Measurement of $D^{0}-\bar{D}^0$ mixing parameters and search for CP violation using $D^{0} \to K^{+}\pi^{-}$ decays

Measurements of charm mixing parameters from the decay-time-dependent ratio of $D^0 \to K^+ \pi^-$ to $D^0 \to K^- \pi^+$ rates and the charge-conjugate ratio are reported. The analysis uses data, corresponding to 3 fb$^{-1}$ of integrated luminosity, from proton-proton collisions at 7 and 8 TeV center-of-mass energies recorded by the LHCb experiment. In the limit of charge-parity (CP) symmetry, the mixing parameters are determined to be $x'^2=(5.5 \pm 4.9) \times 10^{-5}$, $y'= (4.8 \pm 1.0) \times 10^{-3}$, and $R_D=(3.568 \pm 0.066) \times 10^{-3}$. Allowing for CP violation, the mixing parameters are determined separately for $D^0$ and $\bar{D}^0$ mesons yielding $A_D = (-0.7 \pm 1.9) $ %, for the direct CP-violating asymmetry, and $0.75 < |q/p|< 1.24$ at the $68.3$ % confidence level, where $q$ and $p$ are parameters that describe the mass eigenstates of the neutral charm mesons in terms of the flavor eigenstates. This is the most precise determination of these parameters from a single experiment and shows no evidence for CP violation.