Search for the Higgs boson decaying into $\tau$ lepton pairs with the Matrix Element Method and $\tau$ trigger optimization in the CMS experiment at the LHC

I performed my thesis work in Particle Physics at the laboratoire Leprince-Ringuet of the Ecole Polytechnique. I have been involved in the analysis of the data produced in the proton-proton collisions at the Large Hadron Collider (CERN) and collected by the CMS experiment. Particle physics is a scientific field which is currently undergoing very important breakthroughs. The discovery of the Higgs boson is a major step forward as the mass of vector bosons are explained through their interactions with the corresponding field. I worked on the newly discovered heavy boson analysis. As its direct coupling to fermions remained to be exhibited, I focused on the search for the Higgs boson decaying in tau lepton pairs. The Higgs decay into tau pairs is the most promising decay channel to measure the couplings between the Standard Model Higgs boson and the fermions. Indeed, this decay channel benefits from a large expected event rate compared to the other leptonic decay modes. The Higgs boson decaying to tau lepton analysis is particularly challenging at the trigger level because the selection of tau leptons relies on its decay into electron and muon whose energy spectrum is relatively soft because of the two neutrinos in the decay chain. The higher threshold on single physics objects has thus a severe impact on the signal acceptance. I investigated this crucial aspect and I worked to implement a cross trigger using the missing transverse energy to lower the threshold on the single lepton. This approach allows the recovery of 41\% of the signal events. Events with large missing transverse momentum were selected in order to control the trigger rate. My personal contribution consisted in a thorough characterization of such a trigger and the evaluation of the associated uncertainty. The results of this approach lead to an amelioration of 2\% in the exclusion limits computed in the Higgs to taus semileptonic channel. In the Run 2, the centre-of-mass energy of the LHC collisions has been increased to 13 TeV and the instantaneous luminosity will reach $2\cdot 10^{34}$ $cm^{-2}s^{-1}$. To guarantee a successful and ambitious physics program under this intense environment, the CMS Trigger and Data acquisition system must be consolidated. During the first long shutdown of the LHC, the L1 Calorimeter Trigger hardware and architecture have been upgraded, benefiting from the recent microTCA technology allowing the calorimeter granularity to be better exploited with more advanced algorithms. Thanks to the enhanced granularity provided by the new system, an innovative dynamic clustering technique has been developed to obtain an optimized tau selection algorithm. I took the responsibility to develop a complete new tau trigger algorithm at Level-1 (L1, hardware based first level of the CMS trigger system). This original approach is aiming at producing the first hardware tau lepton trigger efficient at a hadron collider. I had the opportunity to present the results of my work at the ICHEP-2014 conference, in Valencia and the proceedings were published in Nuclear Physics B afterwards. During my last year of PhD I focused again on the Higgs decays into di-taus analysis, initiating the very first matrix element (ME) approach in this channel, starting with the most sensitive final state: the semileptonic decay mode of the Higgs boson produced through Vector Boson Fusion (VBF) mechanism. No ME-based analysis using tau leptons has ever been published. The aim is to increase the sensitivity of the analysis to the SM Higgs boson, with respect to the conventional methods such as cut-based and multi-variate analyses. The novelty of my work is the treatment of the tau decay through transfer functions. In addition to the computation of the transfer functions, my contribution consisted also in the full characterization of the method and its validation using Monte Carlo samples. Subsequently, I evaluated its performance in the context of the CMS Higgs into di-taus search. The application of the ME method lead to an amelioration of the analysis significance of $\sim 8 \%$ in the semileptonic channel ($\sim 30 \%$ considering only the VBF-tag categories) and to an observation of the decay $\Hz\to\tau\tau\to\mu\tau_{h}$ with a significance of $3.1\sigma$.