Two-Loop Master Integrals for ${\gamma }^{\ast }\to 3$ Jets: The non-planar topologies

Abstract

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 $\e=(4-d)/2$, 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.

22 pages, LaTeX, version to be published, Note added on numerical checks of the results, typos corrected

References in corpus (1)

• Analytical Result for Dimensionally Regularized Massless Master Non-planar Double Box with One Leg off Shell

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