D^0 \to K^{\pm}π^{\mp} and CP Violation at a τ-charm Factory

We calculate the time-dependent and time-integrated decay rates of $(D^0\bar{D}^0)\rightarrow (K^{\pm}\pi^{\mp})(l^{\pm}X^{\mp})$ at the $\psi(3.77)$ and $\psi(4.14)$ resonances. The possibilities to distinguish between the effects of $D^0-\bar{D}^0$ mixing and doubly Cabibbo suppressed decay (DCSD) are illustrated, and the signal of $CP$ violation induced by the interplay of mixing and DCSD is discussed. Ratios of the decay rates of $(D^0\bar{D}^0)\rightarrow (K^{\pm}\pi^{\mp})(K^{\pm}\pi^{\mp})$ to that of $(D^0\bar{D}^0)\rightarrow (K^+\pi^-)(K^-\pi^+)$ are also recalculated by accommodating $CP$ violation and final-state interactions.