Measurement of the production of a $W$ bosons in association with a charm hadron in $pp$ collisions at $\sqrt{s}=7$ TeV

The production of a $W$ boson in association with a single charm quark is studied using 4.6 fb$^{-1}$ of $pp$ collision data collected with the ATLAS detector at $\sqrt{s}=7~$TeV in 2011. In events where the $W$ boson decays to an electron or muon, the charm quark is tagged by the presence of a charm hadron reconstructed in the decay modes $D^+\rightarrow K^-\pi^+\pi^+$ and $D^{*+}\rightarrow D^0\pi^+$ with $D^{0} \rightarrow K^{-}\pi^{+}$, $D^{0} \rightarrow K^{-}\pi^{+}\pi^0$ or $D^{0} \rightarrow K^{-}\pi^{+}\pi^-\pi^+$ and their charge-conjugate states. The single-charm hadron yield is extracted using the charge correlation between the $W$ and the hadron. The cross-section ratios $\sigma(W^{\pm}D^{(*)\mp})/\sigma(W^{\pm})$ are measured inclusively and differentially as a function of the $D^{(*)+}$ meson transverse momentum and the pseudorapidity of the lepton from the $W$ decay. Results are compared to the predictions of next-to-leading order QCD calculations and the sensitivity to the choice of parton distribution function is presented.