In current searches for D0 anti-D0 mixing, the time evolution of ``wrong-sign decays is used to distinguish between a potential mixing signal and the dominant background from doubly-Cabibbo-suppressed decays. A term proportional to $Delta Mt$ in the expression for the time evolution is often neglected in theoretical discussions and experimental analyses of these processes. We emphasize that, in general, this term does not vanish even in the case of CP invariance. Furthermore, CP invariance is likely to be violated if the rate of D0 anti-D0 mixing is close to the experimental bound. The consequence of either of these two facts is that the strongest existing measured bound is not applicable for constraining New Physics.
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