Sector decomposition via computational geometry

TL;DR

This paper introduces a non-iterative, geometry-based method for sector decomposition in loop integrals, reducing the number of sectors needed by classifying polynomial asymptotics and applying computational geometry algorithms.

Contribution

It presents a novel, non-iterative approach to sector decomposition using convex geometry, improving efficiency over traditional iterative methods.

Findings

Fewer sectors are generated compared to iterative methods.

The method effectively separates infrared divergences.

Implementation demonstrates practical computational advantages.

Abstract

A non-iterative method is presented for the factorization step of sector decomposition method, which separates infrared divergent part from loop integration. This method is based on a classification of asymptotic behavior of polynomials. The problem is converted to ones for convex body in Euclidean space. They are solved with algorithms developed in computational geometry. A test implementation shows that this method produces less number of decomposed sectors than usual iterative sector decompositions.