One-loop pentagon integral in $d$ dimensions from differential equations in $ϵ$-form

Abstract

We apply the differential equation technique to the calculation of the one-loop massless diagram with five onshell legs. Using the reduction to $ϵ$-form, we manage to obtain a simple one-fold integral representation exact in space-time dimensionality. The expansion of the obtained result in $ϵ$ and the analytical continuation to physical regions are discussed.

Comments: 16 pages, 2 figures, v2: minor stylistic corrections, acknowlednments updated