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Journal of Physics A Mathematical and Theoretical

Quantum-mechanical decay laws in the neutral kaons

M. Courbage, Thomas Durt, Seyed Majid Saberi Fathi

Published Feb 28, 2007• 13 citations
Publisher

Abstract

The Hamiltonian Friedrichs model describing the evolution of a two-level system coupled to a continuum is used in order to modelize the decay of the kaon states K1, K2. Using different cut-off functions of the continuous degrees of freedom, we show that this model leads to a CP violation that qualitatively fits with experimental data improving previous numerical estimates. We also discuss the relation of our model to other models of open systems.

DOI
10.1088/1751-8113/40/11/012

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The Hamiltonian Friedrichs model describing the evolution of a two-level system coupled to a continuum is used in order to modelize the decay of the kaon states K1, K2. Using different cut-off functions of the continuous degrees of freedom, we show that this model leads to a CP violation that qualitatively fits with experimental data improving previous numerical estimates. We also discuss the relation of our model to other models of open systems.
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.
The time evolution of the KK system as a two-qubit system is given. The effect which is interpreted as CP violation in neutral kaon decays is explained via violation of quantum correlations during time evolution of the KK system as two-kaons system and description is via Yang-Baxterization and unitary time dependent R-matrices to con- struct Hamiltonian, determining the time evolution of two-kaons sys- tem. The nonseparability ideas and criterion can be extended on all mixing state-antistate system and all CP violation cases in particle physics.
In this article we present a mathematical solution that extends and explores the solution found in chapter 11 of the book “Quantum Mechanics”, from “The Feynman Lectures on Physics”, about the neutral Kaon. The extension is built within the context of the CP symmetry for the two neutral Kaon decays considered in this chapter: (i) In two Pions, starting in the |K1⟩ state; (ii) In three Pions, from the |K2⟩ state. We found two mathematical expressions that allow to accommodate, separately, each one of the mean lifetime for these decays, unlike the solution given by Feynman that allows to accommodate only one of these mean lifetime. The extended solution is approximate because a small break in CPT symmetry is assumed in these decays; however, it has the advantage of avoiding the colloquially commented situation by Feynman of remaining “forever” from the neutral Kaon in the |K2⟩ state in the situation in which the only possible decay channel was in two Pions.