Analytical result for dimensionally regularized massless master non-planar double box with one-leg off shell

Abstract

The dimensionally regularized massless non-planar double box Feynman diagram with powers of propagators equal to one, one leg off the mass shell, i.e., with p 1 2= q 2≠0, and three legs on shell, p i 2=0, i=2,3,4 , is analytically calculated for general values of q 2 and the Mandelstam variables s, t and u (not necessarily restricted by the physical condition s+ t+ u= q 2). An explicit result is expressed through (generalized) polylogarithms, up to the fourth order, dependent on rational combinations of q 2, s, t and u, and simple finite two- and three-fold Mellin–Barnes integrals of products of gamma functions which are easily numerically evaluated for arbitrary non-zero values of the arguments.