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 $\mathrm{d}\mathrm{\Gamma }/\mathrm{d}\cos {\theta }_P=\frac{\mathrm{\Gamma }}{2}(1+P_t{\alpha }_P\cos {\theta }_P)$, 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 ${\alpha }_P^{\mathrm{NNLO}}=0.3792\pm 0.0037$.

• Received 14 March 2018

DOI:https://doi.org/10.1103/PhysRevD.97.094008

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Published by the American Physical Society