On convergence properties of GPD expansion through Mellin/conformal moments and orthogonal polynomials
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 spe...
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| Format: | Article |
| Language: | English |
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Elsevier
2025-01-01
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| Series: | Nuclear Physics B |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S0550321324003286 |
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| author | Hao-Cheng Zhang Xiangdong Ji |
| author_facet | Hao-Cheng Zhang Xiangdong Ji |
| author_sort | Hao-Cheng Zhang |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-e300606dd1884fb89ea047250c5c0d69 |
| institution | Kabale University |
| issn | 0550-3213 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Nuclear Physics B |
| spelling | doaj-art-e300606dd1884fb89ea047250c5c0d692025-01-10T04:37:49ZengElsevierNuclear Physics B0550-32132025-01-011010116762On convergence properties of GPD expansion through Mellin/conformal moments and orthogonal polynomialsHao-Cheng Zhang0Xiangdong Ji1Taishan College, Shandong University, Jinan, Shandong, 250100, China; Corresponding author.Maryland Center for Fundamental Physics, Department of Physics, University of Maryland, 4296 Stadium Dr., College Park, MD 20742, USA; Corresponding author.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.http://www.sciencedirect.com/science/article/pii/S0550321324003286Parton distributionsGPDs global analysisProperties of hadronsQCD phenomenology |
| spellingShingle | Hao-Cheng Zhang Xiangdong Ji On convergence properties of GPD expansion through Mellin/conformal moments and orthogonal polynomials Nuclear Physics B Parton distributions GPDs global analysis Properties of hadrons QCD phenomenology |
| title | On convergence properties of GPD expansion through Mellin/conformal moments and orthogonal polynomials |
| title_full | On convergence properties of GPD expansion through Mellin/conformal moments and orthogonal polynomials |
| title_fullStr | On convergence properties of GPD expansion through Mellin/conformal moments and orthogonal polynomials |
| title_full_unstemmed | On convergence properties of GPD expansion through Mellin/conformal moments and orthogonal polynomials |
| title_short | On convergence properties of GPD expansion through Mellin/conformal moments and orthogonal polynomials |
| title_sort | on convergence properties of gpd expansion through mellin conformal moments and orthogonal polynomials |
| topic | Parton distributions GPDs global analysis Properties of hadrons QCD phenomenology |
| url | http://www.sciencedirect.com/science/article/pii/S0550321324003286 |
| work_keys_str_mv | AT haochengzhang onconvergencepropertiesofgpdexpansionthroughmellinconformalmomentsandorthogonalpolynomials AT xiangdongji onconvergencepropertiesofgpdexpansionthroughmellinconformalmomentsandorthogonalpolynomials |