Elliptic multiscale Feynman integrals

椭圆多尺度费曼积分

• 批准号: 274006707
• 负责人: Professor Dr. Stefan Weinzierl
• 金额: --
• 依托单位: Institut für Physik
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2015
• 资助国家: 德国
• 起止时间: 2014-12-31 至 2022-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/274006707?language=en
• 关键词: Elliptic; multiscale; Feynman; integrals

The goal of this renewal proposal is to extend our knowledge of single-scale elliptic Feynman integrals towards multi-scale elliptic Feynman integrals.Feynman integrals are an indispensable tool for precision calculations in particle physics.There is a class of Feynman integrals, which evaluate to multiple polylogarithm and captures a significant part of integrals occurring in massless quantum field theories.However, for processes involving the Higgs boson, the top quark or $W$/$Z$-bosons we do not want to neglect the masses of the heavy particles.With non-zero internal masses we leave already at two loops the function space of multiple polylogarithms and have to consider elliptic generalisations.In the first funding period we studied successfully single-scale elliptic Feynman integrals.We now plan to extend our knowledge towards multi-scale elliptic Feynman integrals.The concrete goals of this renewal proposal are:(i) to provide a method for the algorithmic construction of a suitable basis of master integrals in the elliptic multi-scale setting.(ii) to study the integration kernels appearing in the differential equations for the master integrals as generalisations of modular forms.(iii) to provide a method for the numerical evaluation of the master integrals in the elliptic multi-scale setting.

这个更新建议的目标是将我们对单尺度椭圆费曼积分的认识扩展到多尺度椭圆费曼积分。费曼积分是粒子物理学中精确计算的不可或缺的工具。有一类费曼积分，其评估为多重对数，并捕获了无质量量子场论中发生的积分的重要部分。然而，对于涉及希格斯玻色子的过程，我们不想忽略重粒子的质量。对于非零的内部质量，我们已经在两个循环中留下了多个多面体的函数空间，并且必须考虑椭圆推广。在第一个基金期间，我们成功地研究了单尺度椭圆费曼积分。我们现在计划将我们的知识扩展到多个多面体。本文的具体目标是：（1）提供一种在椭圆多尺度下构造主积分基的算法. (ii)研究主积分微分方程中出现的积分核作为模形式的推广。(iii)提供一种椭圆多尺度下主积分的数值计算方法。