Neutral kaon system reinvestigated

There has been a revival of interest in testing quantum-mechanical postulates, and also $\mathrm{CPT}$ symmetry in the neutral $K$ meson system. These effects are bound to be very small. If some deviation from our expectation is found, it can be either from new physics, or from use of an invalid formalism. The neutral $K$-$\mathrm{K¯}$ system is described by $2\times 2$ time-independent non-Hermitian effective Hamiltonian. The effective Hamiltonian is derived within the framework of perturbation theory up to the second order in the weak Hamiltonian. In addition, the Wigner-Weisskopf approximation is used. It is known that the correction to this approximation deviates from the exponential decay law. If the correction is large, it will have grave consequences. In this paper, we reexamine these questions. We conclude that all proposed searches for new physics in the $K$ meson decays can proceed without worrying about these corrections to the formalism.