Search for non resonant Higgs boson pair production in the four-lepton two-b-jet final state at $\sqrt{s} = 13~\mathrm{TeV}$ with the CMS experiment at the LHC

This thesis presents the search for non-resonant double Higgs boson (HH) production in the final state where one of the two Higgs bosons decays into four leptons ($4\ell$, with $\ell$ denoting either an electron or a muon), while the other decays into a pair of b quarks ($\mathrm{b}\bar{\mathrm{b}}$), which hadronise in jets. The analysis is performed exploiting the full dataset collected by the CMS experiment in the LHC Run II in proton-proton collisions at $\sqrt{s}=13~\mathrm{TeV}$, corresponding to an integrated luminosity of $137~\mathrm{fb}^{-1}$. The analysis presented is the first search for HH production performed in the $\mathrm{b}\bar{\mathrm{b}}4\ell$ final state and the first HH analysis in the CMS collaboration to be completed with the full Run II dataset. An upper limit on the HH production cross section times the branching fraction in the $\mathrm{b}\bar{\mathrm{b}}4\ell$ final state is set to 30 times the standard model (SM) predictions at 95\% confidence level (CL). Possible modifications of the Higgs boson self coupling are also investigated, and the Higgs boson self coupling modifier $k_\lambda$ is constrained to the range $-9 < k_\lambda < 14$ at 95\% CL.