CPT transformation properties of the exact effective Hamiltonian for neutral kaon and similar complexes

Abstract

CPT-symmetry properties of the exact effective Hamiltonian H(eff) governing the time evolution in the K(0), K(O)-bar (neutral K mesons) subspace implied by such properties of the total Hamiltonian of the system under consideration are examined. We show that H(eff) can commute with CPT - operator only if H does not commute with it. We also find that, in contradistinction to the standard result of the Lee-Oehme-Yang (LOY) theory, Re.<K(0)|H(eff)|K(0)> = Re.<K(0)-bar|H(eff)|K(0)-bar>, i.e., (<K(0)|H(eff)|K(0)> - <K(0)-bar|H(eff)|K(0)-bar>) = 0, only if the total system does not preserve CPT-symmetry. Using more accurate approximation than Weisskopf-Wigner approximation, an estimation of the difference (<K(0)|H(eff)|K(0)> - <K(0)-bar|H(eff)|K(0)-bar>) is found for CPT-invariant generalized Fridrichs-Lee model.