On limitations of T invariance in K decays

Data from the CPLEAR collaboration coupled with the assumption that the Bell-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 η+− can be reproduced with T invariant dynamics through finetuning CPT breaking. The large T odd correlation observed by the KTeV collaboration in KL→π+π−e+e− thus does not yield direct evidence for T violation. In such a world the phase of ϵ′/ϵ is δ2−δ0−φSW∼−(85.5±4)°. Also, K±→π±π0 could exhibit a CPT asymmetry of up to few×10−3 without upsetting any known bound.