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

Abstract

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).

Comments: 5 pages, LATEX, no figures; dedicated to our late colleague and friend P. Kabir; Prodded by our colleagues J. Rosner and Y. Grossman we have clarified how the CPT constraint of equal lifetimes is implemented."