On convergence properties of GPD expansion through Mellin/conformal moments and orthogonal polynomials
Year: 2024
Type: article
Abstract: We examine convergence properties of reconstructing the generalized parton distributions (GPDs) through the universal moment parameterization (GUMP). We provide a heuristic explanation for the connection between the formal summation/expansion and the Mellin-Barnes integral in the literature, and specify the exact convergence condition. We derive an asymptotic condition on the conformal moments of GPDs to satisfy the boundary condition at x = 1 and subsequently develop an approximate formula for GPDs when x > ξ . Since experimental observables constraining GPDs can be expressed in terms of double or even triple summations involving their moments, scale evolution factors, and Wilson coefficients, etc., we propose a method to handle the ordering of the multiple summations and convert them into multiple Mellin-Barnes integrals via analytical continuations of integer summation indices.
Source: Nuclear Physics B
Authors: Hao-Cheng Zhang, Xiangdong Ji
Institutions: Shandong University, University of Maryland, College Park
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: diamond
Funder: University of Maryland
OpenAlex ID: W4404839352