Experimental Constraints to Rephasing-Invariant CP, T and CPT Violating Parameters in the Neutral Kaon System

Abstract

A phenomenological and comprehensive study is given of the (possible) violation of CP, T and CPT symmetries in the KO -go system. Relevant decay amplitudes as well as mixing parameters are parametrized in a rephasing·invariant way, and formulae relevant to phenomenological analyses are derived. An attempt is made to derive constraints on these CP, T and/or CPT violating parameters from available experimental data. It is found, among other things, that the parameters which signal both CP and CPT violations are subject to large errors and at best only one or two orders smaller than those which signal both CP and T violations, the latter being known to be of order 10-3 • Furthermore, it is pointed out that those parameters which signal both T and CPT violations but not CP violation are not yet well constrained experimentally. §

CP, T AND CPT VIOLATIONS IN THE $K^0-\overline{K^0}$ SYSTEM: PRESENT STATUS

“…where 5) δ I being the S-wave ππ scattering phase shift for the isospin I state at an energy of the rest mass of K 0 . ω is a measure of deviation from the ∆I = 1/2 rule, and may be inferred, e.g., from…”

“…(4.14), but also with respect to rephasing of the final states, 5) in spite that the phase parameters α n , β n , ψ n and ψ n themselves are in general not invariant individually with respect to this rephasing. In fact, defining…”

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

“…where 5) δ I being the S-wave ππ scattering phase shift for the isospin I state at an energy of the rest mass of K 0 . ω is a measure of deviation from the ∆I = 1/2 rule, and may be inferred, for example, from…”

“…In this connection, we like to recall, on the one hand, that CP symmetry is violated only at such a tiny level as 10 −3 [1,2], while CP T symmetry is tested at best up to the level one order smaller [3][4][5][6][7] and, on the other hand, that some of the premises of the CP T theorem, e.g., locality, are being challenged by, say, the superstring model.…”

“…In a series of papers [4][5][6][7], we have demonstrated how one may identify or constrain possible violation of CP , T and CP T symmetries in the K 0 -K 0 system in a way as phenomenological and comprehensive as possible. For this purpose, we have first introduced parameters which represent violation of these symmetries in mixing parameters and decay amplitudes in a well-defined way and related them to the experimentally measured quantities.…”