Next-to-leading order QCD corrections to the top quark decay via the Flavor-Changing Neutral-Current operators with mixing effects

In this paper detailed calculations of the complete $\mathcal{O}(\alpha_s)$ corrections to top quark decay widths $\Gamma(t\to q+V)$ are presented ($V=g,\gamma,Z$). Besides describing in detail the calculations in our previous paper (arXiv:0810.3889), we also include the mixing effects of the Flavor-Changing Neutral-Current (FCNC) operators for $t\to q+\gamma$ and $t\to q+Z$, which were not considered in our previous paper. The results for $t\to q+g$ are the same as in our previous paper. But the mixing effects can either be large or small, and increase or decrease the branching ratios for $t\to q+\gamma$ and $t\to q+Z$, depending on the values of the anomalous couplings ($\kappa^{g,\gamma,Z}_{\mathrm{tq}}/\Lambda$, $f^{g,\gamma,Z}_{\mathrm{tq}}$ and $h^{g,\gamma,Z}_{\mathrm{tq}}$).