Mellin-Barnes Integrals: A Primer on Particle Physics Applications

TL;DR

This paper introduces Mellin-Barnes integrals as a powerful technique for higher-order calculations in particle physics, providing practical examples, software tools, and theoretical background for advanced researchers.

Contribution

It offers a comprehensive primer on Mellin-Barnes integrals, including construction, solutions, and software tools, tailored for perturbative quantum field theory applications in particle physics.

Findings

Demonstrates the application of Mellin-Barnes integrals to higher-order corrections

Provides examples and software resources for practical computation

Enhances understanding of analytic and numerical solutions in different kinematic regimes

Abstract

We discuss the Mellin-Barnes representation of complex multidimensional integrals. Experiments frontiered by the High-Luminosity Large Hadron Collider at CERN and future collider projects demand the development of computational methods to achieve the theoretical precision required by experimental setups. In this regard, performing higher-order calculations in perturbative quantum field theory is of paramount importance. The Mellin-Barnes integrals technique has been successfully applied to the analytic and numerical analysis of integrals connected with virtual and real higher-order perturbative corrections to particle scattering. Easy-to-follow examples with the supplemental online material introduce the reader to the construction and the analytic, approximate, and numeric solution of Mellin-Barnes integrals in Euclidean and Minkowskian kinematic regimes. It also includes an overview of the state-of-the-art software packages for manipulating and evaluating Mellin-Barnes integrals. These lecture notes are for advanced students and young researchers to master the theoretical background needed to perform perturbative quantum field theory calculations.