Direct hyperlogarithmic integration offers a strong alternative to differential equation methods for Feynman integration, particularly for multi-particle diagrams. We review a variety of results by the authors in which this method, employed with some care, can compute diagrams of up to eight particles and four loops. We also highlight situations in which this method fails due to an algebraic obstruction. In a large number of cases the obstruction can be associated with a Calabi-Yau manifold.
@article{arxiv.2103.15423,
title = {Direct Integration for Multi-leg Amplitudes: Tips, Tricks, and When They Fail},
author = {Jacob L. Bourjaily and Yang-Hui He and Andrew J. McLeod and Marcus Spradlin and Cristian Vergu and Matthias Volk and Matt von Hippel and Matthias Wilhelm},
journal= {arXiv preprint arXiv:2103.15423},
year = {2021}
}
Comments
16 pages, 5 figures, talk given at the workshop "Antidifferentiation and the Calculation of Feynman Amplitudes"