Efficient Evaluation of Massive Mellin--Barnes Integrals
Janusz Gluza, Tomasz Jelinski, David A. Kosower
TL;DR
This paper introduces a method for efficiently evaluating massive Mellin-Barnes integrals by contour modification and stationary phase analysis, improving computational approaches for complex loop integrals in physics.
Contribution
It presents a novel contour modification technique and an exact solution to the stationary phase differential equation for Mellin-Barnes integrals.
Findings
Enhanced efficiency in evaluating massive Mellin-Barnes integrals.
Development of simple approximations for integration contours.
Applicability to both Euclidean and Minkowski regions.
Abstract
We show how to evaluate one-dimensional Minkowski-region Mellin-Barnes representations arising from massive loop integrals, by modifying the contours of integration. We implement an exact solution to the differential equation determining the contours of stationary phase. We also present several simple approximations to these contours. Our approach points the way to more efficient computations of massless and massive Mellin-Barnes integrals in both Euclidean and Minkowski regions.
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