Measurement of associated production of a $W$ boson and a charm quark in proton–proton collisions at $\sqrt{s}=13\phantom{\rule{0.166667em}{0ex}}\text{Te}\phantom{\rule{0.333333em}{0ex}}$

Measurements are presented of associated production of a $W$ boson and a charm quark ( $W+c$ ) in proton–proton collisions at a center-of-mass energy of 13 $\phantom{\rule{0.166667em}{0ex}}\text{Te}\phantom{\rule{0.333333em}{0ex}}$ . The data correspond to an integrated luminosity of 35.7 $\phantom{\rule{0.166667em}{0ex}}{\text{fb}}^{-1}$ collected by the CMS experiment at the CERN LHC. The $W$ bosons are identified by their decay into a muon and a neutrino. The charm quarks are tagged via the full reconstruction of ${D}^{\ast }{\left(2010\right)}^{±}$ mesons that decay via ${D}^{\ast }{\left(2010\right)}^{±}\to {D}^{0}+{\pi }^{±}\to {K}^{\mp }+{\pi }^{±}+{\pi }^{±}$ . A cross section is measured in the fiducial region defined by the muon transverse momentum ${p}_{T}^{\mu }>26\phantom{\rule{0.166667em}{0ex}}\text{Ge}\phantom{\rule{0.333333em}{0ex}}$ , muon pseudorapidity $|{\eta }^{\mu }|<2.4$ , and charm quark transverse momentum ${p}_{T}^{c}>5\phantom{\rule{0.166667em}{0ex}}\text{Ge}\phantom{\rule{0.333333em}{0ex}}$ . The inclusive cross section for this kinematic range is $\sigma \left(W+c\right)=1026±31\phantom{\rule{0.166667em}{0ex}}\text{(stat)}\begin{array}{c}+76\\ -72\end{array}\phantom{\rule{0.166667em}{0ex}}\text{(syst) pb}$ . The cross section is also measured differentially as a function of the pseudorapidity of the muon from the $W$ boson decay. These measurements are compared with theoretical predictions and are used to probe the strange quark content of the proton.