expressed completely in terms of t:

, The moments of polarized valence and sea quarks in a polarized valon are F = No. of flavors S, NS stand for singlet and non-singlet These moments are defined as:

U accounts for the 2-loop contribution as an extension to LO

Moments of S, NS, G in a valon singlet Gluon

The first moments are defined by: These quantities have simple physical interpretations: They are related to total z-component of quark and gluon spins Using an inverse Mellin transformation

Some conclusions The total quark contribution to the spin of valon, DS=1, almost independent of Q2 i.e. If the valon consisted of only quarks (valence + sea) it would have been enough to account for the entire spin of the valon Evidently, however, there is a sizable gluon contribution Dg which increases with the increase of Q2 Dqsea is consistent with zero . The variation of DS , Dqsea and Dqvalence with Q2 is marginal. The valon structure is generated by perturbative dressing in QCD. With massless quarks, helicity is conserved and hard gluon cnnot induce sea polarization perturbatively. This also agrees with HERMES data.

Orbital angular momentum in a valon Due to large gluon polarization in a valon these results do not add up to give spin ½ of the valon and do not satisfy 1/2 =1/2 DS +Dg. So, considering the sum rule 1/2 =1/2 DS +Dg + Lz We get a negative and large Orbital angular momentum component for a valon, mainly canceling out the gluon contribution.

Polarized Nucleon Structure Function Need to determine DG(y)valon in: We assume that polarized valon distribution is related to the unpolarized (and known) one: F. Arash, PRB 557 (2003)38, PRD 69 (2004) 054024, PRC 67 (2003) 045201 DGj (y)=dFj (y) Gj (y) With condition that at Q20 it behaves as dqvalence in proton

Q2=2 GeV2

Q2=2.5 GeV2

Q2=3 GeV2

Q2=5 GeV2

Q2=10 GeV2

HERMES Data Q2=2.5 GeV2

xgn1

xgd1

First Moments and the Spin of Proton The first moment of the proton structure function is defined by Additional information on the quark polarization comes from nucleon axial couplings which do not evolve with Q2 and can be determined from b-decay

Our results - 1: g3A= 1.234 (ex. 1.2573+- 0.0028) Experiment: a fit to all data at Q2=5 GeV2 Gp1=0.118 +-0.004 +-0.007, Gn1=-0.048 +- 0.005 +-0.005 g3A= 1.234 (ex. 1.2573+- 0.0028) 4%

Our results-2: For Proton, our prediction for DS, the total quark contribution to the spin lies in the range of 0.410 – 0.440 for Q2=[2,10] GeV2. The variation of DS is due to (marginal) Q2 dependence of Dqv in the NLO, compatible with data of Where for the measure range 0.023<x<0.6 they obtained DS = 0.347+- 0.024 +- 0.066

Role of gluon, orbital angular momentum and the spin of proton Our model is able to regenerate all of the experimental data with a good accuracy. It still remains to accommodate the spin of proton. The spin of a valon in the absence of gluon is completely accounted for by the total spin contribution of quarks. The large gluon polarization in valon , however requires a sizable negative orbital angular momentum to compensate the gluon contribution. The implication for proton is that Dgp rises as Q2 increase, being around 0.7 at Q2=1 GeV2 and 1.3 at Q2=14 GeV2. For the same range of Q2 , then Lz varies from - 0.4 to – 0.97. The role of Lz in a valon is to cancel out the gluon contribution completely, but this cancelation in proton is partial, about 40%

Conclusions and Remarks 1. Polarized structure of a valon is calculated in the NLO in QCD, Structure Function of Hadrons (p, n, d ) are obtained. Agreements with the data is good. 2. Gluon polarization receives a large value and increases with Q2 3. Large and negative Orbital angular Momentum Lz is required in valon to cancel out Dg. But the cancelation is partial (40%) in proton