More on Parametrization Relevant to Describe Violation of CP, T and CPT Symmetries in the $K^0-\bar{K^0}$ System

TL;DR

This paper discusses how to parametrise CP, T, and CPT violation in the neutral kaon system, addressing phase ambiguities and presenting rephasing-invariant and dependent parametrizations.

Contribution

It introduces a fully rephasing-invariant parametrization for describing symmetry violations in the $K^0-ar{K^0}$ system, clarifying phase ambiguity issues.

Findings

Presented a rephasing-invariant parametrization.

Compared different parametrizations and their phase ambiguities.

Provided insights into symmetry violation descriptions.

Abstract

To study violation of CP, T and/or CPT symmetries in the $K^0-\bar{K^0}$ systems, one has to parametrize the relevant mixing parameters and decay amplitudes in such a way that each parameter represents violation of these symmetries in a well-defined way. Parametrization is of course not unique and is always subject to phase ambiguities. We discuss these problems with freedom associated with rephasing of final (or intermediate) as well as initial states taken into account. We present a fully rephasing-invariant parametrization and a particular rephasing-dependent parametrization, and give a couple of comments related to these and other possible parametrizations.