# Differences

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+ | ====== TTP00-20 Two-Loop Master Integrals for \gamma^* -> 3 Jets: The planar topologies ====== | ||

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+ | <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. | ||

+ | </hidden> | ||

+ | |**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]] | | ||

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