$\alpha_S$ extraction from inclusive $W^\pm$ and Z cross sections in proton-proton collisions at the LHC

Twenty-eight different measurements of inclusive W$^\pm$ and Z cross sections in pp collisions at the LHC are compared to the corresponding theoretical predictions, at NNLO accuracy in perturbative QCD including NLO electroweak corrections, in order to extract the QCD coupling at the Z pole, $\alpha_s(m_Z)$. The theoretical cross sections are computed for four different parton distribution functions (PDFs): CT14, HERAPDF 2.0, MMHT14, and NNPDF 3.0. The calculated cross sections reproduce well the data within experimental and theoretical uncertainties. A linear fit of the $\alpha_s$ dependence of the theoretical cross sections is used to extract the $\alpha_s(m_Z)$ value that best reproduces the measured cross sections. The 28 $\alpha_s(m_Z)$ values extracted from each measurement are combined into a single result by properly taking into account their uncertainties and correlations. The following NNLO values of the QCD coupling for each one of the PDF sets are obtained: $\alpha_s(m_Z) =0.1181 \pm 0.0016$ (CT14), $0.1209 \pm 0.0015$ (MMHT14), and $0.1163 \pm 0.0019$(NNPDF 3.0), with a final uncertainty at the 1.5% level, in good agreement with the $\alpha_s(m_Z)$ world average.