The canonical form has got baubles

TL;DR

This paper extends the differential equations method in canonical form to six dimensions, solving a massless doublebox integral using harmonic polylogarithms and introducing decorated integrals with increased propagator indices.

Contribution

It demonstrates the application of the canonical form method to six-dimensional integrals, including the construction of a uniform transcendental basis with decorated propagators.

Findings

Achieved a canonical form for six-dimensional master integrals.

Solved the integrals in terms of harmonic polylogarithms up to order 9.

Introduced decorated integrals with increased propagator indices.

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.