The massless non-adjacent double off-shell scalar box integral -- branch cut structure and all-order epsilon expansion

Abstract

We generalize the result of our recent paper on the massless single off-shell scalar box integral to the case of two non-adjacent end points off the light cone. An analytic result in $d=4-2\varepsilon$ dimensions is established in terms of four Gauss hypergeometric ${_2}\mathrm{F}_1$ functions respectively their single-valued counterparts. This allows for an explicit splitting of real and imaginary parts, as well as an all-order $\varepsilon$-expansion in terms of single-valued polylogarithms.