Blowing up Feynman integrals

TL;DR

This paper discusses sector decomposition, a technique involving blow-ups to handle singularities in multi-loop Feynman integrals, and presents an open-source implementation for numerical Laurent series computation, linking coefficients to periods.

Contribution

It introduces an open-source implementation of sector decomposition for numerical evaluation of divergent integrals and demonstrates its use in proving a theorem relating Laurent coefficients to periods.

Findings

Successful numerical computation of Laurent expansions for multi-loop integrals.

Proof of a theorem connecting Laurent coefficients to periods.

Open-source tool enhances analysis of Feynman integrals.

Abstract

In this talk we discuss sector decomposition. This is a method to disentangle overlapping singularities through a sequence of blow-ups. We report on an open-source implementation of this algorithm to compute numerically the Laurent expansion of divergent multi-loop integrals. We also show how this method can be used to prove a theorem which relates the coefficients of the Laurent series of dimensionally regulated multi-loop integrals to periods.