Search for radiative $b$-baryon decays and study of their anomalous photon polarization at LHCb

This thesis presents the study of two radiative b-baryon decays: $\Lambda_b \to \Lambda \gamma$ and $\Xi_b^- \to \Xi^- \gamma$. As a first step, a search for these decays is performed using LHCb data in order to provide a measurement of their branching ratio. As a second step, the signal candidates are used to measure the photon polarization through the helicity formalism. This thesis presents the first measurement of the photon polarization in b-baryon decays using the $\Lambda_b \to \Lambda \gamma$ decay channel, and the first study of the $\Xi_b^- \to \Xi^- \gamma$ gamma decay. The current theoretical framework of the particle physics, the Standard Model (SM), describes the properties of the known particles and their interactions with three of the fundamental forces. However, the SM is unable to provide explanation for some observed phenomena and, thus, needs to be extended. Some of these extensions include new particles, which could affect the photon polarization in the $b \to s \gamma$ transition, present in the studied decay channels. This thesis uses data from proton-proton collisions collected by the LHCb detector during 2016 and 2018. The LHCb detector is one of the main experiments located at the LHC, hosted by CERN. It is optimized to study the properties of rare decays of $b$- and $c$-hadrons. This work is divided in three steps: the selection of the signal sample, the search for the radiative b-baryon decays and the measurement of the photon polarization. The selection criteria to achieve pure signal samples has been developed in this thesis. The precise estimation of the tracking efficiency is crucial in order to provide accurate measurements. An innovative method to compute the tracking efficiency is developed as a work for this thesis. A simultaneous mass fit to the selected candidates is performed to extract the branching ratio. The developed mass fit strategy is validated by means of pseudo-experiments. The photon polarization is extracted from the angular distribution of $b$-baryon decays using the same signal samples. The feasibility of this measurement is checked by performing sensitivity studies to consider the effects of the limited signal yield, the angular resolution and acceptance, and the background contribution. The angular fit strategy is validated using a MC study and, then, used to extract the photon polarization measurement. The implications of these measurements in the current experimental framework are discussed. The analysis strategies described will be used in studies exploiting larger data samples collected by the LHCb in future.