# Differences

This shows you the differences between two versions of the page.

 — preprints:2010:ttp10-18 [2016/03/17 11:03] (current) Line 1: Line 1: + ====== 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. ​ ​ + |**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]] ​  | + | |