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arXiv:1611.04854 · Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences

The quantum CP-violating kaon system reproduced in the electronic laboratory

M. Caruso, Huner Fanchiotti A, Carlos A. García Canal, Miguel Angel Mayosky, A. Veiga

Published Nov 1, 2016• 9 citations

Abstract

The equivalence between the Schrödinger dynamics of a quantum system with a finite number of basis states and a classical dynamics is realized in terms of electric networks. The isomorphism that connects in a univocal way both dynamical systems was applied to the case of neutral mesons, kaons in particular, and the class of electric networks univocally related to the quantum system was analysed. Moreover, under CPT invariance, the relevant ϵ parameter that measures CP violation in the kaon system is reinterpreted in terms of network parameters. All these results were explicitly shown by means of both a numerical simulation of the implied networks and by constructing the corresponding circuits.

DOI: 10.1098/rspa.2016.0615

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The equivalence between the Schrödinger dynamics of a quantum system with a finite number of basis states and a classical dynamics is realized in terms of electric networks. The isomorphism that connects in a univocal way both dynamical systems was applied to the case of neutral mesons, kaons in particular, and the class of electric networks univocally related to the quantum system was analysed. Moreover, under CPT invariance, the relevant ϵ parameter that measures CP violation in the kaon system is reinterpreted in terms of network parameters. All these results were explicitly shown by means of both a numerical simulation of the implied networks and by constructing the corresponding circuits.

It is easy to construct classical 2-state systems illustrating the behavior of the short-lived and long-lived neutral

K

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.

We studied the CP violating phases in the neutral kaon oscillations and decays in the effective field theory of kaons, without going into the quark level, and connected the CP violating parameters to the Bargmann invariants and hence to the geometric phases. We extended this approach to demonstrate how the CP violating parameters appearing in the process of baryogenesis are related to the Bargmann invariants, and hence with the geometric phases of those systems. We then concluded on the applications of such a generalized treatment of CP violating phases.

I report a recent study made in collaboration with M.E. Peskin, on the time dependence of a kaon beam propagating according to a generalization of quantum mechanics due to Ellis, Hagelin, Nanopoulos and Srednicki, in which CP- and CPT-violating signatures arise from the evolution of pure states to mixed states. Constraints on the magnitude of its parameters are established on the basis of existing experimental data. New facilities such as {phi} factories are shown to be particularly adequate to study this generalization from quantum mechanics and to disentangle its parameters from other CPT violating perturbations of the kaon system.

The neutral kaon system offers a unique possibility to perform fundamental tests of CPT invariance, as well as of the basic principles of quantum mechanics. The most recent limits on several kinds of possible CPT violation and decoherence mechanisms, which in some cases might be justified in a quantum gravity framework, are reviewed, including the latest results obtained by the KLOE experiment at the DAΦNE e + e - collider. No deviation from the expectations of quantum mechanics and CPT symmetry is observed, while the precision of the measurements, in some cases, reaches the interesting Planck scale region.