Search for double Higgs events produced via a vector boson fusion mechanism in the decay channel $b\overline{b}4l$ with the CMS experiment at the LHC

The subject of this thesis is the search for Higgs boson pair production events (HH) produced via a vector boson fusion (VBF) mechanism using proton-proton collision data collected at $\sqrt{s}$ = 13 TeV with the Compact Muon Solenoid (CMS) experiment at the Large Hadron Collider (LHC), Conseil Européen pour la Recherche Nucléaire (CERN) . Events in which the two Higgs particles decay in two b-quarks and four charged leptons (ZZ* $\to$ 4l) respectively, also accompanied by two energetic forward jets usually coming from light quarks (HHqq' $\to$ bb4lqq'), are explored to investigate the Vector Boson Fusion (VBF) non-resonant production mechanism. The VBF HH production provides a unique means to infer information about the quartic VVHH Higgs coupling and the already studied HHH trilinear Higgs self-coupling in the Higgs production via the gluon-gluon fusion process, which are fundamental points to shed light on the reality of Brout-Englert-Higgs (BEH) mechanism to give the particles mass and consequently to probe Beyond Standard Model (BSM) theories. The difficulty of the search, uninvestigated up to now, is mainly due to the small value of the signal production cross section weighted with the branching ratios BRs (for the HH production via VBF, with the Higgs mass set to its best fit value of 125.09 GeV, the cross section at $\sqrt{s}$ =13 TeV is approximately 1.723 fb and the corresponding Branching Ratio (BR)s are 2.79 $\times$ $10^{-4}$for H $\to$ ZZ  $\to$ 4l with l = e, $\mu,\tau$, and 5.75 $\times$ 10$^{-1}$ for $H \to b\overline{b}$ ), thus requiring an exclusive event selection in order to efficiently perform a background rejection. Indeed, multivariate analysis techniques of machine learning are applied to improve the signal discrimination from background, the latter being dominated by the associated production of a Higgs boson and a top quark-antiquark pair. The investigation of the HHqq' $\to$$ b\overline{b}4lqq'$ process explores three decay modes of the system 4l that is $4e, 4\mu,2e2\mu$and has required a detailed study of leptons (electrons and muons), light quarks and b-jets reconstruction. Results in terms of upper limits on the signal strength are derived using an integrated luminosity of 59.74 fb$^{-1}$ from the 2018 Run II campaign.