Multiple Series Representations of N -fold Mellin-Barnes Integrals

Ananthanarayan, B and Banik, S and Friot, S and Ghosh, S (2021) Multiple Series Representations of N -fold Mellin-Barnes Integrals. In: Physical Review Letters, 127 (15).

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Abstract

Mellin-Barnes (MB) integrals are well-known objects appearing in many branches of mathematics and physics, ranging from hypergeometric functions theory to quantum field theory, solid-state physics, asymptotic theory, etc. Although MB integrals have been studied for more than one century, until now there has been no systematic computational technique of the multiple series representations of N-fold MB integrals for N>2. Relying on a simple geometrical analysis based on conic hulls, we show here a solution to this important problem. Our method can be applied to resonant (i.e., logarithmic) and nonresonant cases and, depending on the form of the MB integrand, it gives rise to convergent series representations or diverging asymptotic ones. When convergent series are obtained, the method also allows, in general, the determination of a single "master series"for each series representation, which considerably simplifies convergence studies and/or numerical checks. We provide, along with this Letter, a Mathematica implementation of our technique with examples of applications. Among them, we present the first evaluation of the hexagon and double box conformal Feynman integrals with unit propagator powers. © 2021 authors. Published by the American Physical Society.

Item Type:	Journal Article
Publication:	Physical Review Letters
Publisher:	American Physical Society
Additional Information:	The copyright for this article belongs to Authors
Keywords:	Asymptotic analysis; Computation theory; Convergence of numerical methods; Functions; Geometry, Asymptotic theories; Computational technique; Convergent series; Function theory; Hypergeometric functions; Mellin-Barnes integrals; Quantum field theory; Series representations; Simple++; Solid-state physics, Quantum theory
Department/Centre:	Division of Physical & Mathematical Sciences > Centre for High Energy Physics
Date Deposited:	28 Nov 2021 07:13
Last Modified:	28 Nov 2021 07:13
URI:	http://eprints.iisc.ac.in/id/eprint/70419

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