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

TL;DR

This paper investigates the CPT-symmetry properties of the effective Hamiltonian for neutral kaons, revealing that certain expected symmetries only hold if the total system breaks CPT, using advanced approximations beyond standard models.

Contribution

It demonstrates that the effective Hamiltonian's CPT properties differ from traditional results, especially under more accurate approximations, and provides estimations within a generalized model.

Findings

H(eff) commutes with CPT only if H does not commute with it.

Re(<K0|H(eff)|K0>) equals Re(<K0-bar|H(eff)|K0-bar>) only if CPT is broken.

Estimated difference in matrix elements for CPT-invariant models.

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.