Magnetic Distortion Calibration for the LHCb Ring Imaging Cherenkov (RICH) Detector, and the Search for $\mathcal{CP}$ Violation in $\rm{D^{*+}\to D^0(K^-K^+)\pi^+}$ Decays

The asymmetry under simultaneous charge and parity transformation ($\mathcal{CP}$ violation) has driven the understanding of electroweak interactions since its discovery in the kaon system. $\mathcal{CP}$ violation was subsequently discovered in the $B$ system. Charmed mesons form the only heavy neutral meson system in which $\mathcal{CP}$ violation has yet to be observed unambiguously. A study of indirect $\mathcal{CP}$ violation in $D$ mesons through the determination of the parameter $A_{\Gamma}$ is presented using a data sample of $pp$ collisions, corresponding to an integrated luminosity of $37.7~\rm{pb}^{-1}$, collected with the LHCb detector and recorded at the centre-of-mass energy of 7 TeV at the LHC. The parameter $A_{\Gamma}$ is the asymmetry of the effective lifetimes measured in decays of $D^0$ and $\bar{D}^0$ mesons to the $\mathcal{CP}$ eigenstates $K^+K^-$. $A_{\Gamma}$ is sensitive to both the $\mathcal{CP}$ violation parameters $|q/p|$ and $\phi$. Fits to the data sample yield $A_{\Gamma}(KK) = (0.39 \pm 0.55 \pm 0.24) \%$, where the first uncertainty is statistical and the second systematic. This result is consistent with no $\mathcal{CP}$ violation. Critical for this analysis is the particle identification provided by the LHCb Ring Imaging Cherenkov (RICH) system. To ensure good performance, a proper calibration of the RICH photon detectors response is necessary. A system for the calibration of the magnetic distortion induced by the LHCb dipole magnet on the photon detectors is described. The system currently provides the calibration parameters used in the LHCb event reconstruction software and allows for a significant improvement in the overall particle identification performance.