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

TL;DR

This paper provides the first complete next-to-next-to-next-to-leading order (NNNLO) QCD corrections to top-quark decay observables, significantly improving theoretical precision for decay width and helicity fractions relevant for future collider experiments.

Contribution

It introduces the first full NNNLO QCD calculations for top-quark decay, refining predictions for decay width and helicity fractions with unprecedented accuracy.

Findings

NNNLO correction decreases decay width by about 0.8%.

Predicted decay width matches future collider precision requirements.

QCD effects on helicity fractions are negligible at the per-mille level.

Abstract

We present the first complete high-precision QCD corrections to the inclusive decay width $\mathrm{\Gamma}_t$, the $W$-helicity fractions $f_{\mathrm{L,R,0}}$ 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 $\alpha_s$. 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^{+0.003}_{-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.