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Chaos An Interdisciplinary Journal of Nonlinear Science

Wave-function model for the CP violation in mesons

Seyed Majid Saberi Fathi, M. Courbage, Thomas Durt

Published Sep 8, 2017• 4 citations
Publisher

Abstract

In this paper, we propose a simple quantum model of the kaons decay providing an estimate of the CP symmetry violation parameter. We use the two-level Friedrich's Hamiltonian model to obtain a good quantitative agreement with the experimental estimate of the violation parameter for neutral kaons. A temporal wave-function approach, based on an analogy with spatial wave-functions, plays a crucial role in our model.

DOI
10.1063/1.5001188

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arXiv:1512.08437•Dec 28, 2015•3 citations
In this paper, we propose a simple quantum model of the kaons decay providing an estimate of the CP symmetry violation parameter. We use the two-level Friedrich's Hamiltonian model to obtain a good quantitative agreement with the experimental estimate of the violation parameter for neutral kaons. A temporal wave-function approach, based on an analogy with spatial wave-functions, plays a crucial role in our model.
In this paper we propose to associate a temporal two-component wave-function to the decay process of meson particles. This simple quantum model provides a good estimation of the CP symmetry violation parameter. This result is based on our previous paper ("Two-Level Friedrichs model and Kaonic phenomenology", Physics Letters A 362, 100-104 (2007)) where we have shown that the two-level Friedrichs Hamiltonian model makes it possible to provide a qualitatively correct phenomenological model of kaons physics. In this previous paper, we derived a violation parameter that is 14 times larger than the measured quantity. In the present paper we improve our estimation of the violation and obtain the right order of magnitude. The improvement results from a renormalized superposition of the probability amplitudes describing short and long exponential decays. The renormalization occurs because the amplitudes that we are dealing with are associated to the decay rate, and not to the integrated decay rate or survival probability as is usually the case in standard approaches to CP-violation. We also compare with recent experimental data for the mesons D and B and also there the agreement between our model and experimental data is quite satisfying.
It is easy to construct classical 2-state systems illustrating the behavior of the short-lived and long-lived neutral KKK mesons in the limit of CP conservation. The emulation of CP violation is more tricky, but is provided by the two-dimensional motion of a Foucault pendulum. Analogies are drawn between the pendulum and observables in neutral kaon decays. An emulation of CP- and CPT-violation using electric circuits is also discussed.
The founding fathers of the quantum theory already struggled with the different roles of space and time in quantum theory. Position is by default represented by an operator, whereas time is usually treated as a parameter. Time operator models exist, in particular a certain Time Operator model denoted the Temporal Wave Function (T.W.F.). This one extends the Born's rule to the time domain. The statistics of pure exponential decay does not allow to exclude this Born rule for time. However the tiny violation of the combined discrete symmetries PPP (parity) and CCC (charge conjugation) observed in the K-meson system allows us, as we prove in this paper, to discriminate between the standard predictions, made in the framework of the so-called mass-decay matrix formalism, and the T.W.F. predictions. We also present experimental data of a particular CPCPCP violating decay channel, that is in contrast with the prediction of T.W.F. approach model, resulting in its falsification.