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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 ====== 
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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]] ​  | 
 +| |