$CP$, $T$ and/or $CPT$ violations in the $K^0$–$\overline{K^0}$ system - Implications of the KTeV, NA48 and CPLEAR results

Y. Kouchi; Y. Takeuchi; S.Y. Tsai

doi:doi:10.1007/s100520000435

EPJ

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2019 Impact factor 4.389

Particles and Fields

Eur. Phys. J. C 17, 269-277
DOI 10.1007/s100520000435

CP, T and/or CPT violations in the K⁰- $\overline{K^0}$ system

Implications of the KTeV, NA48 and CPLEAR results

Y. Kouchi - Y. Takeuchi - S.Y. Tsai

Atomic Energy Research Institute and Department of Physics, College of Science and Technology, Nihon University,
Kanda-Surugadai, Chiyoda-ku, Tokyo 101-8308, Japan

Received: 14 February 2000 / Revised version: 24 April 2000 /
Published online: 8 September 2000 - © Springer-Verlag 2000

Abstract
The possible violation of the CP, T and/or CPT symmetries in the K⁰- $\overline{K^0}$ 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 or T symmetry is assumed, is also carried out. It is demonstrated that the CP and T symmetries are violated definitively at the level of 10^-4 in $2\pi$ decays and presumably at the level of 10^-3 in the K⁰- $\overline{K^0}$ mixing, and that the Bell-Steinberger relation helps us to establish that CP and T violations are definitively present in K⁰- $\overline{K^0}$ mixing and to test CPT symmetry to a level of $10^{-4} \sim 10^{-5}$ .