Statistical Inspired Parton Distributions and the Violation of QPM Sum Rules

A quantum statistical parametrization of parton distributions has been considered. In this framework, the exclusion Pauli principle connects the violation of the Gottfried sum rule with the Ellis and Jaffe one, and implies a defect in the Bjorken sum rule. However, in terms of standard parametrizations of the polarized distributions a good description of the data is obtained once a large gluon polarization is provided. Interestingly, in this description there is no violation of the Bjorken sum rule. 1 Statistical distributions for partons The experimental results on deep inelastic scattering (DIS) are always an inexhaustible source for deeper insight in the nucleon structure. Among them, the violation of well established sum rules represents the relevant starting point to unveil the mechanisms which rule the parton physics. In particular, the value found by the EMC experiment [1] for the first moment of the structure function g 1(x), Γ p 1 = 0.126 ± 0.010 ± 0.015, results to be smaller than the prediction based on the Ellis and Jaffe sum rule (EJ), I p = (F/2)− (D/18). For this reason it has generated the so-called spin crisis. One of the possible explanations of the EMC measurement is that it is a consequence of a negative gluon contribution [2], −(αs/6π)∆G, with the large positive value of ∆G balanced by a negative and large Lz. The gluonic contribution, which is related to the axial anomaly, is the same for proton and neutron and would not affect the Bjorken sum rule (Bj). An alternative interpretation of the defect in the EJ for the proton can be found if Pauli principle plays an important role in parton distributions. Remarkably, these considerations lead to connect [3] the violation of the EJ with the observed defect in the Gottfried sum rule.