The canonical form has got baubles
Abstract
The method of differential equations in canonical form has proven a powerful tool for solving multiloop Feynman integrals. In this note we test this procedure away from four dimensions. Namely, we consider the simple example of a massless doublebox, expanded in dimensional regularization around six dimensions. We achieve a canonical form for the relevant master integrals and solve them in terms of harmonic polylogarithms up to transcendental order 9. The integral basis of uniform transcendentality requires increasing indices of propagators. According to the standard graphical jargon, this amounts to decorating the integrals with baubles, like on Christmas trees, or rather loops in this case. The results can be useful for studying amplitudes in six dimensions.
Cite
@article{arxiv.1612.07798,
title = {The canonical form has got baubles},
author = {Marco S. Bianchi and Matias Leoni},
journal= {arXiv preprint arXiv:1612.07798},
year = {2016}
}
Comments
16 pages, 1 figure