Institute for Theoretical Particle Physics (TTP)
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preprints:2010:ttp10-18 [2016/03/17 11:03] (current) – created - external edit 127.0.0.1
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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]]   | 
 +| |