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arXiv · 2211.13733

Mellin-Barnes Integrals: A Primer on Particle Physics Applications

Ievgen Dubovyk·Janusz Gluza·Gabor Somogyi
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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.

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Ievgen Dubovyk, Janusz Gluza, Gabor Somogyi. 2022-11-24. Mellin-Barnes Integrals: A Primer on Particle Physics Applications. https://arxiv.org/abs/2211.13733

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