Analytical Result for Dimensionally Regularized

The dimensionally regularized massless non-planar double box Feyn-man diagram with powers of propagators equal to one, one leg off the mass shell, i.e. with p 2 1 = q 2 = 0, and three legs on shell, p 2 i = 0, i = 2, 3, 4, is analytically calculated for general values of q 2 and the Man-delstam 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 .