Subtleties in the BaBar measurement of time-reversal violation

A first measurement of time-reversal (T) asymmetries that are not also CP asymmetries has been recently achieved by the BaBar collaboration. We analyze the measured asymmetries in the presence of direct CP violation, CPT violation, wrong strangeness decays and wrong sign semileptonic decays. We note that the commonly used S_{ψK} and C_{ψK} parameters are CP-odd, but have a T-odd CPT-even part and a T-even CPT-odd part. We introduce parameters that have well-defined transformation properties under CP, T and CPT. We identify contributions to the measured asymmetries that are T conserving. We explain why, in order that the measured asymmetries would be purely odd under time-reversal, there is no need to assume the absence of direct CP violation. Instead, one needs to assume (i) the absence of CPT violation in strangeness changing decays, and (ii) the absence of wrong sign decays.