Методe мерења односа гранања Хигсовог бозона у процесима $H \rightarrow \mu^{+}\mu^{-}$ и $H \rightarrow Z Z^{\star}$ на 1.4 TeV на будућем линеарном сударачу CLIC

This thesis has been done at the CLIC (Compact Linear Collider) project, to be hosted by the European Organisation for Nuclear Research in Geneva (CERN), Switzerland. The CLIC is an option for a future $e^{+}e^{-}$ collider operating at the centre-of-mass energies up to 3 TeV, providing sensitivity to a wide range of new physics phenomena and precision physics measurements at the energy frontier. Operating at three center-of-mass energy stages (350 GeV, 1.4 TeV and 3 TeV), the CLIC enables tight constraints on the Higgs boson couplings. Two measurements of a product of the Higgs production cross-section in WW-fusion and the corresponding branching ratio of the Higgs boson decay, are presended in this thesis. The Higgs boson decay to a pair of muons, being a rare process with a branching ratio of order of 10$^{-4}$, and the Higgs boson decay to a pair of Z bosons are considered, assuming the intermediate CLIC center-of-mass energy of 1.4 TeV. Higgs production cross-section times a branching ratio of a Higgs boson decay is the observable from which Higgs boson couplings can be extracted either from the individual measurements or from a global fit that significantly improves the statistical precision. The samples of signal and background processes are simulated to correspond to the integrated luminosity of 1.5 ab$^{-1}$, equivalent to a four years of of detector operation at the nominal luminosity of 3.7$\cdot$10$^{34}$ cm$^{-2}$s$^{-1}$, assuming an effective up-time of 50%. It has been shown that it is possible to determine the product of the Higgs production cross-section in WW-fusion and the branching ratio of the Higgs boson decay to a pair of muons, ($\sigma_{H\nu_{e}\bar{\nu}_{e}} \times BR(H \rightarrow \mu^{+}\mu^{-})$), with the relative statistical uncertainty of 38%, without beam polarisation, and with the relative statistical uncertainty of 25% assuming electron beam polarisation of -80%. The relative systematic uncertainty is less than 2%. It has also been shown that it is possible to determine the product of the Higgs production cross-section in WW-fusion and the branching ratio of the Higgs boson decay to a pair of Z bosons, ($\sigma_{H\nu_{e}\bar{\nu}_{e}} \times BR(H \rightarrow Z Z^{\star})$), with the relative statistical uncertainty of 17.7% for the hadronic final state ($ZZ^{\star} \rightarrow q_{1} \bar{q}_{1} q_{2} \bar{q}_{2}$), and with the relative statistical uncertainty of 5.6% for the semileptonic final state ($ZZ^{\star} \rightarrow q \bar{q} l^{+} l^{-}$ ), without polarisation included. The relative systematic uncertainty is less than 1%. The relative statistical uncertainty of the Higgs coupling to muons ($g_{H\mu\mu}$) in the model-independent fit is calculated to be 14.1%, at the centre-of-mass energy of 1.4 TeV, and 7.8% at the centre-of-mass energy 3 TeV. Results of the model-dependent fit, which assumes the total Higgs boson width as constrained by the Standard Model, do not give improved measurement accuracy given the limited statistics of the signal. The relative statistical uncertainty of the Higgs coupling to Z bosons ($g_{HZZ}$) extracted from the model-independent fit is 0.8%, at all available CLIC energies. This is due to the fact that the Higgs coupling to Z bosons is primarily determined by the measurements in the Higgstrahlung process at 350 GeV centre-of-mass energy, serving as an imput parametr to the global model-independent fit. The model-dependent fit reduces the relative statistical uncertainty of the Higgs to Z bosons coupling measurements to 0.6%, 0.4% and 0.3%, at centre-of-mass energies of 350 GeV, 1.4 TeV and 3 TeV, respectively, and removes the limitations of the model-independent fit which arise from the limited statistical accuracy of the g HZZ measurement at 350 GeV center-of-mass energy.