A direct test of T symmetry in the neutral K meson system with Ks->pi l nu and Kl->3pi0 at KLOE-2

Quantum entanglement of K and B mesons allows for a direct experimental test of time-reversal symmetry independent of CP violation. The T symmetry can be probed by exchange of initial and final states in the reversible transitions between flavour and CP-definite states of the mesons which are only connected by the T conjugation. While such a test was successfully performed by the BaBar experiment with neutral B mesons, the KLOE-2 detector can probe T-violation in the neutral kaon system by investigating the process with Ks->pi l nu and Kl->3pi0 decays. Analysis of the latter is facilitated by a novel reconstruction method for the vertex of Kl->3pi0 decay which only involves neutral particles. Details of this new vertex reconstruction technique are presented as well as prospects for conducting the direct T symmetry test at the KLOE-2 experiment.