{"title":"On convergence properties of GPD expansion through Mellin/conformal moments and orthogonal polynomials","authors":"Hao-Cheng Zhang , Xiangdong Ji","doi":"10.1016/j.nuclphysb.2024.116762","DOIUrl":null,"url":null,"abstract":"<div><div>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 <span><math><mi>x</mi><mo>=</mo><mn>1</mn></math></span> and subsequently develop an approximate formula for GPDs when <span><math><mi>x</mi><mo>></mo><mi>ξ</mi></math></span>. 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.</div></div>","PeriodicalId":54712,"journal":{"name":"Nuclear Physics B","volume":"1010 ","pages":"Article 116762"},"PeriodicalIF":2.5000,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nuclear Physics B","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0550321324003286","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, PARTICLES & FIELDS","Score":null,"Total":0}
引用次数: 0
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 and subsequently develop an approximate formula for GPDs when . 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.
期刊介绍:
Nuclear Physics B focuses on the domain of high energy physics, quantum field theory, statistical systems, and mathematical physics, and includes four main sections: high energy physics - phenomenology, high energy physics - theory, high energy physics - experiment, and quantum field theory, statistical systems, and mathematical physics. The emphasis is on original research papers (Frontiers Articles or Full Length Articles), but Review Articles are also welcome.