CP, T and/or CPT violations in the $K^0 - \overline K^0$ system

Abstract.

The possible violation of the CP, T and/or CPT symmetries in the $K^0 - \overline K^0$ system is studied from a phenomenological point of view. With this aim, we first introduce parameters which represent the violation of these symmetries in the mixing parameters and decay amplitudes in a convenient and well-defined way and, treating these parameters as small, derive formulas which relate them to the experimentally measured quantities. We then perform numerical analyses, with the aid of the Bell–Steinberger relation, to derive constraints on these symmetry-violating parameters, firstly paying particular attention to the results reported by the KTeV Collaboration and the NA48 Collaboration, and then with the results reported by the CPLEAR Collaboration as well taken into account. A case study, in which either CPT symmetry orT symmetry is assumed, is also carried out. It is demonstrated that the CP andT symmetries are violated definitively at the level of $10^{-4}$ in $2\pi$ decays and presumably at the level of $10^{-3}$ in the $K^0 - \overline K^0$ mixing, and that the Bell–Steinberger relation helps us to establish that CP andT violations are definitively present in $K^0 -\overline K^0$ mixing and to testCPT symmetry to a level of $10^{-4} \sim 10^{-5}$.