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

The theoretical predictions are given for the forward limit of the unpolarized spin-flip isovector generalized parton distribution function $(E^u - E^d)(x, xi, t)$ within the framework of the chiral quark soliton model, with full inclusion of the polarization of Dirac sea quarks. We observe that $[(H^u - H^d) + (E^u - E^d)](x,0,0)$ has a sharp peak around $x=0$, which we interpret as a signal of the importance of the pionic $q bar{q}$ excitation with large spatial extension in the transverse direction. Another interesting indication given by the predicted distribution in combination with Jis angular momentum sum rule is that the $bar{d}$-quark carries more angular momentum than the $bar{u}$-quark in the proton, which may have some relation with the physics of the violation of the Gottfried sum rule.