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 — preprints:2000:ttp00-20 [2016/03/17 11:03] (current) Line 1: Line 1: + ====== TTP00-20 Two-Loop Master Integrals for \gamma^* -> 3 Jets: The planar topologies ====== + + + <​hidden TTP00-20 ​ Two-Loop Master Integrals for \gamma^* -> 3 Jets: The 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 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. + ​ + |**T.Gehrmann,​ E.Remiddi** ​ | + |**  Nucl. Phys.  B601 248-286 2001  **  | + | {{preprints:​2000:​ttp00-20.pdf|PDF}} {{preprints:​2000:​ttp00-20.ps|PostScript}} [[http://​arxiv.org/​abs/​hep-ph/​0008287|arXiv]] ​  | + | |