NNLO QCD corrections to the polarized top quark decay $t(\uparrow )\to X_b+W^{+}$

Abstract

We compute the next-to-next-to-leading order (NNLO) QCD corrections to the decay $t(\uparrow )\to X_b+W^{+}$ of a polarized top quark. The spin-momentum correlation in this quasi two-body decay is described by the polar angle distribution $\mathrm{d}\Gamma /\mathrm{d}\cos {\theta }_P=\frac{\Gamma }{2}(1+P_t{\alpha }_P\cos {\theta }_P)$ where $P_t$ is the polarization of the top quark and ${\alpha }_P$ denotes the asymmetry parameter of the decay. For the latter we find ${\alpha }_P^{\mathrm{NNLO}}=0.3792\pm 0.0037$.

17 pages, 3 figures; v2: added Fig. 2 and 3 and corresponding discussion