$${W}^{{\pm}}{/Z}$$ Cross Section Ratios Through (N)NLO Predictions in QCD

This paper presents $$W^{\pm}/Z$$ cross section ratio predictions for the $$W$$ and $$Z$$ boson productions in their subsequent electron decay channels with next-to-leading order (NLO) and next-to-next-to-leading order (NNLO) calculations in perturbative QCD. The predicted ratios from the fiducial cross sections are primarily compared with the ATLAS measurement based on 13 TeV LHC proton–proton collisions. The predicted fiducial ratios for 14 TeV proton–proton collisions are also presented at (N)NLO accuracies. The 13 TeV and 14 TeV differential distributions for the ratios are provided as a function of the boson transverse momentum at NNLO using different parton distribution functions (PDFs). The 13 TeV and 14 TeV differential distributions for the ratios are also provided for the boson production in association with at least one jet as functions of the first leading jet transverse momentum and absolute pseudorapidity at NLO using various PDF sets. The focus is to predict the ratios more precisely in terms of the reduced theoretical scale uncertainties for the fiducial calculations and to assess sensitivity of the ratios to different PDF sets for the differential calculations. The 13 TeV ratio is predicted as 10.55 $$\pm$$ 0.35 at NLO and 10.57 $$\pm$$ 0.07 at NNLO and found to be in good agreement with the ATLAS data. The 14 TeV ratio is predicted consistently as 10.50 $$\pm$$ 0.36 at NLO and 10.37 $$\pm$$ 0.07 at NNLO. Estimated scale uncertainties are reduced to less than percent level at NNLO in the fiducial ratios. The differential ratios distributions are consistently predicted by using different PDF sets at both 13 TeV and 14 TeV. The differential ratios exhibit more sensitivity to choice of PDF sets in higher regions of the distributions.