Mellin–Barnes meets Method of Brackets: a novel approach to Mellin–Barnes representations of Feynman integrals

Abstract

In this paper, we present a new approach to the construction of Mellin-Barnes representations for Feynman integrals inspired by the Method of Brackets. The novel technique is helpful to lower the dimensionality of MellinBarnes representations in complicated cases, some examples are given.

Mellin–Barnes integrals and the method of brackets

“…The work included reproduces many integral relations using the method of brackets. The results presented here are compared with those developed by Prausa [23]. In his work this author uses a package developed in Mathematica [10].…”

“…where γ is the usual vertical line contour. A similar argument has appeared in [23]. The idea is to use the method of brackets to produce the bracket series associated to (4.3).…”

“…In addition, several known relations for generalized hypergeometric functions have been reestablished by combining the method of brackets and Mellin-Barnes transformations. Our investigation has been motivated by the work of Prausa [23] which proposes an interesting symbolic procedure. Our work compares it with the method of brackets.…”

“…These complement those given for the discrete sums. The results presented here have appeared in [23] as an extension of the method of brackets and used to produce a minimal Mellin-Barnes representations of integrals appearing in connection with Feynman diagrams.…”

MBnumerics: Numerical integration of Mellin-Barnes integrals in physical regions

“…Feynman integrals may be infrared and ultraviolet divergent. To treat these integrals in a consistent and automated way two methods are known: The Mellin-Barnes integral approach [1,2,3,4,5,6,7,8,9,10,11] and the sector decomposition approach [12,13,14,15,16,17].…”