and hadronic τ-Decays in Order : technical aspects

We report on some technical aspects of our calculation of α s 4 corrections to R ( s ) and the semi-leptonic τ decay width [P.A. Baikov, K.G. Chetyrkin and J.H. Kuhn, Phys. Rev. Lett. 101 (2008) 012002, 0801.1821 ; P.A. Baikov, K.G. Chetyrkin and J.H. Kuhn, PoS RADCOR2007 (2007) 023, 0810.4048 ; P.A. Baikov, K.G. Chetyrkin and J.H. Kuhn, Nucl. Phys. Proc. Suppl. 135 (2004) 243]. We discuss the inner structure of the result as well as the issue of its correctness. We demonstrate recently appeared independent evidence positively testing one of two components of our full result.