Vector Boson Fusion trigger and search for Higgs boson pair production at the LHC in the bb$\tau\tau$ channel with the CMS detector

This thesis describes a search for events with a pair of Higgs bosons (HH) in proton-proton collisions at 13 TeV, provided by the Large Hadron Collider, with the CMS (Compact Muon Solenoid) experiment at CERN (Geneva). The study of the Higgs boson pair production allows its trilinear self-coupling ($\lambda_\mathrm{HHH}$) to be measured; moreover, the HH production through Vector Boson Fusion (VBF) gives access to the measurement of the coupling between two Higgs bosons and two vector bosons ($\lambda_\mathrm{2V}$). The values of these parameters are particularly sensitive to the existence of physics beyond the Standard Model: even small variations from the values of the couplings predicted by the theory can lead to a large modification of the cross section. The HH production at the LHC is a very rare process. The production through the main mechanism, by gluon fusion, has a cross section of about 30 fb, followed by the VBF process, which is about 20 times less likely. Therefore, the optimization of the signal selection is essential. Hence, the first part of the thesis work was devoted to the study of algorithms for the Level-1 (L1) trigger system of CMS and a dedicated algorithm for the VBF process was optimized, targeting possible improvements for the search for HH$\rightarrow$bb$\tau\tau$ events. This is the first VBF algorithm for the L1 trigger system and it was included for the data-taking starting as of summer 2017. The events thus selected are available for the ongoing Higgs boson searches, including the search described in this thesis. The rest of the thesis work was dedicated to the analysis of events HH$\rightarrow$bb$\tau\tau$ with the data collected in 2017, starting from a comprehensive study of the data-over-simulation agreement and the development of specific corrections for tau leptons. In addition to the inclusive study of the HH$\rightarrow$bb$\tau\tau$ events, specific event categories for the VBF production were included. The study presented in this thesis is the first dedicated measurement for this production mechanism in the context of the HH$\rightarrow$bb$\tau\tau$ analyses: it lead to the measurement of $\lambda_\mathrm{2V}$, constrained by the observed data between -0.8 and 2.8 times the theoretical prediction.