Generalized parton distributions of the nucleon in the chiral quark soliton model: Sum over all quark states at nonzero skewness and momentum transfer

Abstract

We compute the combinations $E_M=H^{u+d}+E^{u+d}$ and $H_E=H^{u-d}+tE^{u-d}/(4M_N^2)$ of unpolarized generalized parton distributions (GPDs) of the nucleon in the chiral quark soliton model at nonzero skewness $ξ$ and nonzero momentum transfer $t$. The combinations contain the GPDs $H^{u-d}$ and $E^{u+d}$, which are subleading in the expansion in the inverse number of colors. Both combinations are double sums over the quark states. A multipole expansion of the light-cone operators makes the sums computable at every $ξ$ and every $t\le0$. The contribution of the Dirac continuum is summed over the quark states, without an interpolation formula and without a gradient expansion. The first moments satisfy the form-factor sum rules, and the second moments satisfy polynomiality.