Chiral-odd generalized parton distributions in the large-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>N</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:math> limit of QCD: Spin-flavor structure, polynomiality

We study the nonperturbative properties of the nucleon’s chiral-odd generalized parton distributions (transversity 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 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 <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 of the GPDs is performed using the abstract mean-field picture of baryons in the large-<e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msub><e:mi>N</e:mi><e:mi>c</e:mi></e:msub></e:math> limit and its symmetries. We derive a large-<g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msub><g:mi>N</g:mi><g:mi>c</g:mi></g:msub></g:math> relation between the flavor-nonsinglet GPDs <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:msubsup><i:mi>E</i:mi><i:mi>T</i:mi><i:mrow><i:mi>u</i:mi><i:mo>−</i:mo><i:mi>d</i:mi></i:mrow></i:msubsup></i:math> and <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:msubsup><k:mover accent="true"><k:mi>H</k:mi><k:mo stretchy="false">˜</k:mo></k:mover><k:mi>T</k:mi><k:mrow><k:mi>u</k:mi><k:mo>−</k:mo><k:mi>d</k:mi></k:mrow></k:msubsup></k:math> 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-<o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:msub><o:mi>N</o:mi><o:mi>c</o:mi></o:msub></o:math> limit, and for calculations in specific dynamical models.