A "Known" CP Asymmetry in $\tau$ Decays

We point out that dynamics known from the observed CP violation in $K_L\to \pi^{\mp}l^{\pm}\nu$ generate a CP asymmetry of $3.3\cdot 10^{-3}$ in $\tau^{\pm} \to \nu K_L\pi^{\pm}$. CPT invariance requires the same asymmetry in the more approachable transitions $\tau^{\pm} \to \nu K_S\pi^{\pm}$. While little new can be learnt from this fact, it has to be accounted for, since CP asymmetries in $\tau \to \nu K\pi$ channels are prime candidates for revealing the intervention of New Physics. This `known' CP asymmetry provides a very useful calibration point in such searches. It also provides a test of CPT symmetry (as well as the $\Delta Q = \Delta S$ selection rule).