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Measurements are presented of associated production of a W boson and a charmquark (W+c) in proton-proton collisions at a center-of-mass energy of 13 TeV.The data correspond to an integrated luminosity of 35.7 fb$^{-1}$ collected bythe CMS experiment at the CERN LHC. The W bosons are identified by their decayinto a muon and a neutrino. The charm quarks are tagged via the fullreconstruction of D$^*$(2010)$^\pm$ mesons that decay via D$^*$(2010)$^\pm \to$D$^0$ + $\pi^\pm \to$ K$^{\mp}$ + $\pi^\pm$ + $\pi^\pm$. A cross section ismeasured in the fiducial region defined by the muon transverse momentum$p_{T}^{\mu} >$ 26 GeV, muon pseudorapidity $|\eta^{\mu}| <$ 2.4, and charmquark transverse momentum $p_{T}^{c} >$ 5 GeV. The inclusive cross section forthis kinematic range is $\sigma$(W+c) = 1026 $\pm$ 31 (stat)$\substack{+76\\-72}$ (syst) pb. The cross section is also measureddifferentially as a function of the pseudorapidity of the muon from the W bosondecay. These measurements are compared with theoretical predictions and areused to probe the strange quark content of the proton.

Measurement of associated production of a W boson and a charm quark in proton-proton collisions at $\sqrt{s} =$ 13 TeV