New implementation of the sector decomposition on FORM

TL;DR

This paper presents a new implementation of the sector decomposition algorithm within the FORM symbolic manipulation system, enhancing the numerical evaluation of multi-loop Feynman integrals by efficiently handling large expressions.

Contribution

The paper introduces a novel implementation of sector decomposition on FORM, optimized for managing large symbolic expressions in multi-loop integral calculations.

Findings

Successfully applied to multi-loop diagram examples

Improves handling of large symbolic expressions

Facilitates numerical evaluation of Feynman integrals

Abstract

Nowadays the sector decomposition technique, which can isolate divergences from parametric representations of integrals, becomes a quite useful tool for numerical evaluations of the Feynman loop integrals. It is used to verify the analytical results of multi-loop integrals in the Euclidean region, or in some cases practically used in the physical region by combining with other methods handling the threshold. In an intermediate stage of the sector decomposition for the multi-loop integrals, one often has to handle enormously large expressions containing tons of terms. The symbolic manipulation system FORM is originally designed to treat such huge expressions and has a strong advantage for it. In this talk, the implementation of the sector decomposition algorithm on FORM is discussed. A number of concrete examples including cases of multi-loop diagrams are also shown.