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Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

Neutral kaon system reinvestigated

Qing Wang, A. I. Sanda

Published Mar 1, 1997• 11 citations

Abstract

There has been a revival of interest in testing quantum-mechanical postulates, and also $\mathrm{CPT}$ symmetry in the neutral $K$ meson system. These effects are bound to be very small. If some deviation from our expectation is found, it can be either from new physics, or from use of an invalid formalism. The neutral $K$-$\mathrm{K\ifmmode\bar\else\textasciimacron\fi{}}$ system is described by $2\ifmmode\times\else\texttimes\fi{}2$ time-independent non-Hermitian effective Hamiltonian. The effective Hamiltonian is derived within the framework of perturbation theory up to the second order in the weak Hamiltonian. In addition, the Wigner-Weisskopf approximation is used. It is known that the correction to this approximation deviates from the exponential decay law. If the correction is large, it will have grave consequences. In this paper, we reexamine these questions. We conclude that all proposed searches for new physics in the $K$ meson decays can proceed without worrying about these corrections to the formalism.

DOI: 10.1103/physrevd.55.3131

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There has been a revival of interest in testing quantum-mechanical postulates, and also

\mathrm{CPT}

symmetry in the neutral

K

meson system. These effects are bound to be very small. If some deviation from our expectation is found, it can be either from new physics, or from use of an invalid formalism. The neutral

K

-

\mathrm{K\ifmmode\bar\else\textasciimacron\fi{}}

system is described by

2\ifmmode\times\else\texttimes\fi{}2

time-independent non-Hermitian effective Hamiltonian. The effective Hamiltonian is derived within the framework of perturbation theory up to the second order in the weak Hamiltonian. In addition, the Wigner-Weisskopf approximation is used. It is known that the correction to this approximation deviates from the exponential decay law. If the correction is large, it will have grave consequences. In this paper, we reexamine these questions. We conclude that all proposed searches for new physics in the

K

meson decays can proceed without worrying about these corrections to the formalism.

The neutral Kaon system has both CP violation in the mass matrix and a non-vanishing lifetime difference in the width matrix. This leads to an effective Hamiltonian which is not a normal operator, with incompatible (non-commuting) masses and widths. In the Weisskopf-Wigner Approach (WWA), by diagonalizing the entire Hamiltonian, the unphysical non-orthogonal "stationary" states

K_{L,S}

are obtained. These states have complex eigenvalues whose real (imaginary) part does not coincide with the eigenvalues of the mass (width) matrix. In this work we describe the system as an open Lindblad-type quantum mechanical system due to Kaon decays. This approach, in terms of density matrices for initial and final states, provides a consistent probabilistic description, avoiding the standard problems because the width matrix becomes a composite operator not included in the Hamiltonian. We consider the dominant-decay channel to two pions, so that one of the Kaon states with definite lifetime becomes stable. This new approach provides results for the time dependent decay rates in agreement with those of the WWA.

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.

Neutral kaons provide one of the most sensitive systems to test quantum mechanics and CPT violation.In the first part of this report I review the results on CPT violation searches in the kaon system from the CPLEAR, KLOE and KTeV experiments.In the second part, I report tests of quantum coherence related to CPT violation, performed at CPLEAR and KLOE by studying the time evolution of the kaon system.The results show no deviations from the expectations of quantum mechanics and CPT symmetry, and the accuracy reaches the interesting region of the Planck's scale.

The Einstein-Podolsky-Rosen (EPR) entanglement of a neutral K-meson (kaon) pair enjoys the peculiar quantum behaviour of mixing, charge-parity

{\cal CP}

violation (

{\cal C}

- charge conjugation,

{\cal P}

- parity) and two non-orthogonal eigenstates of definite time evolution

K_L

and

K_S

with very different lifetimes. The dynamics of this strange entanglement, experimentally accessible at the

\phi

-factory, makes possible the search for novel phenomena not accessible in any other system, i.e. at interference times and at decoherence times of the single partners after their disentanglement, in order to unveil the nature of the correlation between the two neutral kaons. Until now, the studies have been concentrated on the single kaon intensity distribution between the two decay times

t_1

and

t_2

with

\Delta t = t_2 - t_1 > 0

. Here we show that the entire two single time distributions, before each decay, are physical in both senses: past to future, leading to the state of the living partner at time

t_2

from the observation of the first decay channel at

t_1

, and future to past, leading to the past state of the decayed kaon at time

t_1

from the observation of the second decay channel at

t_2

. Our results thus demonstrate an affirmative answer to the title: it does, the past decayed state depends on the result of the future measurement for the living partner. This novel effect is truly observable through the first decay time distributions. Besides the implications for quantum physics for all

\Delta t

, at large decoherence times the resulting first decayed state is always

K_S

, providing a genuine tag of this kaon state in the decoherence region, and a unique and important experimental tool to prepare a pure

K_S

beam.