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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2408.04133 |
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| _version_ | 1866916507461615616 |
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| author | Zhang, Hao-Cheng Ji, Xiangdong |
| author_facet | Zhang, Hao-Cheng Ji, Xiangdong |
| contents | 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 | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_04133 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On convergence properties of GPD expansion through Mellin/conformal moments and orthogonal polynomials Zhang, Hao-Cheng Ji, Xiangdong High Energy Physics - Phenomenology High Energy Physics - Lattice Nuclear Theory 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. |
| title | On convergence properties of GPD expansion through Mellin/conformal moments and orthogonal polynomials |
| topic | High Energy Physics - Phenomenology High Energy Physics - Lattice Nuclear Theory |
| url | https://arxiv.org/abs/2408.04133 |