Multiple Mellin-Barnes integrals with straight contours
Sumit Banik, Samuel Friot

TL;DR
This paper extends the conic hull method and updates the Mathematica package MBConicHulls.wl to efficiently evaluate multifold Mellin-Barnes integrals with straight contours, aiding in Feynman integral calculations.
Contribution
The authors adapt the conic hull method for straight contours and enhance the MBConicHulls.wl package for automatic multivariable series representations of these integrals.
Findings
Successfully applied to the epsilon-expansion of a massless one-loop pentagon integral.
Provides an efficient computational tool for integrals with straight contours.
Demonstrates the method's effectiveness in practical Feynman integral evaluations.
Abstract
We show how the conic hull method, recently developed for the analytic and non-iterative evaluation of multifold Mellin-Barnes (MB) integrals, can be extended to the case where these integrals have straight contours of integration parallel to the imaginary axes in the complex planes of the integration variables. MB integrals of this class appear, for instance, when one computes the -expansion of dimensionally regularized Feynman integrals, as a result of the application of one of the two main strategies (called A and B in the literature) used to resolve the singularities in of MB representations. We upgrade the Mathematica package MBConicHulls.wl which can now be used to obtain multivariable series representations of multifold MB integrals with arbitrary straight contours, providing an efficient tool for the automatic computation of such integrals. This new feature…
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Taxonomy
TopicsPoint processes and geometric inequalities · Analytic Number Theory Research · Mathematical functions and polynomials
