Measurement of $CP$ asymmetry in radiative charm decays at LHCb

This thesis presents a measurement of $CP$ asymmetry, $A_{CP}$, for radiative decays of charm mesons $D^0 \to V \gamma$, and their charge conjugates, where $V$ denotes vector meson $\bar{K}^{*0}$, $\phi$ or $\rho^0$. The study is based on the proton-proton collision data collected at a centre-of-mass energy of $\sqrt{s} = 8$~TeV by the LHCb experiment in 2012, during Run-1 of the LHC. This data sample corresponds to an integrated luminosity of 2 fb$^{-1}$. Reconstructed neutral $D$ mesons originate from strong decays of the $D^{*\pm}$ states, $D^{*+}\to D^0 \pi^+_s$ and $D^{*-}\to \bar{D}^0 \pi^-_s$, with the soft-pion $\pi_s$ charge used for tagging of a $D$ flavour at the production. The presented analysis is the first study of radiative charm decays at LHCb. \\ Large and irreducible background from decays involving $\pi^0$ mesons, $D^0\to V \pi^0$, is suppressed using a multivariate classifier based on distinguished shapes of energy clusters produced by photons and $\pi^0$ mesons in the LHCb calorimeter system. The signal decays are separated from residual background with the three-dimensional fit to $D^0$ invariant mass $M(D^0)$, the difference between invariant masses of $D^{*+}$ and $D^0$, $\Delta M = M(D^{*+})-M(D^0)$, and $V$-meson helicity angle $\cos{\theta}$, as observables. Correlations observed between $M(D^0)$ and $\Delta M$ observables for both signal and background channels, are modelled based on the corresponding simulation samples. The total $D^0$ and $\bar{D}^0$ signal yields are measured to be: $4263 \pm 193$ events for $D^0\to \bar{K}^{*0}\gamma$ decay, and $216 \pm 29$ events for the $D^0\to \phi\gamma$ decay; no significant signal is observed for the $D^0\to \rho\gamma$ decay. \\ Nuisance asymmetries due to asymmetric charm production and asymmetric detection of positively and negatively charged hadrons, are constrained with high-statistics and high-purity reference channels. The pion-tagged $D^0 \to K^+K^-$ and $D^0 \to \pi^+\pi^-$ decays are chosen as reference channels for $D^0 \to \phi \gamma$ and $D^0 \to \rho^0 \gamma$ signal decays, respectively, whereas $D^0 \to K^- \pi^+ \pi^0$ is used as a reference channel for $D^0 \to \bar{K}^{*0} \gamma$. The nuisance asymmetries are measured to be about $(-1.0 \pm 0.2)\%$ in $D^0 \to K^+K^-$ and $D^0 \to \pi^+\pi^-$ channels, and $(-1.7 \pm 0.3)\%$ in $D^0 \to K^- \pi^+ \pi^0$. They are subtracted from asymmetries measured for the signal channels in order to access $A_{CP}$. \\ The asymmetries for the signal channels are measured by performing the three-dimensional fits in $M(D^0)$ vs. $\Delta M$ vs. $\cos{\theta}$ space, simultaneously to the separated $D^0$ and $\bar{D}^0$ samples. The central values of the asymmetries are still blinded, while their statistical uncertainties are measured to be 5\% for $D^0 \to \bar{K}^{*0} \gamma$ and 12\% for $D^0 \to \phi \gamma$; the Run-1 analysis is not sensitive to the asymmetry in the $D^0 \to \rho^0 \gamma$ decay. The presented measurement is statistically limited. The total systematic uncertainties on the signal $A_{CP}$'s are expected to be below 1\%, and dominated by statistical uncertainties on the asymmetries measured in the reference channels. Unblinding is planned together with the Run-2 measurement, which is currently ongoing.