Chiral-odd generalized parton distributions in the large-𝑁𝑐 limit of QCD: Spin-flavor structure, polynomiality, and sum rules

Kim, June-Young; Weiss, Christian

doi:10.1103/PhysRevD.111.074007

Chiral-odd generalized parton distributions in the large-𝑁_𝑐 limit of QCD: Spin-flavor structure, polynomiality, and sum rules

Journal Article · Wed Apr 09 00:00:00 EDT 2025 · Physical Review D

DOI:https://doi.org/10.1103/PhysRevD.111.074007· OSTI ID:2998099

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Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)

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$$^{𝑢−𝑑}_𝑇$$ and $$\tilde{𝐻}^{𝑢−𝑑}_𝑇$$ 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.

View Accepted Manuscript (DOE)

Research Organization:: Temple Univ., Philadelphia, PA (United States); Thomas Jefferson National Accelerator Facility, Newport News, VA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Nuclear Physics (NP)

Grant/Contract Number:: AC05-06OR23177; SC0023646

OSTI ID:: 2998099

Alternate ID(s):: OSTI ID: 2556767

Report Number(s):: DOE/OR/23177--7740; JLAB-THY--24-4239; arXiv:2411.17634

Journal Information:: Physical Review D, Journal Name: Physical Review D Journal Issue: 7 Vol. 111; ISSN 2470-0010; ISSN 2470-0029

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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