Search for Higgs boson pair production in the $b\bar{b}\tau^+\tau^-$ decay channel with the CMS detector at the LHC

This thesis describes a search for Higgs boson pair ($\text{HH}$) production using proton-proton collision data collected at $\sqrt{s} = 13~\text{TeV}$ with the CMS experiment at the CERN LHC. Events with one Higgs boson decaying into two $\text{b}$ quarks and the other decaying into two $\tau$ leptons ($\text{HH}\to \text{b}\bar{\text{b}}\tau^+\tau^-$) are explored to investigate both resonant and nonresonant production mechanisms. $\text{HH}$ production gives access to the Higgs boson trilinear self-coupling and is sensitive to the presence of physics beyond the standard model. A considerable effort has been devoted to the development of an algorithm for the reconstruction of $\tau$ leptons decays to hadrons ($\tau_\text{h}$) and a neutrino for the Level-1 calorimeter trigger of the experiment, that has been upgraded to face the increase in the centre-of-mass energy and instantaneous luminosity conditions expected for the LHC Run II operations. The algorithm implements a sophisticated dynamic energy clustering technique and dedicated background rejection criteria. Its structure, optimisation and implementation, its commissioning for the LHC restart at $13~\text{TeV}$, and the measurement of its performance are presented. The algorithm is an essential element in the search for $\text{HH}$ production. The investigation of the $\text{HH}\to \text{b}\bar{\text{b}}\tau^+\tau^-$ process explores the three decay modes of the $\tau^+\tau^-$ system with one or two $\tau_\text{h}$ in the final state. A dedicated event selection and categorisation is developed and optimised to enhance the sensitivity, and multivariate techniques are applied for the first time to these final states to separate the signal from the background. Results are derived using an integrated luminosity of $35.9~\text{fb}^{-1}$. They are found to be consistent, within uncertainties, with the standard model background predictions. Upper limits are set on resonant and nonresonant $\text{HH}$ production and constrain the parameter space of the minimal supersymmetric standard model and anomalous Higgs boson couplings. The observed and expected upper limits are about 30 and 25 times the standard model prediction respectively, corresponding to one of the most stringent limits set so far at the LHC. Finally, prospects for future measurements of $\text{HH}$ production at the LHC are evaluated by extrapolating the current results to an integrated luminosity of $3000~\text{fb}^{-1}$ under different detector and analysis performance scenarios.