Measurement of $$W^{\pm }$$-boson differential cross-sections in proton–proton collisions with low pile-up data at $$\sqrt{s} = 5.02$$ TeV and $$13\,\hbox {TeV}$$ with the ATLAS detector

High precision single-differential W±-boson production cross-sections as a function of electron or muon transverse momentum pT or their pseudorapity η, as well as double-differential cross-sections as functions of these variables, are measured in proton–proton collisions at centre-of-mass energies s=5.02 TeV and 13 TeV. The W-boson charge asymmetry as a function of lepton η is also measured. The data, collected in dedicated runs at reduced instantaneous luminosity with the ATLAS detector at the Large Hadron Collider, correspond to integrated luminosities of 255 pb-1 at 5.02 TeV and 338 pb-1 at 13 TeV. The measurements are in agreement with Standard-Model predictions calculated at next-to-next-to-leading-order in the strong coupling constant αs including transverse-momentum resummation at next-to-next-to-leading logarithmic accuracy using several parton distribution functions. The impact of the measured differential cross-sections as a function of lepton η on the determination of these functions is studied using a profiling technique.