The scalar box integral and the Mellin - Barnes representation

TL;DR

This paper provides an exact solution to the scalar box integral using Mellin-Barnes representation, involving hypergeometric functions, analytic continuation, and Laurent expansion, advancing computational techniques in quantum field theory.

Contribution

The paper introduces a novel exact solution method for the scalar box integral employing Mellin-Barnes representation and hypergeometric functions.

Findings

Exact scalar box integral solution obtained

Hypergeometric functions used for resummation

Analytic continuation and Laurent expansion applied

Abstract

We solve exactly the scalar box integral using the Mellin-Barnes representation. Firstly we recognize the hypergeometric functions resumming the series coming from the scalar integrals, then we perform an analytic continuation before applying the Laurent expansion in^2 = (d !' 4)=2 of the result.