It is shown that the neutrino and neutral kaon oscillation processes can be consistently described in quantum field theory using only the mass eigenstates of neutrinos and neutral kaons. The distance-dependent and time-dependent parts of the amplitudes of these processes are calculated and the results turn out to be in accord with those of the standard quantum mechanical description of these processes based on the notion of neutrino flavor states and neutral kaon states with definite strangeness. However, the physical picture of the phenomena changes radically: now there are no oscillations of flavor or definite strangeness states, but, instead of it, there is an interference of amplitudes due to different virtual mass eigenstates.
The neutral kaon system is a sensitive probe of quantum mechanics. We revive a parametrization of non-quantum-mechanical effects that is motivated by considerations of the nature of space-time foam, and show how it can be constrained by new measurements of $K_L \rightarrow 2π$ and $K_{L,S}$ semileptonic decays at LEAR or a $ϕ$ factory.
The neutral kaon system can be effectively described by non-unitary, dissipative, completely positive dynamics that extend the usual treatment. In the framework of open quantum systems, we show how the origin of these non-standard time evolutions can be traced to the interaction of the kaon system with a large environment. We find that D-branes, effectively described by a heat-bath of quanta obeying infinite statistics, could constitute a realistic example of such an environment.
We present some general considerations on possible experimental tests of Bell's locality in the neutral kaon system, and comment on the recent literature on the topic.
The generalized dynamics describing the propagation of neutral kaons in randomly fluctuating media is derived and analyzed. It takes into account possible matter-induced effects leading to loss of phase coherence and dissipation. The study of selected neutral kaon observables indicates that these non-standard effects are amenable to a direct experimental analysis.
We point out that decoherence parameters in the correlated two neutral kaon system breaks the transformation invariance of basis and their magnitude are stringently limited by the experimentally measured magnitudes of CP violation and of the strangeness non conserving $ΔS = \pm 2$ transitions.
In this talk, a brief summary is given of the possibility of using neutral-kaon oscillations to bound CPT- and Lorentz-breaking parameters in an extension of the minimal standard model.
A brief review of the theoretical status of CP violation in decays of neutral kaons is presented. We focus on three important topics: $\varepsilon$, $\varepsilon'/\varepsilon$ and $K_L\toπ^0ν\barν$.
In relation with experiments on correlated kaons at phi-factories, it is shown that the request of complete positivity is necessary in any physically consistent description of neutral kaons as open quantum systems.
We study the behaviour of correlated neutral kaons produced in phi-meson decays under the hypothesis that the quantum mechanical time-evolution is completely positive. We show that planned experiments at phi-factories could give precise bounds on the phenomenological parameters of the model.
We present a systematic phenomenological analysis of the tests of CPT symmetry that are possible within an {\em open} quantum-mechanical description of the neutral kaon system that is motivated by arguments based on quantum gravity and string theory. We develop a perturbative expansion in terms of the three small CPT-violating parameters admitted in this description, and provide expressions for a complete set of $K \rightarrow 2π, 3π$ and $π\ellν$ decay observables to second order in these small parameters. We also illustrate the new tests of CPT symmetry and quantum mechanics that are possibl…
The basic feature of the measurement of CPT violation in the neutral kaon system is overviewed beginning with noting the physical implication of CPT violation. After describing $K^0-\bar{K}^0$ system at length, how CPT test is possible is illustrated with adding a few remarks on it.
During the recent years experiments with neutral kaons have yielded remarkably sensitive results which are pertinent to such fundamental phenomena as CPT invariance (protecting causality), time-reversal invariance violation, coherence of wave functions, and entanglement of kaons in pair states. We describe the phenomenological developments and the theoretical conclusions drawn from the experimental material. An outlook to future experimentation is indicated. An overview of formal similarities in fields outside neutral kaons is included.
It is shown that if antiparticles are realized in quantum field theory by negative frequency states, which nevertheless have positive energy density, the resulting theory provides a qualitative explanation for the experiments on the neutral K mesons, without assumming any symmetry violation.
During the recent years experiments with neutral kaons have yielded remarkably sensitive results which are pertinent to such fundamental phenomena as CPT invariance (protecting causality), time-reversal invariance violation, coherence of wave functions, and entanglement of kaons in pair states. We describe the phenomenological developments and the theoretical conclusions drawn from the experimental material. An outlook to future experimentation is indicated.
A quantitative formulation of Bohr's complementarity principle and interferometric duality is discussed and applied to the neutral kaon system. Recent measurements by the CPLEAR Collaboration can be easily interpreted in terms of ``neutral kaon interferometry'' illustrating and confirming those basic principles of quantum mechanics.
We show that $CPT$ is in general violated in a non-quantum-mechanical way in the effective low-energy theory derived from string theory, as a result of apparent world-sheet charge non-conservation induced by stringy monopoles corresponding to target-space black hole configurations. This modification of quantum mechanics does not violate energy conservation. The magnitude of this effective spontaneous violation of $CPT$ may not be be far from the present experimental sensitivity in the neutral kaon system. We demonstrate that our previously proposed stringy modifications to the quantum-mechanic…
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.
We study the effects on oscillations in the neutral-Kaon system from lepton and hadron self-energy loops in the W-boson propagators. The corresponding W box diagrams are evaluated by attaching the external quark lines to covariant vertex functions for the composite Kaons, integrating over all off-shell momenta. We find that the ratio of the imaginary and real parts of the amplitude is of the same size as with the experimental value of the modulus of the CP-violating parameter epsilon.
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.
We quantify the limits on quark-antiquark mass differences imposed by the neutral kaon mass system. In particular, we find that an upper limit to the mass difference of 10^{-3} eV exists if mass differences across quark flavors are uncorrelated. In the upcoming antihydrogen experiments this limit on quark mass difference would allow a measurement of electron-positron mass difference up to a relative precision level of 10^{-15}.
A model is developed for electromagnetic form factors of the charged and neutral K-mesons. The formalism is based on ChPT Lagrangians with vector mesons. The form factors, calculated without fitting parameters, are in a good agreement with experiment for space-like and time-like photon momenta. Contribution of the two-kaon channels to the muon anomalous magnetic moment a_μis calculated.
We consider the contributions of the exotic quarks and gauge bosons to the mass difference between the short- and the long-lived neutral kaon states in $SU(3)_C \times SU(3)_L \times U(1)_N$ model. The lower bound $M_{Z'} \sim$ 14 TeV is obtained for the extra neutral gauge boson ${Z'}^0$. Ranges for values of one of the exotic quark masses and quark mixing parameters are also presented.
We study the $K^0_S-K^0_L$ asymmetries and $CP$ violations in charm-baryon decays with neutral kaons in the final state. The $K^0_S-K^0_L$ asymmetry can be used to search for two-body doubly Cabibbo-suppressed amplitudes of charm-baryon decays, with the one in $Λ^+_c\to pK^0_{S,L}$ as a promising observable. Besides, it is studied for a new $CP$-violation effect in these processes, induced by the interference between the Cabibbo-favored and doubly Cabibbo-suppressed amplitudes with the neutral kaon mixing. Once the new CP-violation effect is determined by experiments, the direct $CP$ asymmetry…
It is considered the state of $K^0$ before the decay as that embedded into the vacuum of $+ \bar K^0 - \bar K^0$. Since the state of $K^0_S$ has the lifeitme $τ_S$, and the state of $K^0_L$ has the lifeitme $τ_L$, the vacuum of $+ \bar K^0 - \bar K^0$ is polarized. Due to the polarization of the vacuum, $2τ_S/τ_L$ of $K^0_S$ decay with the delay $\approx τ_L$. Thus CP-invariance holds true in the decays of neutral kaons.
We report an extension of charged kaon transverse momentum ($p_T$) spectra at mid-rapidity ($\mid y\mid <$ 0.5) up to 15 GeV/$c$, neutral kaon $p_T$ spectra up to 12 GeV/$c$ using events triggered by the Barrel Electro-Magnetic Calorimeter (BEMC) from p+p collisions at $\sqrt{s_{NN}}$ = 200 GeV. The $K^{\pm}/π^{\pm}$ and $K^{0}/π^{\pm}$ at high $p_T$ are compared in p+p and Au+Au collisions, and nuclear modification factor ($R_{AA}$)for pion, kaon, proton and rho are discussed. The $R_{AA}$ for kaon in central collisions are consistent with theory calculation having jet conversion in a plasma …
In recent work on experimental tests of quantum-gravity-motivated phenomenological models, a significant role has been played by the so-called ``$κ$'' deformations of Poincaré symmetries. Sensitivity to values of the relevant deformation length $λ$ as small as $5 \cdot 10^{-33}m$ has been achieved in recent analyses comparing the structure of $κ$-Poincaré symmetries with data on the gamma rays we detect from distant astrophysical sources. We investigate violations of CPT symmetry which may be associated with $κ$-Poincaré in the physics of the neutral-kaon system. A simple estimate indicates th…
Strangeness oscillations in decays of neutral kaons are suggested to be used as an analyzer to investigate detailed properties of heavy flavor hadrons and their decays. Here we briefly explain why, where, and to what problems this approach may be applied.
We present a novel method to perform a direct T (time reversal) symmetry test in the neutral kaon system, independent of any CP and/or CPT symmetry tests. This is based on the comparison of suitable transition probabilities, where the required interchange of in <-> out states for a given process is obtained exploiting the Einstein-Podolsky-Rosen correlations of neutral kaon pairs produced at a $ϕ$-factory. In the time distribution between the two decays, we compare a reference transition like the one defined by the time ordered decays $(\ell^-,ππ)$ with the T -conjugated one defined by $(3π^0,…
The charged and neutral kaon form factors are calculated as a phenomenological application of the QCD Dyson-Schwinger equations. The results are compared with the pion form factor calculated in the same framework and yield \mbox{$F_{K^\pm}(Q^2) > F_{π^\pm}(Q^2)$} on \mbox{$Q^2\in[0,3]$~GeV$^2$}; and a neutral kaon form factor that is similar in form and magnitude to the neutron charge form factor. These results are sensitive to the difference between the kaon and pion Bethe-Salpeter amplitude and the $u$- and $s$-quark propagation characteristics.
We investigate the influence of charged kaon condensation in hadronic sector on the formation of the electron-free charge neutral quark matter of equipartition of three light flavors, i.e., a phenomenon called ``enforced electrical neutrality" of the color-flavor locked (CFL) phase. We employ the chiral quark model which is assumed to be applicable, "bottom-up," toward chiral restoration while accessible to kaon condensation in the hadronic sector. Approaching "bottom-up" the high density regime is more appropriate in addressing the properties of compact stars than approaching "top-down" from …
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 Bohr's complementarity principle, the quantum eraser phenomenon and various forms of Bell inequalities.
We relate the asymmetries in the charged pions energy in the decay into $π^+π^-π^0$ of $K_L$ and of the tagged neutral kaons. The former asymmetry is a given combination of $\Re(ε)$, $\Im(ε)$, and $|ε'|$. Moreover, the non-violating CP asymmetry allows a test for the $χ$PT predictions within the Zel'dovich approach for the final state interaction.
An equivalence between the $\mathrm{Schr\ddot{o}dinger}$ dynamics of a quantum system with a finite number of basis states and a classical dynamics is presented. The equivalence is an isomorphism that connects in univocal way both dynamical systems. We treat the particular case of neutral kaons and found a class of electric networks uniquely related to the kaon system finding the complete map between the matrix elements of the effective Hamiltonian of kaons and those elements of the classical dynamics of the networks. As a consequence, the relevant $ε$ parameter that measures CP violation in t…
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.
The neutral-kaon system constitutes a fantastic and unique laboratory for the study of CPT symmetry and the basic principles of quantum mechanics, and a $ϕ$-factory represents a unique opportunity to push forward these studies. The experimental results show no deviation from the expectations of quantum mechanics and CPT symmetry, while the extreme precision of the measure- ments, in some cases, reaches the interesting Planck-scale region. At present the KLOE-2 experiment is collecting data with an upgraded detector with the aim of significantly improving these kinds of experimental tests.
We consider departures from hamiltonian dynamics in the evolution of neutral kaons due to their interactions with environment that generate entanglement among them. We propose a phenomenological model of stochastic re-scattering and estimate the coefficients of the effective hamiltonian and decoherence terms. Finally we analyze the interplay between the weak interaction and matter effects and propose the observables suitable to measure the matter characteristics of CPT violation and decoherence.
We study the kaon polarizabilities in the framework of Chiral Perturbation Theory to order $p^4$. For the neutral kaon we find that them vanish and they have the first non-zero contribution to order $p^6$. We also emphasize the theoretical potential of an eventual measuremnet of the kaon polarizabilities, in particular of the neutral kaon ones.
For the entangled neutral kaon system we formulate a Bell inequality sensitive to CP violation in mixing. Via this Bell inequality we obtain a bound on the leptonic CP asymmetry which is violated by experimental data. Furthermore, we connect the Bell inequality with a decoherence approach and find a lower bound on the decoherence parameter which practically corresponds to Furry's hypothesis.
Recent and upcoming Fermilab experiments to probe the origin of CP violation and to search for CPT violation are reviewed for an audience of theoretical particle physics graduate students.
We comment on CP, T and CPT violation in the light of interesting new data from the CPLEAR and KTeV Collaborations on neutral kaon decay asymmetries. Other recent data from the CPLEAR experiment, constraining possible violations of CPT and the $ΔS = ΔQ$ rule, exclude the possibility that the semileptonic-decay asymmetry $A_{T}$ measured by CPLEAR could be solely due to CPT violation, confirming that their data constitute direct evidence for T violation. The CP-violating asymmetry in $K_L \to e^-e^+π^-π^+$ recently measured by the KTeV Collaboration does not by itself provide direct evidence fo…
The aim of this contribution is to illustrate two basic aspects of quantum mechanics applied to the neutral kaon system. We first describe a recent quantitative formulation of Bohr's complementarity principle for free--space evolution of single kaons and entangled kaon pairs. We then show that the neutral kaon system is also suitable for an optimal demonstration of the ``quantum eraser'', including its operation in the ``delayed choice'' mode. In our discussions, strangeness oscillations play the role of the traditional interference pattern linked to wave--like behaviour. The role of the two i…
A completely relativistic quark model in the Bethe-Salpter framework is employed to calculate the exclusive production ratio of the neutral over charged Kaon pair in $e^+e^-$ annihilation continuum region for center of mass energies smaller than the $J/Ψ$ mass. The valence quark charge plays the key rôle. The cancellation of the diagrams for the same charge case (in $K_S + K_L$) and the non-cancellation of the diagrams for the different charge case (in $K^-+K^+$) lead to the ratio as $(m_s-m_d)^2/M_{Kaon}^2 \sim 1/10$.
Neutral kaons, and probably also neutrinos, exhibit oscillations between flavor eigenstates, as a result of being produced in a superposition of mass eigenstates. Several recent papers have addressed the question of the energies and momenta of the components of these states, and their effect on the coherence of the states and on the wavelength of the oscillations. We point out that the mass eigenstates need have neither equal momentum nor equal energy, but can nevertheless be coherent, and that a correct treatment of the kinematics recovers the usual result for the wavelength of the flavor osc…
We describe a scheme of stochastic implementations of quantum teleportation and entanglement swapping in terms of neutral kaons. In this scheme, the kaon whose state is to be teleported collides with one of the two entangled kaons in an Einstein-Podolsky-Rosen state. Subsequent detection of the outgoing particles of the collision completes the two-qubit projection on Alice side. There appear novel features, which connects quantum information science with fundamental laws of particle physics.
The problem of particle oscillation is considered in a pedagogical and comprehensive way. Examples from K, B and neutrino physics are given. Conceptual difficulties of the traditional approach to particle oscillation are discussed. It is shown how the probability current density and the wave packet treatments of particle oscillations resolve some problems. It is also shown that only full field theoretical approach is free from conceptual difficulties. The possibility of oscillation of particles produced together with kaons or neutrinos is considered in full wave packet quantum mechanics langua…
We consider the covariant formulation of the kaon mixing in the context of the propagator method. It results important to check the possibility of a sizable effect in the vacuum regeneration of kaons. We discuss all those terms which may give relevant contributions to modify the exponential decay law of the Wigner-Weisskopf narrow width approximation. Moreover, we examine the characteristic structure of the complex singularities of the matrix propagator and we provide a generalized form of the Bell-Steinberger unitarity sum rule.
The rate of the beta decay of neutral kaons is calculated within the meson dominance approach taking into account the relation between the KKρand ππρcoupling constants which follows from the vector meson dominance in electromagnetic interactions and isospin symmetry. The decay rate transforms into the following branching fraction summed over the charge states indicated: B(K0L -> K+- e-+ nu)=(2.53+-0.10)x10^{-9}. The error is dominated by our estimate of isospin violating effects. Experimental aspects of such a measurement are discussed.
This paper contains a detailed analysis of the properties of the scalar product of short and long living superpositions of neutral $|K_{0}>$, $|{\bar{K}}_{0}>$ mesons. It is shown for the exact effective Hamiltonian for neutral meson subsystem that the scalar product of its eigenvectors, which correspond with these short and long living superpositions, can not be real with the assumption of CPT conserved and CP violated. The standard conclusion obtained within the Lee-Oehme-Yang theory of neutral kaons is that in this case such a product should be real.
The Leggett-Garg inequality (LGI) as a temporal analogue of Bell's inequality, derived using the notion of realism, is applied in a hitherto unexplored context involving the weak interaction induced two-state oscillations of decaying neutral kaons and neutrinos. The maximum violation of LGI obtained from the quantum mechanical results is significantly higher for the oscillating neutrinos compared to that for the kaons. Interestingly, the effect of CP non-invariance for the kaon oscillation is to enhance this violation while, for neutrinos, it is sensitive to the value of the mixing parameter.
We study the properties of time evolution of the $K^{0}-\bar{K}^{0} $ system in spectral formulation. Within the one--pole model we find the exact form of the diagonal matrix elements of the effective Hamiltonian for this system. It appears that, contrary to the Lee--Oehme--Yang (LOY) result, these exact diagonal matrix elements are different if the total system is CPT--invariant but CP--noninvariant.
The KLOE collaboration recently reported bounds on the directional dependence of the lifetime of the short-lived neutral kaon K_S with respect to the cosmic microwave background dipole anisotropy. We interpret their results in a general framework developed to probe Lorentz violation in the weak interaction. In this approach a Lorentz-violating tensor χ_{μν} is added to the standard propagator of the W boson. We derive the K_S decay rate in a naive tree-level model and calculate the asymmetry for the lifetime. By using the KLOE data the real vector part of χ_{μν} is found to be smaller than 10^…
The KLOE collaboration recently reported bounds on the directional dependence of the lifetime of the short-lived neutral kaon $K^0_S$ with respect to the dipole anisotropy of the cosmic microwave background. We interpret their results in an effective field theory framework developed to probe the violation of Lorentz invariance in the weak interaction and previously applied to semileptonic processes, in particular $β$ decay. In this approach a general Lorentz-violating tensor $χ^{μν}$ is added to the standard propagator of the $W$ boson. We perform an exploratory study of the prospects to searc…
In the presence of photons, the neutral $K_{\ell 4}$ decay, $K^0\toπ^0π^-\ell^+ν_\ell$, can be parameterized in terms of three vectorial, one anomalous, and one tensorial form factors. We present here analytic expressions of two vectorial form factors, $f$ and $g$, calculated at one-loop level in the framework of chiral perturbation theory based on the effective Lagrangian including mesons, photons, and leptons. These expressions may then be used to disentangle the Isospin breaking part from the measured form factors and hence improve the accuracy in the determination of $ππ$ scattering parame…
