Chiral-odd generalized parton distributions in the large- <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>N</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>c</mml:mi> </mml:mrow> </mml:msub>

We investigate the nucleon’s chiral-odd generalized parton distribution functions (GPDs) in the large- <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msub> <a:mi>N</a:mi> <a:mi>c</a:mi> </a:msub> </a:math> limit of quantum chromodynamics (QCD). Extending previous work [] on the leading-order contribution in the <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mn>1</c:mn> <c:mo>/</c:mo> <c:msub> <c:mi>N</c:mi> <c:mi>c</c:mi> </c:msub> </c:math> 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 <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mi>m</e:mi> </e:math> 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 ( <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mi>m</g:mi> <g:mo>=</g:mo> <g:mn>1</g:mn> </g:math> ) 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 reasonable agreement with lattice QCD predictions.