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 $\mathrmΓ_t$, the $W$-helicity fractions $f_{\mathrm{L,R,0}}$ and semi-inclusive distributions for the top-quark decay process $t \rightarrow b + W^+ + X_{\mathrm{\tiny QCD}}$ at NNNLO in the strong coupling constant $α_s$. In particular, the pure NNNLO QCD correction decreases the $\mathrmΓ_t$ 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 $\mathrmΓ_t = 1.3148^{+0.003}_{-0.005} + 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 $f_{\mathrm{L,R,0}}$ 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.

Figures (2)

• Figure 1: The scale dependence of the fixed-order results for $\mathrm{\Gamma}_t$ in $\mu/m_t \in [0.1, 1]$
• Figure 2: The $W$-energy distribution in $t$-quark decay observed in the $t$-quark rest frame.