Searches for $CP$ violation in multi-body charm decays and studies of radiation damage in the LHCb VELO detector

This thesis presents two searches for direct charge-parity ($CP$) violation in multi-body decays in the charm-sector at LHCb, the development of techniques for performing model-independent searches for direct $CP$ violation in multi-body decays, and the development of studies of radiation damage effects in the LHCb vertex detector. LHCb is a dedicated experiment to study New Physics in the decays of heavy hadrons at the Large Hadron Collider (LHC) at CERN. The detector includes a high precision vertex detector surrounding the $pp$ interaction region made with silicon strip sensors. Studies of the effects of radiation damage in LHC run-2 for the operation of this detector are presented and the determination of the operational bias voltages of the silicon strip sensors is discussed. An unbinned model independent technique for $CP$ violation searches in multi-body decays called the energy test is used for the first time. The selection and treatment of the coordinates used to describe the phase-space of the decay are discussed. The conventional model-independent techniques, which test for parity-even $CP$ violation, are modified to create a new approach for testing for parity-odd $CP$ violation. The first applications of the energy test in $CP$ violation searches are made with $D^0 \rightarrow \pi^-\pi^+\pi^0$ and $D^0 \rightarrow \pi^-\pi^+\pi^-\pi^+$ decays, using data collected by LHCb. The world's best sensitivity to $CP$ violation in both decays is obtained. The first search uses the $D^0 \rightarrow \pi^-\pi^+\pi^0$ decay data collected in 2012 at a proton-proton centre-of-mass energy of $\sqrt{s} =$ 8 TeV corresponding to an integrated luminosity of 2.0 fb$^{-1}$. The data are found to be consistent with the hypothesis of $CP$ symmetry with a $p$-value of $(2.6\pm 0.5)\%$. This is the first $CP$ violation search at LHCb using the $\pi^0$. The second search uses $D^0 \rightarrow \pi^-\pi^+\pi^-\pi^+$ decay data from proton-proton collisions collected in 2011 and 2012 at centre-of-mass energies of $\sqrt{s} =$ 7 TeV and 8 TeV, corresponding to an integrated luminosity of 3.0 fb$^{-1}$. The $D^0 \rightarrow \pi^-\pi^+\pi^-\pi^+$ study also presents the first application of the new parity-odd $CP$ violation test. The data are found to be consistent with the hypothesis of $CP$ symmetry with a $p$-value of $(4.6 \pm 0.5)\%$ in the parity-even case, and marginally consistent with a $p$-value of $(0.6 \pm 0.2)\%$ in the parity-odd case, corresponding to a significance for $CP$ non-conservation of 2.7 standard deviations.