A fresh look at neutral meson mixing

In this work we show that the existence of a complete biorthonormal set of eigenvectors of the effective Hamiltonian governing the time evolution of neutral meson system is a necessary condition for diagonalizability of such a Hamiltonian. We also study the possibility of probing the $CPT$ invariance by observing the time dependence of cascade decays of type $P^{\circ }(\overline{P^{\circ }})\to \{M_a,M_b\}X\to fX$ by employing such basis and exactly determine the $CPT$ violation parameter by comparing the time dependence of the cascade decays of tagged $P^{\circ }$ and tagged $\overline{P^{\circ }}$.