Chiral-odd generalized parton distributions in the large-$N_{c}$ limit of QCD: Spin-flavor structure, polynomiality, sum rules

TL;DR

This paper investigates the nonperturbative properties of chiral-odd generalized parton distributions (GPDs) in the large-$N_c$ limit of QCD, revealing their spin-flavor structure, polynomiality, and sum rules, with implications for phenomenology and modeling.

Contribution

It derives relations between chiral-odd GPDs in the large-$N_c$ limit and tests them against lattice QCD results, advancing understanding of nucleon structure.

Findings

Large-$N_c$ relation between $E_T^{u-d}$ and $ ilde H_T^{u-d}$ GPDs.

Polynomiality and sum rules are satisfied within the mean-field approximation.

Provides a framework for analyzing chiral-odd GPDs in phenomenology and models.

Abstract

We study the nonperturbative properties of the nucleon's chiral-odd generalized parton distributions (transversity GPDs) in the large-$N_c$ limit of QCD. This includes the parametric ordering of the spin-flavor components, the polynomiality property of the moments, and the sum rules connecting the GPDs with the tensor form factors. A multipole expansion in the transverse momentum transfer is used to enumerate and interpret the structures in the nucleon matrix element of the chiral-odd partonic operator, including monopole, dipole and quadrupole terms. The $1/N_c$ expansion of the GPDs is performed using the abstract mean-field picture of baryons in the large-$N_c$ limit and its symmetries. We derive a large-$N_c$ relation between the flavor-nonsinglet GPDs $E_T^{u-d}$ and $\tilde H_T^{u-d}$ and test it with recent lattice QCD results. We show that the polynomiality property and sum rules of the GPDs are fulfilled with the restricted realization of translational and rotational invariance in the mean-field picture. The results provide a basis for the phenomenological analysis of chiral-odd GPDs and hard exclusive processes in the large-$N_c$ limit, and for calculations in specific dynamical models.