Top-Quark Decay at Next-to-Next-to-Next-to-Leading Order in QCD

Abstract

We present the first complete high-precision QCD corrections to the inclusive decay width ${\mathrm{\Gamma }}_t$, the $W$-helicity fractions $f_{\mathrm{L},\mathrm{R},0}$ and semi-inclusive distributions for the top-quark decay process $t\to b+W^{+}+X_{\mathrm{QCD}}$ at NNNLO in the strong coupling constant ${\alpha }_s$. In particular, the pure NNNLO QCD correction decreases the ${\mathrm{\Gamma }}_t$ by about $0.8\%$ of the previous NNLO result at the top-quark pole mass scale, exceeding the error estimated by the usual scale-variation prescription. After taking into account all sources of errors, we get ${\mathrm{\Gamma }}_t=1.3148_{-0.005}^{+0.003}+0.027(m_t-172.69)\text{GeV}$, the error of which meets the request by future colliders. On the other hand, the NNNLO QCD effects on $f_{\mathrm{L},\mathrm{R},0}$ are found to be much smaller, at the level of one per-mille for the dominating $f_0$, predestining them to act as precision observables for the top-quark decay process.

Comments: additional examples included and bugs fixed in supplementary files