Generalized parton distribution functions and the nucleon spin sum rules in the chiral quark soliton model

Abstract

The theoretical predictions are given for the forward limit of the unpolarized spin-flip isovector generalized parton distribution function $({E}^{u}\ensuremath{-}{E}^{d})(x,\ensuremath{\xi},t)$ within the framework of the chiral quark soliton model, with full inclusion of the polarization of Dirac sea quarks. We observe that $[({H}^{u}\ensuremath{-}{H}^{d})+({E}^{u}\ensuremath{-}{E}^{d})](x,0,0)$ has a sharp peak around $x=0$, which we interpret as a signal of the importance of the pionic $q\overline{q}$ excitation with large spatial extension in the transverse direction. Another interesting indication given by the predicted distribution in combination with Ji's angular momentum sum rule is that the $\overline{d}$ quark carries more angular momentum than the $\overline{u}$ quark in the proton, which may have some relation with the physics of the violation of the Gottfried sum rule.