Real-time analysis for studies of charge parity and lepton flavour violation in b-meson decays at LHCb

Trigger systems of high energy physics experiments are crucial to the processing of the immense quantities of data produced from particle collisions. The LHCb experiment underwent a major upgrade between Runs 2 and 3 of the LHC, in which the trigger system was redeveloped from a hardware-and software-based model to an entirely software-based model. This thesis presents measurements with proton-proton collision data recorded by the LHCb experiment for both of these models, and the commissioning of the software-based trigger. The first ever measurement of the time-integrated untagged CP asymmetry in the decay of Bs0 -> Ds- pi+, , is presented, performed with of 5.4 fb^-1 of data recorded in 2016-18. The measured values in the Ds- -> h- h+ pi- decay modes of the Ds-, are consistent with the Standard Model of particle physics, down to a precision of O(10^-3). An ongoing measurement of the lepton flavour universality ratio in B+ -> J/psi(l+ l-) K+ decays, r_J/psi, using 4.5 fb^-1 data recorded in 2024 is then presented. This measurement validates the techniques used to evaluate efficiencies and data-simulation differences on these newest datasets, ahead of analyses in the rare B+ -> K+ l+ l- decay modes. The impact of removing the hardware trigger is discussed throughout the thesis; the realisation of the anticipated improvements in trigger efficiencies is demonstrated explicitly.