On limitations of T invariance in K decays

Data from the CPLEAR collaboration coupled with the assumption that the Bel l-Steinberger relation holds have provided direct evidence for T violation. In this note we investigate what we can say about T violation without such an assumption. We show that both the modulus and the phase of eta(+-) can be reproduced with T invariant dynamics through finetuning CPT breaking. Th e large T odd correlation observed by the KTeV collaboration in K-L --> pi( +) pi(-) e(+) e(-) thus does not yield direct evidence for T violation. In such a world the phase of epsilon'/epsilon is delta(2) - delta(0) - phi(SW) similar to -(85.5 +/- 4)degrees. Also, K+/- --> pi(+/-) pi(0) could exhibi t a CPT asymmetry of up to few X 10(-3) without upsetting any known bound. (C) 1999 Published by Elsevier Science B.V. All rights reserved.