A "Known" CP Asymmetry in $τ$ Decays

Abstract

We point out that dynamics known from the observed CP violation in $K_L\to π^{\mp}l^{\pm}ν$ generate a CP asymmetry of $3.3\cdot 10^{-3}$ in $τ^{\pm} \to νK_Lπ^{\pm}$. CPT invariance requires the same asymmetry in the more approachable transitions $τ^{\pm} \to νK_Sπ^{\pm}$. While little new can be learnt from this fact, it has to be accounted for, since CP asymmetries in $τ\to νKπ$ 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 $ΔQ = ΔS$ selection rule).