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preprints:2010:ttp10-18 [2016/03/17 11:03] (current)
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 +====== TTP10-18 Four Loop Massless Propagators: ​ an Algebraic ​ Evaluation of All  Master Integrals ====== 
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 +      <hidden TTP10-18 ​ Four Loop Massless Propagators: ​ an Algebraic ​ Evaluation of All  Master Integrals > The old "​glue--and--cut"​ symmetry of massless propagators,​ first 
 +established ​ in [1], leads --- after reduction to \ice{corresponding} master integrals 
 +is performed --- to a host of non-trivial ​ relations between the latter. ​  
 +The relations ​ constrain the master integrals so tightly that  they all  can 
 + be analytically expressed in terms of only few, essentially 
 +trivial, watermelon-like integrals. As a consequence  
 +we arrive at  explicit analytical results for all master 
 +integrals appearing in the process of reduction of massless 
 +propagators ​ at three and four loops. The transcendental structure of the results suggests ​ a clean  explanation of the well-known ​ mystery ​ of the absence of   even zetas ($\zeta_{2n}$) ​  
 +in the  Adler function and other similar functions essentially reducible 
 +to  massless propagators. Once a reduction of massless propagators at five loops is  available, ​ our approach should be also applicable for explicitly ​ performing the corresponding ​ five-loop master integrals. ​ </​hidden>​ 
 +|**P.A. Baikov and K.G. Chetyrkin** ​ |  
 +|** Nucl.Phys. B837 186-220 2010  **  | 
 +| {{preprints:​2010:​ttp10-18.pdf|PDF}} {{preprints:​2010:​ttp10-18.ps|PostScript}} [[http://​arxiv.org/​abs/​1004.1153|arXiv]] [[http://​ttp.kit.edu/​Progdata/​ttp10/​ttp10-18|Programs and Data]] ​  | 
 +| |