Definition and calibration of the hadronic recoil in view of the measurement of the $W$ boson mass with the CMS experiment

Although the Standard Model of particle physics might appear as a complete theory, there are several theoretical problems and experimental observations which suggest that it is not the complete and definitive theory. For this reason, new physics is searched for both directly, and through precise measurements of standard model observables. A measurement of the mass of the $W$ boson with a relative precision of $10^{-4}$ is of primary interest because of the small uncertainty in its theoretical prediction, and because the LHC experiments have already collected several hundreds of millions of $W$ boson decays, which allow precise measurements of its properties. Such a measurement may represent a turning point in the world of particle physics, showing that the SM is inconsistent at this energy scale. In order to achieve such precision, it is requested to master the detector, the analysis, and the theoretical predictions at an unprecedented level. A study of the hadronic recoil is described in this thesis, resulting in a new and better experimental definition of this quantity. The power of the new definition is tested in terms of systematic uncertainties on the $W$ mass measurement, which are evaluated in a new and original way.