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Register a new userNeutral Kaons without Weisskopf-Wigner Approximation
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Authors
Ya. I. Azimov
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The model-independent formalism is constructed to describe decays of mixed particles without using the Weisskopf-Wigner approximation. Limitations due to various symmetries are traced for neutral $K-$mesons. As an application we show that effects of $CPT-$violation and going beyond WWA may be separated and studied independently.
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We establish the relation between the Wigner-Weisskopf theory for the description of an unstable system and the theory of coupling to an environment. According to the Wigner-Weisskopf general approach, even within the pole approximation (neglecting the background contribution) the evolution of a total system subspace is not an exact semigroup for the multi-channel decay, unless the projectors into eigesntates of the reduced evolution generator $W(z)$ are orthogonal. In this case these projectors must be evaluated at different pole locations $z_alpha eq z_beta$. Since the orthogonality relation does not generally hold at different values of $z$, for example, when there is symmetry breaking, the semigroup evolution is a poor approximation for the multi-channel decay, even for a very weak coupling. Nevertheless, there exists a possibility not only to ensure the orthogonality of the $W(z)$ projectors regardless the number of the poles, but also to simultaneously suppress the effect of the background contribution. This possibility arises when the theory is generalized to take into account interactions with an environment. In this case $W(z)$, and hence its eigenvectors as well, are {it independent} of $z$, which corresponds to a structure of the coupling to the continuum spectrum associated with the Markovian limit.
We briefly illustrate a few tests of quantum mechanics which can be performed with entangled neutral kaon pairs at a Phi-factory. This includes a quantitative formulation of Bohrs complementarity principle, the quantum eraser phenomenon and various forms of Bell inequalities.
In this paper we present a novel CPT symmetry test in the neutral kaon system based, for the first time, on the direct comparison of the probabilities of a transition and its CPT reverse. The required interchange of in $leftrightarrow$ out states for a given process is obtained exploiting the Einstein-Podolsky-Rosen correlations of neutral kaon pairs produced at a $phi$-factory. The observable quantities have been constructed by selecting the two semileptonic decays for flavour tag, the $pipi$ and $3pi^0$ decays for CP tag and the time orderings of the decay pairs. The interpretation in terms of the standard Weisskopf-Wigner approach to this system, directly connects CPT violation in these observables to the violating $Redelta$ parameter in the mass matrix of $K^0$-$bar{K^0}$, a genuine CPT violating effect independent of $Delta Gamma$ and not requiring the decay as an essential ingredient. Possible spurious effects induced by CP violation in the decay and/or a violation of the $Delta S= Delta Q$ rule have been shown to be well under control. The proposed test is thus fully robust, and might shed light on possible new CPT violating mechanisms, or further improve the precision of the present experimental limits. It could be implemented at the DA$Phi$NE facility in Frascati, where the KLOE-2 experiment might reach a statistical sensitivity of $mathcal{O}(10^{-3})$ on the newly proposed observable quantities.
Quantum marking and quantum erasure are discussed for the neutral kaon system. Contrary to other two-level systems, strangeness and lifetime of a neutral kaon state can be alternatively measured via an active or a passive procedure. This offers new quantum erasure possibilities. In particular, the operation of a quantum eraser in the delayed choice mode is clearly illustrated.
Quantum marking and quantum erasure are discussed for the neutral kaon system. Contrary to other two-level systems, strangeness and lifetime of a neutral kaon state can be alternatively measured via an active or a passive procedure. This offers new quantum erasure possibilities. In particular, the operation of a quantum eraser in the delayed choice mode is clearly illustrated.
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