2021/12/17 by B. Ananthanarayan, Sumit Banik, Ananthanarayan, B. +5
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph) #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Mathematical functions and polynomials #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.2112.09679
openalex publication_date 2021/12/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Method of Brackets (MoB) is a technique used to compute definite integrals, that has its origin in the negative dimensional integration method. It was originally proposed for the evaluation of Feynman integrals for which, when applicable, it gives the results in terms of combinations of (multiple) series. We focus here on some of the limitations of MoB and address them by studying the Mellin-Barnes (MB) representation technique. There has been significant process recently in the study of the latter due to the development of a new computational approach based on conic hulls (see Phys. Rev. Lett. 127, 151601 (2021)). The comparison between the two methods helps to understand the limitations of the MoB, in particular when termwise divergent series appear. As a consequence, the MB technique is found to be superior over MoB for two major reasons: 1. the selection of the sets of series that form a series representation for a given integral follows, in the MB approach, from specific intersections of conic hulls, which, in contrast to MoB, does not need any convergence analysis of the involved series, and 2. MB can be used to evaluate resonant (i.e. logarithmic) cases where MoB fails due to the appearance of termwise divergent series. Furthermore, we show that the recently added Rule 5 of MoB naturally emerges as a consequence of the residue theorem in the context of MB.