On the Khalfin's improvement of the LOY effective Hamiltonian for neutral meson complex

The general properties of the effective Hamiltonian for neutral meson system improved by L.A. Khalfin in 1980 are studied. It is shown that contrary to the standard result of the Lee--Oehme--Yang (LOY) theory, the diagonal matrix elements of this effective Hamiltonian can not be equal in a CPT invariant system. It is also shown that the scalar product of short, $|K_{S}>$, and long, $|K_{L}>$, living superpositions of neutral kaons can not be real when CPT symmetry is conserved in the system under considerations whereas within the LOY theory such a scalar product is real.