On Limitations of T Invariance in K Decays

Abstract

Data from the CPLEAR collaboration coupled with the assumption that the Bell-Steinberger relation holds have provided {\em direct} evidence for \ot~violation. In this note we investigate what we can say about \ot~violation {\em without} such an assumption. We show that both the modulus and the phase of $η_{+-}$ can be reproduced with \ot~{\em invariant} dynamics through finetuning \cpt~breaking. The large \ot~odd correlation observed by the KTeV collaboration in $K_L \to π^+π^- e^+ e^-$ thus does not yield direct evidence for \ot~violation. In such a world the phase of $\frac{ε'}ε$ is $δ_2-δ_0-ϕ_{SW}\sim -(85.5\pm 4)^\circ$. Also, $K^{\pm} \to π^{\pm} π^0$ could exhibit a \cpt~asymmetry of up to few$\times 10^{-3}$ without upsetting any known bound.