Measurement of the W boson mass and the calibration of the muon momentum with the ATLAS detector

In this thesis measurement of the $W$-boson mass based on data collected during 2011 in proton-proton collisions at a centre-of-mass energy of $7~\mathrm{TeV}$ with the ATLAS detector at the Large Hadron Collider (LHC) is presented. In the Standard Model, the $W$-boson mass depends on the top quark mass and the Higgs-boson mass through higher order corrections. Therefore, a precise measurements the mass of the top quark, $W$- and Higgs-boson, provide a stringent test of the Standard Model. Any observed inconsistency can be an indirect proof of the physics beyond the Standard Model. Previous measurements of the mass of the $W$ boson are performed at the Large electron-positron collider, and at the Tevatron proton-antiproton collider with the CDF and D0 experiments. The current world average value of the $W$-boson mass is $m_W=80385\pm15~\mathrm{MeV}$, while the most precise single measurement with an uncertainty of $19~\mathrm{MeV}$ is performed with the CDF experiment. On the other hand, the indirect constraint on the $W$-boson mass from the global electroweak fit predicts $m_W=80358 \pm 8~\mathrm{MeV}$. At hadron colliders, the $W$-boson mass is determined through its lepton (electron and muon) decays from the Jacobian peaks of the final state kinematic distributions, such as the transverse momentum of the electron and muon, the transverse momentum of the neutrino and the $W$-boson transverse mass. The $W$-boson mass is extracted by comparing these mass sensitive distributions in the data to the set of corresponding template distributions generated using the Monte Carlo simulation of the detector response. The mass is determined by means of $\chi^2$ minimisation with statistical and systematic uncertainties accounted for. The measurement of the $W$-boson mass represents a major challenge, requiring a true understanding of the detector performance (i.e. precise determination of reconstruction efficiency and lepton momentum resolution, as well as the neutrino transverse momentum), and an accurate modeling of the parton distribution functions and the lepton angular distributions. The conventional approach for determining the neutrino energy is from balancing the detected energy in the transverse plane of all reconstructed particles in the event: jets, electrons, photons, tau-leptons, muons and the energies reconstructed in the calorimeter cells which are not associated with any other object. For the ¥Wboson-boson mass measurement an algorithm based on hadronic recoil is developed, so that the transverse momentum of the neutrino becomes a derived quantity from the vector sum of the hadronic recoil and the lepton transverse momentum. The hadronic recoil is calculated as a vector sum of all of the transverse energy of all reconstructed detector signals in the calorimeters, excluding the energy deposits associated to the decay electrons and muons. The hadronic recoil calibration exploits the $Z \rightarrow\ell\ell$ decays, since the $W$- and $Z$-bosons are produced from very similar partonic processes and have similar decay kinematics. The recoil calibration procedure is sensitive to the following sources of systematic uncertainties: the limited statistics of the calibration sample, the differences in the hadronic response between $Z$- and $W$-boson events and on pile-up (additional proton--proton interactions). Muon momentum calibration is based on reference samples of $J/\psi\rightarrow\mu\mu$, $Z\rightarrow\mu\mu$ and $\Upsilon\rightarrow\mu\mu$ decays. The simulated muon momentum is corrected so it matches the measured muon momentum in experimental data. The muon momentum resolution is determined with an uncertainty in ranges from 1.7 % at central pseudorapidity and for transverse momentum $p_{\rm T}=10~\mathrm{GeV}$, to 4 % at large pseudorapidity and $p_{\rm T}=100~\mathrm{GeV}$, while the muon momentum scale is known with an uncertainty of 0.05 % to 0.2 % depending on pseudorapidity. For the $W$-boson mass measurement, after all selection requirements, there is $7.8 \times 10^6$ candidates in the $W\rightarrow \mu \nu$ channel and $5.9¥times 10^6$ candidates in the $W\rightarrow e \nu$ channel. Obtained result for the $W$-boson mass measurement with the ATLAS experiment is: \begin{eqnarray} \nonumber m_W &=& 80370 \pm 7 \,(\textrm{stat.}) \pm 11 \,(\textrm{exp. syst.}) \pm 14 \,(\textrm{mod. syst.}) ~\mathrm{MeV}\\ \nonumber &=& 80370 \pm 19 ~\mathrm{MeV}, \end{eqnarray} where the first uncertainty is statistical, the second corresponds to the experimental systematic uncertainty, and the third to the physics modelling systematic uncertainty. The experimental uncertainty accounts the uncertainties from electron energy and muon momentum calibration and their reconstruction efficiencies, the hadronic recoil calibration, and background processes. The physics modeling systematic uncertainty comes from inaccurate modeling of the $W$-boson production and decay processes in proton--proton collisions at the LHC. The $W$-boson mass measurement is compatible with the current world average value and with the Standard Model prediction. The obtained result is similar in precision to the currently leading measurements performed by the CDF experiment.