标题： 几何方法用于多重梅林-巴恩斯积分的解析求值 显示英文标题

标题： Geometrical methods for the analytic evaluation of multiple Mellin-Barnes integrals

摘要： 最近开发的两种分析计算多重复合梅林-巴纳茨（MB）积分的技术被介绍。 这两种方法都基于定义与MB被积函数方便相关联的几何对象，这些对象可以与多元残差分析结合，推导出MB积分的级数表示。 第一种方法基于引入圆锥包和考虑后者特定的交集，而第二种方法则基于点配置及其正规三角剖分。 在简要描述了这两种方法（已在MBConicHulls.wl Mathematica包中实现自动化）之后，我们回顾了它们的一些应用。 特别是，我们展示了如何使用圆锥包方法获得复杂费曼积分的第一个解析计算，例如无质量非壳上共形六边形和双盒。 然后我们表明，三角剖分方法更加高效，因为它能够以更快的方式计算这些非平凡对象以及更困难的对象。 显示英文摘要

摘要： Two recently developed techniques of analytic evaluation of multifold Mellin-Barnes (MB) integrals are presented. Both approaches rest on the definition of geometrical objets conveniently associated with the MB integrands, which can then be used along with multivariate residues analysis to derive series representations of the MB integrals. The first method is based on introducing conic hulls and considering specific intersections of the latter, while the second one rests on point configurations and their regular triangulations. After a brief description of both methods, which have been automatized in the MBConicHulls.wl Mathematica package, we review some of their applications. In particular, we show how the conic hulls method was used to obtain the first analytic calculation of complicated Feynman integrals, such as the massless off-shell conformal hexagon and double-box. We then show that the triangulation method is even more efficient, as it allows one to compute these nontrivial objects and harder ones in a much faster way.