Optimisation of a multivariate analysis technique for the $\mathbf{{t\bar{t}}}$ background rejection in the search for Higgs boson pair production in $\mathbf{b\bar{b}\tau^+\tau^-}$ decay channel with the CMS experiment at the LHC

This thesis reports the optimisation of a multivariate analysis technique for the search for Higgs boson pair ($HH$) production. $HH$ production gives an access to the Higgs boson trilinear self-coupling and is sensitive to the presence of physics beyond the Standard Model. Both resonant and nonresonant production mechanisms are investigated exploring events with one Higgs boson decaying into two $b$ quarks and the other decaying into two $\tau$ leptons ($HH\rightarrow b\bar{b}\tau^+\tau^{-}$). This process is studied through the examination of the three decay modes of the $\tau^+\tau^{-}$ system, with one or two $\tau$ decaying into hadrons in the final state. The search uses proton-proton collision data collected at $\sqrt{s}=13$ TeV with the CMS experiment at the CERN LHC, corresponding to an integrated luminosity of 35.9 fb$^{{-}1}$. The main effort has been devoted to design and develop a multivariate technique to separate the signal from the $t\bar{t}$ background. This technique has been applied for the first time to all the three final states and has proved to be an essential element to enhance the sensitivity. No evidence for the presence of a signal has been found and results are found to be consistent, within uncertainties, with the standard model background predictions. Upper limits are set at $95\%$ confidence level on resonant and nonresonant $HH$ production. The expected and observed upper limits are about 15$\times \sigma_{HH}^{SM}$ and 10$\times \sigma_{HH}^{SM}$, respectively, corresponding to the most stringent limits set so far at the LHC.