Triggering new discoveries: development of advanced HLT1 algorithms for detection of long-lived particles at LHCb

The work presented in this thesis constitutes a significant contribution to the first high level trigger (HLT1) of the LHCb experiment, based on the Allen project. In Allen, the entire HLT1 sequence of reconstruction algorithms has been designed to be executed on GPU cards. The work in this thesis has contributed to propel the project forward, enabling the LHCb trigger during the Run3, to successfully select real-time events at a frequency of $30$ MHz. An extensive effort has been performed during the Allen development program, leading to the creation of a Allen performance portability layer which enables framework to be executed in several architectures. Furthermore, inside this framework contribution to several key algorithms have been presented. One of these algorithms, termed HybridSeeding, efficiently reconstructs the tracks produced in the SciFi detector (T-tracks). Another algorithm, named VELO-SciFi Matching, building upon the former, allows the reconstruction of long tracks with a momentum precision better than $1\%$. Additionally, a new algorithm named Downstream has been conceived, developed and incorporated into HLT1 for first time. A fast and efficient search of hits in the UT detector is performed, and a fast neural network (NN) is applied to reject ghost tracks. It allows to reconstruct downstream tracks with an efficiency of $70\%$ and a ghost rate below $20\%$. This is the first time that a NN is developed for GPUs inside Allen. This new algorithm will allow the selection of long-lived particles at HLT1 level, opening up new opportunities within both the Standard Model and its extensions. Of particular note is its implication in expanding the search scope for exotic long-lived particles, spanning from 100 ps to several nanosecons, a domain unexplored until now by the LHCb experiment. This, in turn, enhances the sensitivity to new particles predicted by theories that include a dark sector, heavy neutral leptons, supersymmetry, or axion-like particles. In addition, the LHCb's ability to detect particles from the Standard Model, such as $\Lambda$ and K${_s}$, is greatly augmented, thereby enhancing the precision of analyses involving b and c hadron decays. The integration of the HLT1 selection lines derived from the Downstream algorithm into the LHCb's real-time monitoring infrastructure will be important for the data taking during Run3 and beyond, and notably for the present alignment and calibration of the UT detector. The precision in measuring observables which are sensitive to physics beyond the Standard Model, such as the rare $\Lambda_b \to \Lambda\gamma$ decay channel, will be greatly augmented. In this thesis a study of the measurement of the branching fraction of the $\Lambda_b \to \Lambda\gamma$ decay relative to the $B \to K{^*}\gamma$ channel has been performed. The analysis procedure, including selection, reconstruction and background rejection, has been described. A evaluation of the main systematic uncertainties affecting the measurement has been included. It has been concluded that the statistical precision for Run3 will be below $2\%$ as a result of the inclusion of downstream tracks. The measurement of the photon polarisation in these transitions will also benefit from the increase in the yield, reaching a $10\%$ precision in the $\alpha\gamma$ parameter. Measurements of the CP asymmetry in $\Lambda_b \to \Lambda\gamma$ decays will also reach higher precision.