Chiral-odd generalized parton distributions in the large-Nc limit of QCD: Next-to-leading-order contributions

We investigate the nucleon's chiral-odd generalized parton distribution functions (GPDs) in the large-Nc limit of QCD. Extending previous work on the leading-order contribution in the 1/Nc 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.