Determination of the strong coupling constant α${}_S$(m${}_Z$) from measurements of inclusive W${}^{\pm }$ and Z boson production cross sections in proton-proton collisions at $\sqrt{S}$ = 7 and 8 TeV

Twelve measurements of inclusive cross sections of W${}^{\pm }$ and Z boson production, performed in proton-proton collisions at centre-of-mass energies of 7 and 8 TeV, are compared with perturbative quantum chromodynamics calculations at next-to-next- to-leading order (NNLO) accuracy obtained with the CT${}_{14}$, HERAPDF${}_{2.0}$, MMHT${}_{14}$, and NNPDF${}_{3.0}$ parton distribution functions (PDFs). Data and theory agree well for all PDF sets, taking into account the experimental and theoretical uncertainties. A novel procedure is employed to extract the strong coupling constant at the Z pole mass from a detailed comparison of all the experimental fiducial cross sections to the corresponding NNLO theoretical predictions, yielding α${}_S$(m${}_Z$)=0.1163${}_{-0.0031}^{+0.0024}$ (CT${}_{14}$), 0.1072${}_{-0.0040}^{+0.0023}$ (HERAPDF${}_{2.0}$), 0.1186 ± 0.0025 (MMHT${}_{14}$), and 0.1147 ± 0.0023 (NNPDF${}_{3.0}$). Using the results obtained with the CT${}_{14}$ and MMHT${}_{14}$ PDFs, which yield the most robust and stable α${}_S$(m${}_Z$) extractions, a value α${}_S$(m${}_Z$)=0.1175${}_{-0.0028}^{+0.0025}$ is determined.