Institute for Theoretical Particle Physics (TTP)


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preprints:2000:ttp00-20 [2016/03/17 11:03] (current)
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 +====== 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.  
 + </hidden> 
 +|**T.Gehrmann, E.Remiddi**  |  
 +|**  Nucl. Phys.  B601 248-286 2001  **  | 
 +| {{preprints:2000:ttp00-20.pdf|PDF}} {{|PostScript}} [[|arXiv]]   | 
 +| |