Second Order QCD Corrections to $\Gamma (t\to Wb)$

Abstract

Corrections of $O({\alpha }_s^2)$ to the decay of the top quark into a W boson and a bottom quark are calculated. The method is based on an expansion of the top quark propagator for small external momentum, q, as compared to the top quark mass, M_t. The physical point q^2 = M_t^2 is reached through Padé approximations. The described method allows to take effects induced by a finite W boson mass into account. The numerical relevance of the result is discussed. Important cross-checks against recent results for the decay rate $b\to ul\bar{\nu }$ and the two-loop QED corrections to $\mu$-decay are performed.

Latex, 21 pages, 1 figure included as ps-file. Minor changes; reference added. Version to be published in PRD. The complete paper is also available via anonymous ftp at ftp://ttpux2.physik.uni-karlsruhe.de/ttp99/ttp99-25/ or via www at http://www-ttp.physik.uni-karlsruhe.de/Preprints/

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