Searches for $CP$ violation in $D^{+} \to K^{-}K^{+}\pi^{+}$ decay at the LHCb Experiment

This thesis documents searches for direct $CP$ violation in the Cabibbo-suppressed $D^{+} \to K^{-}K^{+}\pi^{+}$ decay at the LHCb experiment. Two complementary analyses are described. Direct $CP$-violating asymmetries are predicted to exist in singly Cabibbo-suppressed charm decays with magnitudes of up to $\mathcal{O}(10^{-3})$ in the Standard Model, and can be enhanced to the percent level by contributions from new physics. No such asymmetry has yet been observed. The LHCb detector is a forward spectrometer with a precise vertex detector and powerful particle identification capabilities, designed to collect large, pure samples of charm and $B$ decays. Data collected at LHCb in 2010 corresponding to an integrated luminosity of 35 pb$^{-1}$ are used to perform a model-independent search for direct $CP$ violation in the $D^{+} \to K^{-}K^{+}\pi^{+}$ decay. The Dalitz plot is divided into bins and a $\chi^{2}$ test of the compatibility of the dataset with no $CP$ violation is performed. No evidence of $CP$ violation is found. A second search for $CP$ violation in the region of the $D^{+} \to K^{-}K^{+}\pi^{+}$ Dalitz plot around the $\phi$ resonance is described. The charge asymmetry in this decay is calculated and compared to that in the control channel $D^{+} \to K^{-}K^{+}\pi^{+}$. The 1.0 fb$^{-1}$ of data collected at LHCb in 2011 are used. The $CP$-violating asymmetry is found to be $(-0.04\pm0.14\pm0.14)\%$ where the uncertainties are statistical and systematic, respectively. A new observable sensitive to $CP$ violation that varies across the $\phi$ resonance is defined and measured, and is consistent with no $CP$ violation at the current level of sensitivity. In addition, the $CP$-violating asymmetry in the decay $D_s^{+} \to K_S^0\pi^{+}$ is determined to be $(0.61\pm0.83\pm0.14)\%$. There is no evidence for $CP$ violation in either channel. The prospects for new results using data collected in 2012 are very promising and a significant improvement in our understanding of these decays is anticipated.