Measurement of the inclusive cross sections for W and Z boson production in proton-proton collisions at $\sqrt{s}$ = 5.02 and 13 TeV

Measurements of fiducial and total inclusive cross sections for W and Z boson production are presented in proton-proton collisions at $\sqrt{s}$ = 5.02 and 13 TeV. Electron and muon decay modes ($\mathrm{\ell }$ = e or $\mu$) are studied in the data collected with the CMS detector in 2017, in dedicated runs with reduced instantaneous luminosity. The data sets correspond to integrated luminosities of 298 $\pm$ 6 pb${}^{-1}$ at 5.02 TeV and 206 $\pm$ 5 pb${}^{-1}$ at 13 TeV. Measured values of the products of the total inclusive cross sections and the branching fractions at 5.02 TeV are $\sigma$(pp $\to$ W+X) $\mathcal{B}$(W $\to$ $\mathrm{\ell }\nu$) = 7300 $\pm$ 10 (stat) $\pm$ 60 (syst) $\pm$ 140 (lumi) pb, and $\sigma$(pp $\to$ Z+X) $\mathcal{B}$(Z $\to$ ${\mathrm{\ell }}^{+}{\mathrm{\ell }}^{-}$) = 669 $\pm$ 2 (stat) $\pm$ 6 (syst) $\pm$ 13 (lumi) pb for the dilepton invariant mass in the range of 60-120 GeV. The corresponding results at 13 TeV are 20480 $\pm$ 10 (stat) $\pm$ 170 (syst) $\pm$ 470 (lumi) pb and 1952 $\pm$ 4 (stat) $\pm$ 18 (syst) $\pm$ 45 (lumi) pb. The measured values agree with cross section calculations at next-to-next-to-leading-order in perturbative quantum chromodynamics. Fiducial and total inclusive cross sections, ratios of cross sections of W${}^{+}$ and W${}^{-}$ production as well as inclusive W and Z boson production, and ratios of these measurements at 5.02 and 13 TeV are reported.