Search for rare four-body charm decays with electrons in the final state and long track reconstruction for the LHCb trigger

The rare four-body charm decays D⁰ → π⁺π^-e⁺e^- and D⁰ → K⁺K^-e⁺e^- receive contributions from flavour-changing neutral current c →u l⁺l^- transitions. Measurements of such decays are unique probes of beyond-the-standard-model effects as new heavy particles can contribute in electroweak quantum loops. The search for these rare charm decays is presented using a sample of proton-proton collisions data collected during the Run 2 of LHC (2015-2018), corresponding to an integrated luminosity of 6 fb^-1 and recorded with a center-of-mass energy of 13 TeV at the LHCb experiment. The goal of the study is the first observation of these decays and their branching fraction measurement. The analysis is limited by the statistics and the low hardware-trigger efficiency on the electrons. The upgrade of the LHCb detector, which was recently completed and is now being commissioned, will record data with a five times greater instantaneous luminosity and with a new trigger system, and this analysis is therefore expected to greatly benefit from it. The trigger system was completely redesigned for the upgrade by removing the first-level hardware trigger stage and selecting events with a fully software-based trigger at the 30 MHz collision rate of the LHC. This demanding task is performed by the first step of the high-level trigger, optimised for Graphic Processing Units (GPUs). In order to select interesting events, the trigger must reconstruct the tracks traversing the whole LHCb detector and leaving hits in the three tracking detectors: the vertex locator, the upstream tracker and the scintillating fiber tracker. However, at the beginning of the Run 3 of LHC (2022), the upstream tracker was not yet installed, leading to the necessity of modifying the long track reconstruction strategy. A new algorithm presented in this thesis allows the reconstruction of tracks traversing the whole LHCb detector without using the upstream tracker information. This reconstruction method was successfully tested and commissioned throughout the 2022 data taking and currently used in production in 2023. (author)