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

V.A. Smirnov
2001 Physics Letters B  
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\neq 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
more » ... 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.
doi:10.1016/s0370-2693(01)00083-1 fatcat:yqbxrmib6raf5pvuwvxqcbn7ry