Two-loop master integrals for γ* → 3 jets:: the non-planar topologies

The calculation of the two-loop corrections to the three-jet production rate and to event shapes in electron-positron annihilation requires the computation of a number of two-loop four-point master integrals with one off-shell and three on-shell legs. Up to now, only those master integrals corresponding to planar topologies were known. In this paper. we compute the yet outstanding non-planar master integrals by solving differential equations in the external invariants which are fulfilled by these master integrals. We obtain the master integrals as expansions in epsilon = (4 - d)/2. where d is the space-time dimension. The fully analytic results are expressed in terms of the two-dimensional harmonic polylogarithms already introduced in the evaluation of the planar topologies. (C) 2001 Elsevier Science B,V, All rights reserved.