English

The canonical form has got baubles

High Energy Physics - Theory 2016-12-23 v1

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.

Keywords

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

R2 v1 2026-06-22T17:32:53.147Z