Reduction of one-massless-loop with scalar boxes in $n+2$ dimensions

TL;DR

This paper explores a dimensional shift technique to simplify the calculation of coefficients in the decomposition of one-massless-loop Feynman diagrams, leveraging the divergence-free nature of scalar boxes in higher dimensions.

Contribution

It introduces a method of shifting dimensions from n to n+2 to streamline the computation of scalar integral coefficients in loop diagrams.

Findings

Scalar boxes in n+2 dimensions are free of infrared divergences.

Dimensional shift simplifies the decomposition process.

Method improves efficiency in loop diagram calculations.

Abstract

All one-massless-loop Feynman diagrams could be written like a linear combination of scalar boxes, triangles an bubbles in $n$ dimensions plus rational terms. However, the four-point scalar integrals in $n+2$ dimensions are free of infrared divergences. We are going to change the dimensions of the scalar boxes $n \to n+2$ and the using of this degree of freedom to simplify the computation of coefficients of the decomposition.