Direct-to-Symbol Integration from Landau Analysis

Abstract

We propose a Landau-analysis-inspired strategy for directly computing the symbol of integrals that evaluate to multiple polylogarithms in twisted cohomology. The central idea is to identify all ways in which singular hypersurfaces, twisted hypersurfaces, and integration boundaries can interact when external parameters are varied, giving rise to logarithmic or algebraic branch points. By tracking how an integral is modified when analytically continued around each of its branch points, we can recursively construct its symbol. We illustrate this approach by outlining an efficient algorithm for computing the symbol of finite integrals over twisted hyperplane arrangements, when they are expanded around special values of the twist parameter. This algorithm can be used to compute the (transcendental) integrands of cosmological correlators in conformally coupled theories to any order in the twist expansion.

18 pages, 10 figures. Ancillary Mathematica code included