Measurements of charm mixing and $C!P$ violation using $D^0 to K^pm pi^mp$ decays

Measurements of charm mixing and $C!P$ violation parameters from the decay-time-dependent ratio of $ D^0 to K^+ pi^- $ to $ D^0 to K^- pi^+ $ decay rates and the charge-conjugate ratio are reported. The analysis uses $overline{B}to D^{*+} mu^- X$, and charge-conjugate decays, where $D^{*+}to D^0 pi^+$, and $D^0to K^{mp} pi^{pm}$. The $pp$ collision data are recorded by the LHCb experiment at center-of-mass energies $sqrt{s}$ = 7 and 8 TeV, corresponding to an integrated luminosity of 3 fb$^{-1}$. The data are analyzed under three hypotheses: (i) mixing assuming $C!P$ symmetry, (ii) mixing assuming no direct $C!P$ violation in the Cabibbo-favored or doubly Cabibbo-suppressed decay amplitudes, and (iii) mixing allowing either direct $C!P$ violation and/or $C!P$ violation in the superpositions of flavor eigenstates defining the mass eigenstates. The data are also combined with those from a previous LHCb study of $D^0to K pi$ decays from a disjoint set of $ D^{*+} $ candidates produced directly in $pp$ collisions. In all cases, the data are consistent with the hypothesis of $C!P$ symmetry.