Direct contour deformation with arbitrary masses in the loop

TL;DR

This paper introduces a method for constructing deformation vectors in loop momentum space to facilitate numerical loop integration with arbitrary masses, extending previous techniques from massless cases.

Contribution

It extends existing contour deformation techniques to handle arbitrary masses in the loop, enabling more general numerical loop integrations.

Findings

Enables numerical loop integration with arbitrary masses.

Extends previous massless contour deformation methods.

Improves the flexibility of loop calculation techniques.

Abstract

We present a method, which constructs a suitable deformation vector in loop momentum space, when the loop integration is done numerically with the help of the subtraction method. The method presented here extends previously discussed techniques from the massless case to the general case of arbitrary masses in the loop.