Measurement of the production cross section of a $W$ boson with a single charm quark using the ATLAS detector at the Large Hadron Collider

This thesis presents the measurement of the production cross section of a $W$ boson with a single charm quark in 7 TeV proton-proton collisions using the ATLAS detector at the Large Hadron Collider. The data analysed correspond to an integrated luminosity of 4.6 fb$^{-1}$ and were collected during 2011. This is the first time that ATLAS data have been used for this particular measurement. This cross section is of particular interest as a probe of the strange quark density of the proton. Typically, the strange quark density is considered to be suppressed relative to that of the other light-quarks in the proton sea. However, some analyses suggest a more symmetric composition of light-quarks in the proton sea. The results of this study aim to improve the precision of the determination of the strange quark density. The analysis uses events where the $W$ boson decays to a muon and a neutrino. In such events, the charm quark is identified by its semileptonic decay to a soft muon within a hadronic jet. The charge correlation between the $W$ boson and the soft muon is exploited to reduce the backgrounds substantially. The analysis results are combined with those obtained using additional decay channels. The measured cross section provides further constraint for the determination of the strange quark density, advancing the knowledge of the fundamental structure of the proton. The results are compared with predictions of next-to-leading-order QCD calculations obtained using various parton distribution function parameterisations. Additionally, the ratio of the strange-to-down sea-quark distributions is determined to be $0.96^{+0.26}_{-0.30}$ at $Q^2=1.9$ GeV$^{2}$. This supports the hypothesis of a symmetric composition of light-quarks in the proton sea. The cross section ratio $\sigma(W^+ + \overline{c})/\sigma(W^- + c)$ is also determined and compared with different predictions for the asymmetry of the strange and anti-strange quark distribution functions.