Angular Analysis of the decay $B^0 \to \phi K^*(892)^0$

The LHCb experiment is a single-arm forward spectrometer situated at the Large Hadron Collider, CERN. LHCb is optimised for the precision study of beauty and charm flavoured hadrons and in 2011 collected 1 fb$^{-1}$ of proton-proton collision data at a centre-of-mass energy of 7 TeV. The aim of LHCb is to search for rare decays and make precise measurements of Charge-Parity $(\textit{CP})$ violation in the beauty and charm sectors. In the Standard Model the decay $B^0 \to \phi K^*(892)^0$ is described by a loop mediated process, providing a sensitive test for new physics. In this decay, signs of $\textit{CP}$ violation could indicate the presence of physics beyond the Standard Model. This thesis presents a study of the flavour eigenstate $B^0 \to \phi(\to K^+K^-) K^*(892)^0(\to K^+\pi^-)$ and its charge conjugate $\overline{B}^0$-decay. The decay products form an admixture of $\textit{CP}$-even and $\textit{CP}$-odd eigenstates, which can have longitudinal or transverse polarisation. An angular analysis is performed to disentangle these different contributions and the polarisation amplitudes and strong phases are measured. No difference is observed between $B^0$ and $\overline{B}{^0}$ amplitudes, supporting the hypothesis that $\textit{CP}$ is conserved in this decay. In addition, the Triple Product Asymmetries (TPAs) are determined from the products of the polarisation amplitudes and strong phases. $\textit{True}$ TPAs are zero in the event that $\textit{CP}$ symmetry is conserved, while $\textit{fake}$ TPAs can arise due to final-state interactions. Although the measured true TPAs are consistent with zero, several significant fake TPAs are observed.