QCD corrections to Top-Quark Decay at $\alpha_s^3$

We present the first complete high-precision results for the top-quark decay width $\Gamma_t$, $W$-helicity fractions and semi-inclusive distributions for the top-quark decay process to the third order in the strong coupling constant $\alpha_s$. We find, in particular, that the pure $\mathcal{O}(\alpha_s^3)$ correction decreases $\Gamma_t$ by $0.8\%$ of the previous $\mathcal{O}(\alpha_s^2)$ result, exceeding considerably the error estimated by the usual scale-variation prescription. With this critical piece of correction incorporated, our to-date most precise theoretical prediction meets the request by future colliders. This computation is achieved by a very efficient approach, applied recently also to the calculation of $\mathcal{O}(\alpha_s^3)$ QCD correction to lepton-pair invariant-mass spectrum in B-meson semi-leptonic decay.