Abstract
The hadronic ($\Gamma^{\rm W}_{\rm had}$) and total ($\Gamma^{\rm W}_{\rm tot}$) widths of the W boson, computed at least at next-to-next-to-leading-order (NNLO) accuracy, are combined to derive a new precise prediction for the hadronic W branching ratio ${\cal B}^{\rm W}_{\rm had} \equiv \Gamma^{\rm W}_{\rm had}/\Gamma^{\rm W}_{\rm tot}$ = $0.682 \pm 0.011_{\rm par}$, using the experimental Cabibbo-Kobayashi-Maskawa (CKM) matrix elements, or ${\cal B}^{\rm W}_{\rm had} = 0.6742 \pm 0.0002_{\rm th} \pm 0.0001_{\rm par}$ assuming CKM unitarity, with uncertainties dominated by the input parameters of the calculations. Comparing the theoretical predictions and experimental measurements for various W decay observables, the NNLO strong coupling constant at the Z pole, $\alpha_s(m_Z) = 0.117 \pm 0.042_{\rm exp} \pm 0.004_{\rm th} \pm 0.001_{\rm par}$, as well as the charm-strange CKM element, $\rm V_{cs}$ = 0.973 $\pm$ 0.004$_{\rm exp}$ $\pm$ 0.002$_{\rm par}$, can be extracted under different assumptions. We also show that W decays provide today the most precise test of CKM unitarity for the 5 quarks lighter than $m_{\rm W}$, $\sum_{ u,c,d,s,b} |V_{ ij}|^2 = 1.999 \pm 0.008_{\rm exp} \pm 0.001_{\rm th}$. Perspectives for $\alpha_s$ and $\rm V_{cs}$ extractions from W decays measurements at the LHC and future $e^+e^-$ colliders are presented.
Highlights
The strong coupling αs is one of the fundamental parameters of the Standard Model (SM), setting the scale of the strength of the strong interaction theoretically described by Quantum Chromodynamics (QCD)
At the same time, that the measurements of W decays provide today the most stringent test of CKM matrix unitarity for all quarks lighter than the top quark
The final most precise extraction of the QCD coupling from W decays is αs(m2Z) = 0.117 ± 0.042exp ± 0.004th ± 0.001par, with a relative uncertainty of 35%, obtained from BhWad or RW imposing CKM unitarity
Summary
The strong coupling αs is one of the fundamental parameters of the Standard Model (SM), setting the scale of the strength of the strong interaction theoretically described by Quantum Chromodynamics (QCD). The hadronic Z width –measured with 0.1% experimental uncertainty in e+e− collisions, and theoretically known up to next-to-NNLO (N3LO), i.e. O αs QCD corrections– provides, combined with other Z-pole observables, a powerful constraint on the current αs world average [4]. A complete expression of including all computed higher-order terms was lacking until recently This situation changed with the work of [5] that obtained including so-far missing mixed QCD + electroweak O (αsα) corrections, improving upon the previous calculations of one-loop O (αs) QCD and O (α) electroweak terms [6,7,8], and two-loop O αs , threeloop O αs3 [9,10], and four-loop O αs4 [11] QCD corrections. The developments presented here should motivate high-quality measurements of W decays using the large datasets available at the LHC, as well as improve the αs extraction benchmarks expected from W measurements at future e+e− colliders such as ILC [14], FCC-ee [15], and CEPC [16]
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