Ananthanarayan, B and Banik, S and Friot, S and Pathak, T (2023) Method of Brackets: Revisiting a technique for calculating Feynman integrals and certain definite integrals. In: Physical Review D, 108 (8).
|
PDF
phy_rev_108_8_2023.pdf - Published Version Download (510kB) | Preview |
Abstract
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 progress recently in the study of the latter due to the development of a new computational approach based on conic hulls see B. Ananthanarayan et al., Multiple Series Representations of N-fold Mellin-Barnes Integrals, Phys. Rev. Lett. 127, 151601 (2021)PRLTAO0031-900710.1103/PhysRevLett.127.151601. 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. © 2023 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the "https://creativecommons.org/licenses/by/4.0/"Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Funded by SCOAP3.
| Item Type: | Journal Article |
|---|---|
| Publication: | Physical Review D |
| Publisher: | American Physical Society |
| Additional Information: | The copyright for this article belongs to authors. |
| Department/Centre: | Division of Physical & Mathematical Sciences > Centre for High Energy Physics |
| Date Deposited: | 10 Dec 2024 19:49 |
| Last Modified: | 10 Dec 2024 19:49 |
| URI: | http://eprints.iisc.ac.in/id/eprint/85401 |
Actions (login required)
 |
View Item |
