Study of the decay $B^0 \rightarrow D^0D^0K^+\pi^−$ with the LHCb experiment

The decay $B^0 \rightarrow D^0D^0K^+\pi^−$ is studied using data from proton-proton collisions collected by the LHCb experiment. The decay is observed for the first time, with $297 \pm 14$ signal candidates observed in data collected during 2011, 2012 and 2016. The branching fraction is measured relative to that of a control channel $B^0 \rightarrow D^{*-}D^0K^+$, which is topologically similar and has the same final state particles. The ratio of branching fractions is measured to be $$\mathcal{R}=(14.2\pm1.1\pm1.0)\%,$$ where the first uncertainty is statistical and the second is systematic. Using the most precise result published for the branching fraction of the control channel, the absolute branching fraction of $B^0 \rightarrow D^0D^0K^+\pi^−$ decays is thus determined to be $$\mathcal{B}(B^0 \rightarrow D^0D^0K^+\pi^−)=(3.50\pm0.27\pm0.26\pm0.30)×10^{−4},$$ where the third uncertainty is due to the branching fraction of the control channel. Studies towards a subsequent amplitude analysis of this decay, using additional data collected in 2017 and 2018, are also presented. The analysis of this decay mode will provide insights on hadronic uncertainties in golden modes at LHCb such as $B^0 \rightarrow K^{*0}\mu+\mu^−$, and provide opportunities for spectroscopy to observe new and known states. Furthermore, this thesis outlines the development of the TORCH time-of-flight detector and calibration studies performed on its front-end electronics. This novel detector will enhance the particle identification capabilities of future upgrades of the LHCb experiment.