Search for a charged Higgs boson in $\tau\nu_{tau}$ and $t\bar{b}$ decays in proton-proton collisions at $\sqrt{s}=7$ and $8$ TeV with the CMS detector

The Large Hadron Collider (LHC) started the first proton-proton collisions at a center-of-mass energy of 7 TeV in 2010. Soon thereafter, the experiments started collecting data and were able to rediscover the Standard Model (SM) in a few months, thanks to the very good understanding of the detectors, and their already precise calibrations. The LHC took data at $\sqrt{s}=7$~TeV and 8~TeV in the years 2010-2011 and 2012, respectively: the peak of his intensive data taking has been, in 2012, the discovery, by the CMS and ATLAS experiment s, of a neutral boson with a mass of approximately 125\unit{\GeV}. The properties of the new boson are consistent with those predicted for the Standard Model (SM) Higgs boson, and models with an extended Higgs sector are constrained by the measured properties of the new boson: the discovery of another scalar boson, neutral or charged, would represent unambig uous evidence for the presence of physics beyond the SM. Charged Higgs bosons are predicted in models consisting of at least two Higgs doublets, of which the simplest are the two-Higgs-doublet models (2HDM). Among the physical Higgs bosons predicted by these models, the charged ones ($H^{+}$ an d its charge conjugate, $H^{-}$) have been chosen as topic for this Thesis. At the LHC, the charged Higgs boson can be studied in top quark decays, if the mass of the charged Higgs boson is smaller than the mass difference between the top and the bottom quarks, \ie $m_{H^+} < (m_t-m_b)$, or in associated production with a top quark if $m_{H^+} > (m_t-m_b)$. In the latter case, top quarks are also part of the decay chain of the charged Higgs boson. In this Thesis, a charged Higgs boson is searched for across the whole mass range. In the case $m_{H^+} < (m_t-m_b)$, studied at a center-of-mass energy of 7~TeV, the lepton+tau final state is selected: the main background in that case is the contribution from events with jets misidentified as taus, hence a dedicated data driven technique is employed to improve the estimate of that contribution. In the case $m_{H^+} > (m_t-m_b)$, where most BSM scenarios predict a charged Higgs boson decay into a top and a bottom quark, the dilepton final state is investigated, being more sensitive to the presence of a charged Higgs boson. Two measurements of SM parameters, the top mass at 7~TeV and the top pair production cross section at 8~TeV, are presented first, as ways of obtaining a better understanding of the calibration of the CMS detector. A search for a charged Higgs boson decaying into a tau lepton and a neutrino is presented next, in the final state characterized by one muon and one hadronically decaying tau. A previous publication by the CMS collaboration had set upper limits of the order of 5\% for the branching ratio $\mathcal{B}(t\to H^{+}\bar{b})$, by using almost half of the data collected at 7~TeV by the CMS detector. That result has been improved in the context of this Thesis, by analyzing the full 7~TeV dataset and applying more advanced statistical methods (improving the data driven determination of the main background, and exploiting the polarization properties of the tau lepton in order to improve the sensitivity of the result): the improvement has been of the order of 50\%, bringing the upper limit on $\mathcal{B}(t\to H^{+}\bar{b})$ down to $\sim 2--3$\%. A search for a charged Higgs boson with a mass larger than the top quark mass is presented next, that has been performed using the 8~TeV data using two main final states: the lepton+tau final state, that in this mass region is characterized by a very low sensitivity, and the dilepton final state. In this mass regime, for the majority of the theoretical scenarios, the charged Higgs boson decays either into a tau and a neutrino, or into a top quark and a b quark. The production mechanism changes as well, and is characterized by the associate production of a top quark and a charged Higgs, sometimes with an additional b quark. The decay into a top quark and a b quark, together with the production mechanism, justifies the use of the dilepton final state as a flagship for the search strategy. The result of this search represented the first direct search ever for a heavy charged Higgs boson decaying into a top quark and a b quark. Finally, an overview is made of the perspectives for charged Higgs boson searches in the context of the ongoing LHC run at a center-of-mass energy of 13~TeV.