Mixing of neutral charmed mesons and tests forCPviolation in their decays

Abstract

The reactions $e^{+}{e}^{-}\to D^0{\overline{D}}^0+m\left({\pi }^0\right)+n\left(\gamma \right)$, followed by decays of the charmed mesons to eigenstates of $\mathrm{CP}$, satisfy selection rules which allow tests of $\mathrm{CP}$ invariance. When the $e^{+}{e}^{-}$ reactions proceed through one virtual photon and $n$ is even (odd), the decay products of the two neutral charmed mesons will have opposite (equal) $\mathrm{CP}$ to the approximation in which $\mathrm{CP}$ is conserved. Final states with even $\mathrm{CP}$ include $\pi \pi$ and, approximately, $K_L^0{\pi }^0$; the final state $K_S^0{\pi }^0$ is nearly $\mathrm{CP}$-odd. It is shown that when both neutral charmed mesons decay to identical final states, the signal for $\mathrm{CP}$ violation always contains a factor related to the amount of $D^0-{\overline{D}}^0$ mixing, and hence is small if this mixing is small (as in the standard charm model). When two different final states are observed, the signal for $\mathrm{CP}$ violation contains such a factor only in certain models, of which the superweak model is an example.