CP,T and/or CPT Violations in the K0-K0bar System --Implications of the KTeV,NA48 and CPLEAR Results

Abstract

Possible violation of CP, T and/or CPT symmetries in the $\ko$-$\kob$ system is studied from a phenomenological point of view. For this purpose, we first introduce parameters which represent violation of these symmetries in 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 to these symmetry-violating parameters, firstly paying particular attention to the results reported by KTeV Collaboration and NA48 Collaboration, and then with the results reported by CPLEAR Collaboration as well taken into account. A case study, in which either CPT symmetry or T symmetry is assumed, is also carried out. It is demonstrated that CP and T symmetries are violated definitively at the level of 10^{-4} in $2π$ decays and presumably at the level of 10^{-3} in the $\ko-\kob$ mixing, and that the Bell-Steinberger relation helps us to establish CP and T violations being definitively present in the $\ko-\kob$ mixing and to test CPT symmetry to a level of 10^{-4} ~ 10^{-5}.