Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2000-08-28
Nucl.Phys.B601:248-286,2001
Physics
High Energy Physics
High Energy Physics - Phenomenology
27 pages, LaTeX, Appendices extended considerably: contain now complete table of two-dimensional Harmonic polylogarithms up to
Scientific paper
10.1016/S0550-3213(01)00057-8
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 up to now unknown two-loop four-point master integrals with one off-shell and three on-shell legs. In this paper, we compute those master integrals which correspond to planar topologies by solving differential equations in the external invariants which are fulfilled by the master integrals. We obtain the master integrals as expansions in $\e=(4-d)/2$, where $d$ is the space-time dimension. The results are expressed in terms of newly introduced two-dimensional harmonic polylogarithms, whose properties are shortly discussed. For all two-dimensional harmonic polylogarithms appearing in the divergent parts of the integrals, expressions in terms of Nielsen's polylogarithms are given. The analytic continuation of our results to other kinematical situations is outlined.
Gehrmann Thomas
Remiddi Ettore
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