How to testCP,T, andCPT invariance in the three photon decay of polarized3 S 1 positronium

We investigate whether and how the three photon decay of polarizedj=1 positronium (Ps), in particular³ S ₁ Ps, can be used for tests ofCP, T, andCPT invariance. A general analysis is made in terms of thePs decay matrix. We consider some angular correlations sensitive to possibleCP violation and calculate their expectation values assuming thatCP violation occurs in thePs mass matrix only. Furthermore we discuss some models ofCP violation in the lepton sector and their implications forCP violation inPs mixing and decay. Finally we calculate the contributions due to photon-photon final state interactions to some correlations which are naively, i.e. in the Coulomb approximation,T-andCPT-odd.