CERN Accelerating science

Article
Report number	hep-ph/0101124 ; CERN-TH-2001-005
Title	Two-Loop Master Integrals for $\gamma^{*} \to 3$ Jets : the Non-Planar Topologies
Author(s)	Gehrmann, T ; Remiddi, E
Affiliation	(CERN) ; (Univ. Bologna and INFN, Italy)
Publication	2001
Imprint	12 Jan 2001
Number of pages	22
In:	Nucl. Phys. B 601 (2001) 287-317
DOI	10.1016/S0550-3213(01)00074-8
Subject category	Particle Physics - Phenomenology
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.

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