Study and extrapolation of the H$\, \rightarrow \, \mu \bar{\mu}$ performances to full Run 3 luminosity and High Luminosity - LHC

Since the discovery of the Higgs boson in 2012 by the ATLAS and the CMS collaborations at CERN, the interactions of the Higgs boson with the other fundamental particles are continuously studied at different mass scales. However, the first evidence of the interaction between the Higgs boson and muons has only recently been presented by the CMS collaboration in a paper published in September 2020. The CMS paper included searches for the processes in which Higgs boson was produced by all four production modes and combined data of Run 2 and Run 1 at various integrated luminosities and center of mass energies. This dissertation estimates the performance for the future analyses about H$\rightarrow\, \mu\bar{\mu}$ produced through the Vector Boson Fusion mode to the end of the LHC Run 3 (2024, 300 fb$^{-1}$) and High Luminosity-LHC (2040, 3000 fb$^{-1}$) luminosities. A total of 3 $\times 10^{8}$ simulated events amounting to 26 TB of Monte Carlo data were analyzed, including both signal and background processes. Plots of different variables of the particles are presented for the LHC Run 3 and High Luminosity-LHC analyses. The fit of the original analysis is repeated after having scaled the normalization of samples (both signal and background) to expected luminosities, using the Run 3 and HL-LHC cuts. The results show that with increasing luminosity, there will be an appreciable increase in the significance and decrease in uncertainties on the measurement of the VBF H$\rightarrow\, \mu\bar{\mu}$ cross-section in future analyses.