Development of machine learning based $\tau$ trigger algorithms and search for Higgs boson pair production in the bb$\tau$$\tau$ decay channel with the CMS detector at the LHC

This Thesis presents the study of the Higgs boson pair (HH) production in the final state with a pair of b quarks and a pair of $\tau$ leptons (bb$\tau$$\tau$), exploiting proton-proton collisions data collected at 13 TeV centre-of-mass energy with the CMS detector at the CERN large hadron collider (LHC), corresponding to 138 fb$^{-1}$ accumulated during the Run-2 data-taking period (2015-2018). The bb$\tau$$\tau$ decay channel gives a good trade-off between a sizable branching fraction (7.3%) and the purity of the $\tau$ selection, ensuring the good rejection of the background contributions. The study of HH production gives access to the measurement of the Higgs boson self-coupling ($\lambda$$_{HHH}$). In the context of the Standard Model (SM), this coupling is the only parameter governing the shape of the Higgs potential and it is precisely predicted by the theory; therefore, a measurement of $\lambda$$_{HHH}$ is a test of the validity of the SM and allows us to shed light on the process of electroweak symmetry breaking. In the context of Beyond the SM (BSM) theories (with a particular interest in effective field theories), $\lambda$HHH can assume values larger than that predicted by the SM, greatly enhancing the HH production cross section; the measurement of deviations from the SM prediction would open the road to yet another new era of physics. Upper limits on the SM signal are set at 95% Confidence Level (CL) to be 3.3 and 124 times the SM for $\sigma$(gg → HH) and $\sigma$(qq → HH), respectively. The results are also interpreted in the context of 20 different independent BSM scenarios for which 95% CL limits are set. The experimental context of this Thesis is the restart of LHC operations in 2022 for its Run-3, a new phase with collisions at an energy of 13.6 TeV and instantaneous luminosity of 2 − 2.6 × 10$^{34}$ $cm$ $^{-2}$ s$^{-1}$. In Run-3, the hardware capabilities of the CMS Level-1 Trigger (L1T) are unchanged with respect to Run-2. This requires the development of bolder and more sophisticated approaches to optimise available algorithms to guarantee the success of the CMS physics program. Especially interesting is the optimisation of the L1T section that exploits calorimetric information. As part of this Thesis, a new machine learning method based on a neural network has been developed for the calibration applied in the L1T to calorimeter energy deposits; it exploits data for the calibration of single detector objects, and its promising performance is evaluated against the offline reconstruction of electrons and hadronic jets. The calorimetric information is then optimally used by the algorithm for the reconstruction and identification of hadronically decaying $\tau$ leptons ($\tau$$_{h}$), whose optimisation for the Run-3 is performed in this Thesis employing a new, simple, and more informative approach; the same optimization scheme is also successfully employed for the e/$\gamma$ algorithm. The performance of this approach is evaluated using data collected during Run-3. At the same time, the CMS collaboration is striving for its Phase-2 upgrade program, which is intended to match the ambitious High-Luminosity LHC (HL-LHC) physics program starting in 2029. The considerably increased volume of data collected by the HL-LHC will ensure the statistical power for the detailed study of $\lambda$$_{HHH}$ and possibly its measurement; on the other hand, the larger instantaneous luminosity will require the full replacement of the L1T with hardware of increased capabilities based on state-of-the-art Field Programmable Gate Arrays (FPGAs) to efficiently collect data. To exploit the FPGA capabilities to the maximum, a new machine learning algorithm for the reconstruction, identification, and calibration of $\tau$$_{h}$ candidates in the L1T has been developed as part of this Thesis. This algorithm exploits convolutional neural networks implemented in FPGA firmware and ensures largely enhanced performance compared to standard approaches. All the technical advancement developed within this Thesis has one goal: improving the sensitivity of CMS analyses to the measurement of the Higgs boson self-coupling during the ongoing and future Runs of the LHC.