  Measurements of the inclusive and normalised differential cross sections are
presented for the production of single top quarks in association with a W boson
in proton-proton collisions at a centre-of-mass energy of 13 TeV. The data used
were recorded with the CMS detector at the LHC during 2016-2018, and correspond
to an integrated luminosity of 138 fb$^{-1}$. Events containing one electron
and one muon in the final state are analysed. For the inclusive measurement, a
multivariate discriminant, exploiting the kinematic properties of the events is
used to separate the signal from the dominant $\mathrm{t\bar{t}}$ background. A
cross section of 79.2 $\pm$ 0.9 (stat) $^{+7.7}_{-8.0}$ (syst) $\pm$ 1.2 (lumi)
pb is obtained, consistent with the predictions of the standard model. For the
differential measurements, a fiducial region is defined according to the
detector acceptance, and the requirement of exactly one jet coming from the
fragmentation of a bottom quark. The resulting distributions are unfolded to
particle level and agree with the predictions at next-to-leading order in
perturbative quantum chromodynamics.
