Analytic result for the top-quark width at next-to-next-to-leading order in QCD

TL;DR

This paper provides the first complete analytic NNLO QCD calculation of the top-quark decay width, incorporating off-shell effects and offering the most precise theoretical prediction with uncertainties below 1%.

Contribution

It delivers the first full analytic NNLO QCD results for top-quark decay width, including off-shell W effects, expressed in harmonic polylogarithms, and assesses theoretical uncertainties comprehensively.

Findings

Top-quark width calculated as 1.331 GeV for m_t=172.69 GeV.

Results are valid across the entire m_W^2 range and match previous limits.

Uncertainties are less than 1%, improving precision of top-quark decay predictions.

Abstract

We present the first full analytic results of next-to-next-to-leading order (NNLO) QCD corrections to the top-quark decay width $\Gamma(t\to Wb)$ by calculating the imaginary part of three-loop top-quark self-energy diagrams. The results are all expressed in terms of harmonic polylogarithms and valid in the whole region $0\le m_W^2\le m_t^2$. The expansions in the $m_W^2\to 0$ and $m_W^2\to m_t^2$ limits coincide with previous studies. Our results can also be taken as the exact prediction for the lepton invariant mass spectrum in semileptonic $b\to u$ decays. We also analytically compute the decay width including the off-shell $W$ boson effect up to NNLO in QCD for the first time. Combining these contributions with electroweak corrections and the finite $b$-quark mass effect, we determine the most precise top-quark width to be 1.331 GeV for $m_t=172.69$ GeV. The total theoretical uncertainties including those from renormalization scale choice, top-quark renormalization scheme, input parameters, and missing higher-order corrections are scrutinized and found to be less than $1\%$.