IBP reduction via Gr\"obner bases in a rational double-shift algebra
High Energy Physics - Phenomenology
2023-06-14 v2 High Energy Physics - Theory
Mathematical Physics
math.MP
Abstract
We report on an approach to integration-by-parts reduction based on Gr\"obner bases. We establish the underlying noncommutative rational double-shift algebra wherein the integration-by-parts relations form a left ideal. We describe in detail the one-loop massless box as an example where we achieved the full reduction to master integrals by means of the Gr\"obner basis approach, and report on the performance of the implementation. We also identify potential bottlenecks in more complicated examples and elaborate on interesting further directions.
Cite
@article{arxiv.2207.09275,
title = {IBP reduction via Gr\"obner bases in a rational double-shift algebra},
author = {Mohamed Barakat and Robin Brüser and Tobias Huber and Jan Piclum},
journal= {arXiv preprint arXiv:2207.09275},
year = {2023}
}
Comments
11 pages, 2 figures, contribution to the proceedings of "Loops and Legs in Quantum Field Theory - LL2022, 25-30 April, 2022, Ettal, Germany''. v2: Minor revision, reference added