${\alpha }_s$ and ${\mathrm{V}}_{\mathrm{cs}}$ determination, and CKM unitarity test, from W decays at NNLO

Abstract

The hadronic (${\Gamma }_{\mathrm{had}}^{\mathrm{W}}$) and total (${\Gamma }_{\mathrm{tot}}^{\mathrm{W}}$) 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 ${\mathcal{B}}_{\mathrm{had}}^{\mathrm{W}}\equiv {\Gamma }_{\mathrm{had}}^{\mathrm{W}}/{\Gamma }_{\mathrm{tot}}^{\mathrm{W}}$ = $0.682\pm 0.011_{\mathrm{par}}$, using the experimental Cabibbo-Kobayashi-Maskawa (CKM) matrix elements, or ${\mathcal{B}}_{\mathrm{had}}^{\mathrm{W}}=0.6742\pm 0.0002_{\mathrm{th}}\pm 0.0001_{\mathrm{par}}$ 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, ${\alpha }_s(m_Z)=0.117\pm 0.042_{\exp }\pm 0.004_{\mathrm{th}}\pm 0.001_{\mathrm{par}}$, as well as the charm-strange CKM element, ${\mathrm{V}}_{\mathrm{cs}}$ = 0.973 $\pm$ 0.004${}_{\exp }$ $\pm$ 0.002${}_{\mathrm{par}}$, 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 $m_{\mathrm{W}}$, ${\sum }_{u,c,d,s,b}|V_{ij}{|}^2=1.999\pm 0.008_{\exp }\pm 0.001_{\mathrm{th}}$. Perspectives for ${\alpha }_s$ and ${\mathrm{V}}_{\mathrm{cs}}$ extractions from W decays measurements at the LHC and future $e^{+}{e}^{-}$ colliders are presented.

Comments: 8 pages, 7 figures. Updated version with minor changes to match published version in Phys. Lett. B