标题： 关于通过Mellin/保角矩和正交多项式研究GPD展开的收敛性质 显示英文标题

标题： On convergence properties of GPD expansion through Mellin/conformal moments and orthogonal polynomials

摘要： 我们研究了通过通用矩参数化（GUMP）重建广义部分子分布（GPDs）的收敛性质。我们对文献中形式求和/展开与Mellin-Barnes积分之间的联系提供了启发式解释，并指定了确切的收敛条件。我们推导了GPDs的共formal矩满足在$x=1$处边界条件的渐近条件，随后在$x>\xi$时发展出一个近似公式用于GPDs。由于限制GPDs的实验可观测量可以用涉及它们的矩、尺度演化因子和Wilson系数等的双重甚至三重求和来表示，我们提出了一种处理多重求和顺序的方法，并通过整数求和指标的解析延拓将其转化为多重Mellin-Barnes积分。 显示英文摘要

摘要： 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 $x>\xi$. 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.