Measurements of the Higgs boson mass and width in the four-lepton final state and electron reconstruction in the CMS experiment at the LHC

This thesis document reports measurements of the mass and width of the new boson re- cently discovered at the Large Hadron Collider (LHC), candidating to be the Standard Model Higgs boson. The analysis uses proton-proton collision data recorded by the Compact Muon Solenoid (CMS) detector at the LHC, corresponding to integrated luminosities of $5.1~fb^{−1}$ at $7~$TeV center of mass energy and $19.7~fb^{−1}$ at $8~$TeV center of mass energy. Set of events selecting Higgs boson via the $H\to ZZ$ decay channel, where both $Z$ bosons decay to electron or muon lepton pairs, is used for the Higgs boson properties measurements. A precise measurement of its mass has been performed and gives $125.6\pm0.4\mbox{(stat)}\pm0.2\mbox{(syst)}~$GeV. Constraints on the Higgs boson width were established using its off-shell production and decay to a pair of $Z$ bosons, where one $Z$ boson decays to an electron or muon pair, and the other to an electron, muon, or neutrino pair. The obtained result is an upper limit on the Higgs boson width of $22~$MeV at a 95% confidence level, which is 5.4 times the expected value in the standard model at the measured mass. Throughout the thesis, a particular attention has been put on the elec- tron momentum estimation. The combination of the momentum estimate with the tracker and the energy measurement with the electromagnetic calorimeter, allowing a significant improvement of the low transverse impulsion electrons measurement of the momentum, has been revisited and played an essential role in the Higgs boson discovery in the 4 leptons decay channel. The electron energy scale and resolution have been measured with very high precision using the $Z$ boson decaying in electrons.