标题： 最小割与费曼积分的基因约束 显示英文标题

标题： Minimal Cuts and Genealogical Constraints on Feynman Integrals

摘要： 我们介绍了一种有效的方法来推导单个费曼积分间断性的层次约束。 该方法可以应用于任意圈数和粒子多重性，并适用于任意配置的有质量或无质量的虚粒子。 所得的约束在维度正则化中对所有阶次成立，并通过排除有序对间断性（即使它们被（任意数量的）其他间断性分隔开）来补充扩展施泰因曼关系——这些关系限制了相邻顺序间断性。 我们专注于一组优选的层次约束，我们称之为 \emph{系谱约束条件}，它决定了哪些奇点可以由作用于费曼积分中出现的间断性的某些 \emph{最小割集}作为始祖所产生。 虽然推导给定费曼积分的所有层次约束通常需要确定（膨胀的）兰道方程的所有解，但这些系谱约束只需最少的信息即可得出。 我们在一环、二环和三环的例子中展示了此新方法的强大功能，并提供了证据表明系谱约束比扩展施泰因曼关系更显著地限制了费曼积分的解析结构。 显示英文摘要

摘要： We introduce an efficient method for deriving hierarchical constraints on the discontinuities of individual Feynman integrals. This method can be applied at any loop order and particle multiplicity, and to any configuration of massive or massless virtual particles. The resulting constraints hold to all orders in dimensional regularization, and complement the extended Steinmann relations -- which restrict adjacent sequential discontinuities -- by disallowing ordered pairs of discontinuities from appearing even when separated by (any number of) other discontinuities. We focus on a preferred class of hierarchical constraints, which we refer to as \emph{genealogical constraints}, that govern what singularities can follow from certain \emph{minimal cuts} that act as the primogenitors of the discontinuities that appear in Feynman integrals. While deriving the full set of hierarchical constraints on a given Feynman integral generally requires identifying all solutions to the (blown up) Landau equations, these genealogical constraints can be worked out with only minimal information about what singularities may appear. We illustrate the power of this new method in examples at one, two, and three loops, and provide evidence that genealogical constraints restrict the analytic structure of Feynman integrals significantly more than the extended Steinmann relations.