Direct T-violation measurements and T-odd effects in decay experiments

Motivated by the recent experimental announcements for direct measurements of time-reversal non-invariance in the neutral kaon system, we make a comparative discussion of the CPLEAR and KTeV measurements. The most suitable way to consistently incorporate the mixing, the time evolution and the decays of kaons, is to describe the neutral kaon system as a system with a non-Hermitean Hamiltonian. In this framework, the physical (decaying) incoming and outgoing states are distinct and belong to dual spaces. Moreover, since they are eigenstates of the full Hamiltonian, they never oscillate. This is directly manifest in the orthogonality conditions of the physical states, which entirely determine the evolution of the kaon system. Along these lines we conclude: CPLEAR studies K0-bar{K0} oscillations, a process where initial and final states can be reversed, the CPLEAR asymmetry being an effect directly related to the definition of time-reversal. Conclusively, CPLEAR provides a direct measurement of T-violation without any assumption either on unitarity or on CPT-invariance. The KTeV experiment studies in particular the process KL -> pi+ pi- e+ e- where they measure a T-odd effect. However, using unitarity together with estimates of the final state interactions, it should be possible to determine whether this effect can be identified with a genuine T-reversal violation.