Chiral-odd generalized parton distributions in the large-$N_{c}$ limit of QCD: Next-to-leading-order contributions

TL;DR

This paper extends the analysis of chiral-odd generalized parton distributions (GPDs) in the large-$N_c$ limit of QCD by including next-to-leading-order contributions, deriving their properties, and providing numerical estimates that agree with lattice QCD.

Contribution

It provides the first complete derivation and numerical estimation of next-to-leading-order chiral-odd GPDs in the large-$N_c$ limit, including their polynomiality and sum rules.

Findings

Derived the spin-flavor structure of chiral-odd GPDs.

Proved polynomiality property for the moments of GPDs.

Numerical estimates agree with lattice QCD predictions.

Abstract

We investigate the nucleon's chiral-odd generalized parton distribution functions (GPDs) in the large-$N_c$ limit of QCD. Extending previous work on the leading-order contribution in the $1/N_c$ expansion, we focus on the next-to-leading-order contributions and provide a complete set of flavor-singlet and flavor-non-singlet chiral-odd GPDs. This study includes the derivation of the spin-flavor structure of the baryon matrix element of the chiral-odd operator, the proof of the polynomiality property and associated sum rules, and numerical estimates based on the gradient expansion. The spin-flavor structure of the nucleon matrix element is interpreted through a multipole expansion in the transverse momentum transfer, leading to the definition of multipole mean-field GPDs. Using these GPDs as the basis of our analysis, we take their $m$-th moments and demonstrate the polynomiality property within the mean-field framework, making use of discrete symmetries in the proof. In particular, the first moments ($m = 1$) of the GPDs are related to the nucleon tensor form factors, as generally required. By performing a gradient expansion, we compute the chiral-odd GPDs and present numerical estimates. Our results show good agreement with lattice QCD predictions.