A Phenomenological Study of Violation of CP and CPT Symmetries in the Neutral Kaon System

Abstract

913A phenomenological study is given of the (possible) violation of CP and CPT symmetries in the A"'-K" system. Special attention is paid to the problem of phase ambiguity and phase convention.Mixing parameters and decay amplitudes are parametrized in a rephasing invariant way, and the well-known parameters 7'/+-and 7' /oo describing 2Jr modes as well as various leptonic asymmetries are expressed in terms of these parameters. The parameters E and L1 characterizing mixing between ) in terms of the strangeness eigenstates I~> and IK 0 ) and the CP eigenstates IK, 0 ) and IK2°>, their transformation property under CP, T and CPT operations is examined and the problem of phase ambiguity is discussed. Formulae relevant for a phenomenological analysis of 2;r decay modes at

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

“…ℓ , and our mixing parameters ε and δ as well, are all invariant with respect to rephasing of |K 0 and |K 0 , 11) in spite that α K itself is not invariant with respect to this rephasing [4,18]. F I , ε I , F ℓ and ε ℓ are however not invariant with respect to rephasing of the final states [7,19],…”

“…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.…”

“…(3) A case study with either CP T or T symmetry assumed is also carried out. (4) The relevant decay amplitudes are parametrized in a convenient form, with freedom associated with rephasing of both the initial and final states, as discussed explicitly and thoroughly in [4,18,19], taken into account.…”

“…2 The K 0 -K 0 mixing and the Bell-Steinberger relation Let |K 0 and |K 0 be eigenstates of the strong interaction with strangeness S = +1 and −1, related to each other by (CP ), (CP T ) and T operations as [4,18,19,21] (…”