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arXiv:hep-ph/9710236 · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

How devious are deviations from quantum mechanics: The case of the B0B0 system

Reinhold A. Bertlmann, Walter Grimus

Published Jul 8, 1998• 26 citations
arXivHTMLPDF

Abstract

Considering semileptonic decays of the entangled ${B}^{0}{B}^{0}$ state which is generated in the decay of $\ensuremath{\Upsilon}(4S),$ we simply multiply the quantum-mechanical interference term by a factor $(1\ensuremath{-}\ensuremath{\zeta})$ and use the ``decoherence parameter'' \ensuremath{\zeta} as a measure for deviations from quantum mechanics. We investigate several consequences of this modification of semileptonic ${B}^{0}{B}^{0}$ decays. In particular, we show that when confronted with the experimental values of the ratio R=(no. like-sign dilepton events)/(no. opposite-sign dilepton events) and of the ${B}_{H}\ensuremath{-}{B}_{L}$ mass difference, the ensuing one standard deviation range of the decoherence parameter depends strongly on the basis in the ${B}^{0}--{B}^{0}$ space used to build the entangled ${B}^{0}{B}^{0}$ state. On the other hand, in quantum mechanics physical quantities are, of course, independent of such arbitrary basis choices.

DOI
10.1103/physrevd.58.034014

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Considering semileptonic decays of the entangled B0B0{B}^{0}{B}^{0}B0B0 state which is generated in the decay of \ensuremathΥ(4S),\ensuremath{\Upsilon}(4S),\ensuremathΥ(4S), we simply multiply the quantum-mechanical interference term by a factor (1\ensuremath−\ensuremathζ)(1\ensuremath{-}\ensuremath{\zeta})(1\ensuremath−\ensuremathζ) and use the ``decoherence parameter'' \ensuremath{\zeta} as a measure for deviations from quantum mechanics. We investigate several consequences of this modification of semileptonic B0B0{B}^{0}{B}^{0}B0B0 decays. In particular, we show that when confronted with the experimental values of the ratio R=(no. like-sign dilepton events)/(no. opposite-sign dilepton events) and of the BH\ensuremath−BL{B}_{H}\ensuremath{-}{B}_{L}BH​\ensuremath−BL​ mass difference, the ensuing one standard deviation range of the decoherence parameter depends strongly on the basis in the B0−−B0{B}^{0}--{B}^{0}B0−−B0 space used to build the entangled B0B0{B}^{0}{B}^{0}B0B0 state. On the other hand, in quantum mechanics physical quantities are, of course, independent of such arbitrary basis choices.
In the context of the entangled B0B0{B}^{0}{B}^{0}B0B0 state produced at the $\ensuremath{\Upsilon}(4S)$ resonance, we consider a modification of the usual quantum-mechanical time evolution with a dissipative term, which contains only one parameter denoted by $\ensuremath{\lambda}$ and respects complete positivity. In this way a decoherence effect is introduced in the time evolution of the two-particle B0B0{B}^{0}{B}^{0}B0B0 state, which becomes stronger with increasing distance between the two particles. While our model of time evolution has decoherence for the two-particle system, we assume that, after the decay of one of the two B mesons, the resulting one-particle state obeys the purely quantum-mechanical time evolution. From the data on dilepton events we derive an upper bound on $\ensuremath{\lambda}.$ We also show how $\ensuremath{\lambda}$ is related to the so-called ``decoherence parameter'' $\ensuremath{\zeta},$ which parametrizes decoherence in neutral flavored meson-antimeson systems.
We consider strangeness correlations of the Einstein-Podolski-Rosen type in K0K0{K}^{0}{K}^{0}K0K0 pairs created in a ${J}^{\mathrm{PC}}{=1}^{\ensuremath{-}\ensuremath{-}}$ state as a function of time under the hypothesis that spontaneous decoherence takes place. We parametrize the degree of decoherence by a factor $(1\ensuremath{-}\ensuremath{\zeta})$ which multiplies the quantum-mechanical interference terms occurring in the amplitudes for like and unlike strangeness events and discuss the dependence of this procedure on the basis chosen in ${K}^{0}\ensuremath{-}{K}^{0}$ space to which the interference terms correspond. Consequently, all statements about the ``decoherence parameter'' $\ensuremath{\zeta}$ inferred from experimental data are basis dependent as well. We illustrate this point by estimating the value of $\ensuremath{\zeta}$ for the two bases KL,KS{{K}_{L}{,K}_{S}}KL​,KS​ and K0,K0{{K}^{0},{K}^{0}}K0,K0 with the help of recent data of the CPLEAR experiment.
A bstract With the advent of Belle II and the LHCb upgrade, the precision measurements of various B-Physics observables are on cards. This holds significant potential for delving into physics beyond the standard model of electroweak interactions. These measurements can also serve as means to establish limits on phenomena occurring at much finer length scales, such as quantum decoherence, which may arise due to potential discreteness in space-time or non-trivial topological effects. In this work, we set up the formalism to investigate the impact of quantum decoherence on several potential observables in B meson systems. The approach employs the trace-preserving Kraus operator formalism, extending unitary evolution to non-unitary dynamics while maintaining complete positivity. In this formalism, the decoherence effects are parametrized in terms of a single parameter. Through the analysis of purely leptonic, semileptonic, and non-leptonic decays of B mesons, we identify observables that could, in principle, be influenced by decoherence. The theoretical expressions are provided without neglecting the impact of decay width difference (∆Γ) and CP violation in mixing. Considering that many of these observables can be measured with high precision using the abundant data collected by LHCb and Belle II, our formalism can be applied to establish constraints on the decoherence parameter through multiple decay channels. This offers an alternative set-up for such studies, which, at present, are predominantly conducted in the neutrino sector.
The neutral B-meson pair produced at the U(4S) should ex- hibit a non-local correlation of the type discussed by Einstein, Podol- ski, and Rosen. The time-dependent flavour asymmetry of the B mesons decaying into flavour eigenstates is used to test such a cor- relation. The asymmetry obtained from semileptonic B 0 decays is in agreement with the prediction from quantum mechanics and far away from the predictions of the local realistic models tested. The observation of partial decoherence in EPR systems could be a sig- nal for New Physics: we have tested for such effects, and found our results are consistent with no decoherence.
A model for intrinsic decoherence in quantum mechanics is proposed, based on a simple modification of unitary Schr\"odinger evolution. On sufficiently small time scales the system evolves by a random sequence of unitary phase changes generated by the Hamiltonian. The Schr\"odinger equation is obtained to zeroth order in the expansion parameter. Higher-order corrections lead to a loss of coherence in the energy basis. The rate of coherence loss becomes very large as the energy scale of the system is increased. The expansion parameter determines an uncertainty in the time step on very short times scales. A number of testable consequences are derived including anomalous dispersion of a free particle, decay of oscillatory systems, destruction of interference-fringe visibility, and a phase shift of interference fringes.
Abstract Moving to more subtle experiments, we consider how the standard formulation of quantum mechanics predicts and explains interference phenomena. Tracking the conditions under which one observes interference phenomena leads to the notion of quantum decoherence. We see why one must sharply distinguish between collapse phenomena and decoherence phenomena on the standard formulation of quantum mechanics. While collapses explain determinate measurement records, environmental decoherence just produces more complex, entangled states where the physical systems involved lack ordinary physical properties. We characterize the quantum-mechanical wave function as both an element of a Hilbert space and a complex-valued function over a configuration space. We also discuss how the wave function is interpreted in the standard theory.