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 ${\eta }_{+-}$ can be reproduced with \ot~{\em invariant} dynamics through finetuning \cpt~breaking. The large \ot~odd correlation observed by the KTeV collaboration in $K_L\to {\pi }^{+}{\pi }^{-}{e}^{+}{e}^{-}$ thus does not yield direct evidence for \ot~violation. In such a world the phase of $\frac{{ϵ}^{\prime }}{ϵ}$ is ${\delta }_2-{\delta }_0-{\varphi }_{SW}\sim -(85.5\pm 4{)}^{\circ }$. Also, $K^{\pm }\to {\pi }^{\pm }{\pi }^0$ could exhibit a \cpt~asymmetry of up to few$\times 10^{-3}$ without upsetting any known bound.

Comments: Considerable revision of the original paper with a change in title; the text has been augmented significantly to explain more explicitely the assumptions made (or not made) and to correct inaccuracies. 15 pages, LATEX file