Two-loop master integrals for γ∗→3 jets: the non-planar topologies Original Research Article

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 ϵ=(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.