Search for resonant di-Higgs production in CMS and development of a model independent approach to look for new physics at the LHC

Despite the numerous experimental confirmations of the Standard Model (SM), this framework is believed not to be the complete theory of fundamental interactions. Many scenarios of physics beyond the SM (BSM) are postulated to solve some of the SM deficiencies. In this thesis we perform searches for new physics exploiting 13 TeV proton-proton collisions provided by the Large Hadron Collider and recorded by the Compact Muon Solenoid detector. We present the very first search for resonant Higgs pair production, X → hh, where one of the h decays into a b-quark pair and the other into two leptons plus two neutrinos via vector bosons. This process is predicted in several BSM scenarios such as Warped Extra Dimension or Two Higgs Doublet Model. The observations are found to be compatible with the SM expectations and limits are set on the signal production cross section for resonance masses from mX = 260 GeV to 900 GeV, for both spin-0 and spin-2 particles. The second part of the thesis discusses the development of an innovative approach to search for new physics that allows to probe a large range of deviations from the SM predictions. While model independent searches probe in general the tails of various observables, this analysis is designed to be sensitive in phase space regions widely populated by SM processes. The final discriminant results from a recursive separation of the backgrounds based on the Matrix Element Method.