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D. Boyanovsky - One of the best experts on this subject based on the ideXlab platform.

  • superhorizon entanglement entropy from Particle Decay in inflation
    Journal of High Energy Physics, 2014
    Co-Authors: Louis Lello, D. Boyanovsky, R Holman
    Abstract:

    In inflationary cosmology all Particle states Decay as a consequence of the lack of kinematic thresholds. The Decay of an initial single Particle state yields an entangled quantum state of the product Particles. We generalize and extend a manifestly unitary field theoretical method to obtain the time evolution of the quantum state. We consider the Decay of a light scalar field with mass M ≪ H with a cubic coupling in de Sitter space-time. Radiative corrections feature an infrared enhancement manifest as poles in � = M 2 /3H 2 and we obtain the quantum state

  • entanglement entropy in Particle Decay
    Journal of High Energy Physics, 2013
    Co-Authors: Louis Lello, D. Boyanovsky, R Holman
    Abstract:

    The Decay of a parent Particle into two or more daughter Particles results in an entangled quantum state as a consequence of conservation laws in the Decay process. Recent experiments at Belle and BaBar take advantage of quantum entanglement and the correlations in the time evolution of the product Particles to study CP and T violations. If one (or more) of the product Particles are not observed, their degrees of freedom are traced out of the pure state density matrix resulting from the Decay, leading to a mixed state density matrix and an entanglement entropy. This entropy is a measure of the loss of information present in the original quantum correlations of the entangled state. We use the Wigner-Weisskopf method to construct an approximation to this state that evolves in time in a manifestly unitary way. We then obtain the entanglement entropy from the reduced density matrix of one of the daughter Particles obtained by tracing out the unobserved states, and follow its time evolution. We find that it grows over a time scale determined by the lifetime of the parent Particle to a maximum, which when the width of the parent Particle is narrow, describes the phase space distribution of maximally entangled Bell-like states. The method is generalized to the case in which the parent Particle is described by a wave packet localized in space. Possible experimental avenues to measure the entanglement entropy in the Decay of mesons at rest are discussed.

  • superhorizon entanglement entropy from Particle Decay in inflation
    arXiv: Cosmology and Nongalactic Astrophysics, 2013
    Co-Authors: Louis Lello, D. Boyanovsky, R Holman
    Abstract:

    In inflationary cosmology all Particle states Decay as a consequence of the lack of kinematic thresholds. The Decay of an initial single Particle state yields an \emph{entangled quantum state of the product Particles}. We generalize and extend a manifestly unitary field theoretical method to obtain the time evolution of the quantum state. We consider the Decay of a light scalar field with mass $M\ll H$ with a cubic coupling in de Sitter space-time. Radiative corrections feature an infrared enhancement manifest as poles in $\Delta=M^2/3H^2$ and we obtain the quantum state in an expansion in $\Delta$. To leading order in $\Delta$ the pure state density matrix describing the Decay of a Particle with sub-horizon wavevector is dominated by the emission of superhorizon quanta, describing \emph{entanglement between superhorizon and subhorizon fluctuations and correlations across the horizon}. Tracing over the superhorizon degrees of freedom yields a mixed state density matrix from which we obtain the entanglement entropy. Asymptotically this entropy grows with the \emph{physical} volume as a consequence of more modes of the Decay products crossing the Hubble radius. A generalization to localized wave packets is provided. The cascade Decay of single Particle states into many Particle states is discussed. We conjecture on \emph{possible} impact of these results on non-gaussianity and on the ``low multipole anomalies'' of the CMB.

  • entanglement entropy in Particle Decay
    arXiv: High Energy Physics - Theory, 2013
    Co-Authors: Louis Lello, D. Boyanovsky, R Holman
    Abstract:

    The Decay of a parent Particle into two or more daughter Particles results in an entangled quantum state as a consequence of conservation laws in the Decay process. Recent experiments at Belle and BaBar take advantage of quantum entanglement and the correlations in the time evolution of the product Particles to study CP and T violations. If one (or more) of the product Particles are not observed, their degrees of freedom are traced out of the pure state density matrix resulting from the Decay, leading to a mixed state density matrix and an entanglement entropy. This entropy is a measure of the loss of information present in the original quantum correlations of the entangled state. We use the Wigner-Weisskopf method to construct an approximation to this state that evolves in time in a {\em manifestly unitary} way. We then obtain the entanglement entropy from the reduced density matrix of one of the daughter Particles obtained by tracing out the unobserved states, and follow its time evolution. We find that it grows over a time scale determined by the lifetime of the parent Particle to a maximum, which when the width of the parent Particle is narrow, describes the phase space distribution of maximally entangled Bell-like states. The method is generalized to the case in which the parent Particle is described by a wave packet localized in space. Possible experimental avenues to measure the entanglement entropy in the Decay of mesons at rest are discussed.

  • Particle Decay during inflation self Decay of inflaton quantum fluctuations during slow roll
    Physical Review D, 2005
    Co-Authors: D. Boyanovsky, H. J. De Vega, N. G. Sanchez
    Abstract:

    Particle Decay during inflation is studied by implementing a dynamical renormalization group resummation combined with a small $\ensuremath{\Delta}$ expansion. $\ensuremath{\Delta}$ measures the deviation from the scale invariant power spectrum and regulates the infrared. In slow-roll inflation, $\ensuremath{\Delta}$ is a simple function of the slow-roll parameters ${ϵ}_{V},{\ensuremath{\eta}}_{V}$. We find that quantum fluctuations can self-Decay as a consequence of the inflationary expansion through processes which are forbidden in Minkowski space-time. We compute the self-Decay of the inflaton quantum fluctuations during slow-roll inflation. For wavelengths deep inside the Hubble radius the Decay is enhanced by the emission of ultrasoft collinear quanta, i.e., bremsstrahlung radiation of superhorizon quanta which becomes the leading Decay channel for physical wavelengths $H\ensuremath{\ll}{k}_{\mathrm{p}\mathrm{h}}(\ensuremath{\eta})\ensuremath{\ll}H/({\ensuremath{\eta}}_{V}\ensuremath{-}{ϵ}_{V})$. The Decay of short wavelength fluctuations hastens as the physical wave vector approaches the horizon. Superhorizon fluctuations Decay with a power law ${\ensuremath{\eta}}^{\ensuremath{\Gamma}}$ in conformal time where in terms of the amplitude of curvature perturbations ${△}_{\mathcal{R}}^{2}$, the scalar spectral index ${n}_{s}$, the tensor to scalar ratio $r$ and slow-roll parameters: $\ensuremath{\Gamma}\ensuremath{\simeq}[32{\ensuremath{\xi}}_{V}^{2}{△}_{\mathcal{R}}^{2}/({n}_{s}\ensuremath{-}1+\frac{r}{4}{)}^{2}][1+\mathcal{O}({ϵ}_{V},{\ensuremath{\eta}}_{V})]$. The behavior of the growing mode ${\ensuremath{\eta}}^{{\ensuremath{\eta}}_{V}\ensuremath{-}{ϵ}_{V}+\ensuremath{\Gamma}}/\ensuremath{\eta}$ features an anomalous scaling dimension $\ensuremath{\Gamma}$. We discuss the implications of these results for scalar and tensor perturbations as well as for non-Gaussianities in the power spectrum. The recent Wilkinson Map Anisotropy Probe data suggests $\ensuremath{\Gamma}\ensuremath{\gtrsim}3.6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}$.

H. J. De Vega - One of the best experts on this subject based on the ideXlab platform.

  • Particle Decay during inflation self Decay of inflaton quantum fluctuations during slow roll
    Physical Review D, 2005
    Co-Authors: D. Boyanovsky, H. J. De Vega, N. G. Sanchez
    Abstract:

    Particle Decay during inflation is studied by implementing a dynamical renormalization group resummation combined with a small $\ensuremath{\Delta}$ expansion. $\ensuremath{\Delta}$ measures the deviation from the scale invariant power spectrum and regulates the infrared. In slow-roll inflation, $\ensuremath{\Delta}$ is a simple function of the slow-roll parameters ${ϵ}_{V},{\ensuremath{\eta}}_{V}$. We find that quantum fluctuations can self-Decay as a consequence of the inflationary expansion through processes which are forbidden in Minkowski space-time. We compute the self-Decay of the inflaton quantum fluctuations during slow-roll inflation. For wavelengths deep inside the Hubble radius the Decay is enhanced by the emission of ultrasoft collinear quanta, i.e., bremsstrahlung radiation of superhorizon quanta which becomes the leading Decay channel for physical wavelengths $H\ensuremath{\ll}{k}_{\mathrm{p}\mathrm{h}}(\ensuremath{\eta})\ensuremath{\ll}H/({\ensuremath{\eta}}_{V}\ensuremath{-}{ϵ}_{V})$. The Decay of short wavelength fluctuations hastens as the physical wave vector approaches the horizon. Superhorizon fluctuations Decay with a power law ${\ensuremath{\eta}}^{\ensuremath{\Gamma}}$ in conformal time where in terms of the amplitude of curvature perturbations ${△}_{\mathcal{R}}^{2}$, the scalar spectral index ${n}_{s}$, the tensor to scalar ratio $r$ and slow-roll parameters: $\ensuremath{\Gamma}\ensuremath{\simeq}[32{\ensuremath{\xi}}_{V}^{2}{△}_{\mathcal{R}}^{2}/({n}_{s}\ensuremath{-}1+\frac{r}{4}{)}^{2}][1+\mathcal{O}({ϵ}_{V},{\ensuremath{\eta}}_{V})]$. The behavior of the growing mode ${\ensuremath{\eta}}^{{\ensuremath{\eta}}_{V}\ensuremath{-}{ϵ}_{V}+\ensuremath{\Gamma}}/\ensuremath{\eta}$ features an anomalous scaling dimension $\ensuremath{\Gamma}$. We discuss the implications of these results for scalar and tensor perturbations as well as for non-Gaussianities in the power spectrum. The recent Wilkinson Map Anisotropy Probe data suggests $\ensuremath{\Gamma}\ensuremath{\gtrsim}3.6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}$.

  • Particle Decay during inflation: self-Decay of inflaton quantum fluctuations during slow roll
    Physical Review D, 2005
    Co-Authors: D. Boyanovsky, H. J. De Vega, N. G. Sanchez
    Abstract:

    Particle Decay during inflation is studied by implementing a dynamical renormalization group resummation combined with a small Delta expansion. Delta measures the deviation from the scale invariant power spectrum and regulates the infrared. In slow roll inflation, Delta is a simple function of the slow roll parameters epsilon_V, eta_V.We find that quantum fluctuations can self-Decay as a consequence of the inflationary expansion through processes which are forbidden in Minkowski space-time. We compute the self-Decay of the inflaton quantum fluctuations during slow roll inflation.For wavelengths deep inside the Hubble radius the Decay is enhanced by the emission of ultrasoft collinear quanta, i.e. bremsstrahlung radiation of superhorizon quanta which becomes the leading Decay channel for physical wavelengths H

  • Particle Decay in inflationary cosmology
    Physical Review D, 2004
    Co-Authors: D. Boyanovsky, H. J. De Vega
    Abstract:

    We investigate the relaxation and Decay of a Particle during inflation by implementing the dynamical renormalization group. This investigation allows us to give a meaningful definition for the Decay rate in an expanding universe. As a prelude to a more general scenario, the method is applied here to study the Decay of a Particle in de Sitter inflation via a trilinear coupling to massless conformally coupled Particles, both for wavelengths much larger and much smaller than the Hubble radius. For superhorizon modes we find that the Decay is of the form eta^{Gamma1} with eta being conformal time and we give an explicit expression for Gamma1 to leading order in the coupling which has a noteworthy interpretation in terms of the Hawking temperature of de Sitter space-time. We show that if the mass M of the Decaying field is << H then the Decay rate during inflation is enhanced over the Minkowski spacetime result by a factor 2H/[pi M]. For wavelengths much smaller than the Hubble radius we find that the Decay law is e^{-alpha/[k H C(eta)} with C(eta) the scale factor and alpha determined by the strength of the trilinear coupling. This result suggests a suppression of power for long wavelength modes upon horizon crossing. In all cases we find a substantial enhancement in the Decay law as compared to Minkowski space-time. These results suggest potential implications for the spectrum of scalar density fluctuations as well as non-gaussianities.

R Holman - One of the best experts on this subject based on the ideXlab platform.

  • superhorizon entanglement entropy from Particle Decay in inflation
    Journal of High Energy Physics, 2014
    Co-Authors: Louis Lello, D. Boyanovsky, R Holman
    Abstract:

    In inflationary cosmology all Particle states Decay as a consequence of the lack of kinematic thresholds. The Decay of an initial single Particle state yields an entangled quantum state of the product Particles. We generalize and extend a manifestly unitary field theoretical method to obtain the time evolution of the quantum state. We consider the Decay of a light scalar field with mass M ≪ H with a cubic coupling in de Sitter space-time. Radiative corrections feature an infrared enhancement manifest as poles in � = M 2 /3H 2 and we obtain the quantum state

  • entanglement entropy in Particle Decay
    Journal of High Energy Physics, 2013
    Co-Authors: Louis Lello, D. Boyanovsky, R Holman
    Abstract:

    The Decay of a parent Particle into two or more daughter Particles results in an entangled quantum state as a consequence of conservation laws in the Decay process. Recent experiments at Belle and BaBar take advantage of quantum entanglement and the correlations in the time evolution of the product Particles to study CP and T violations. If one (or more) of the product Particles are not observed, their degrees of freedom are traced out of the pure state density matrix resulting from the Decay, leading to a mixed state density matrix and an entanglement entropy. This entropy is a measure of the loss of information present in the original quantum correlations of the entangled state. We use the Wigner-Weisskopf method to construct an approximation to this state that evolves in time in a manifestly unitary way. We then obtain the entanglement entropy from the reduced density matrix of one of the daughter Particles obtained by tracing out the unobserved states, and follow its time evolution. We find that it grows over a time scale determined by the lifetime of the parent Particle to a maximum, which when the width of the parent Particle is narrow, describes the phase space distribution of maximally entangled Bell-like states. The method is generalized to the case in which the parent Particle is described by a wave packet localized in space. Possible experimental avenues to measure the entanglement entropy in the Decay of mesons at rest are discussed.

  • superhorizon entanglement entropy from Particle Decay in inflation
    arXiv: Cosmology and Nongalactic Astrophysics, 2013
    Co-Authors: Louis Lello, D. Boyanovsky, R Holman
    Abstract:

    In inflationary cosmology all Particle states Decay as a consequence of the lack of kinematic thresholds. The Decay of an initial single Particle state yields an \emph{entangled quantum state of the product Particles}. We generalize and extend a manifestly unitary field theoretical method to obtain the time evolution of the quantum state. We consider the Decay of a light scalar field with mass $M\ll H$ with a cubic coupling in de Sitter space-time. Radiative corrections feature an infrared enhancement manifest as poles in $\Delta=M^2/3H^2$ and we obtain the quantum state in an expansion in $\Delta$. To leading order in $\Delta$ the pure state density matrix describing the Decay of a Particle with sub-horizon wavevector is dominated by the emission of superhorizon quanta, describing \emph{entanglement between superhorizon and subhorizon fluctuations and correlations across the horizon}. Tracing over the superhorizon degrees of freedom yields a mixed state density matrix from which we obtain the entanglement entropy. Asymptotically this entropy grows with the \emph{physical} volume as a consequence of more modes of the Decay products crossing the Hubble radius. A generalization to localized wave packets is provided. The cascade Decay of single Particle states into many Particle states is discussed. We conjecture on \emph{possible} impact of these results on non-gaussianity and on the ``low multipole anomalies'' of the CMB.

  • entanglement entropy in Particle Decay
    arXiv: High Energy Physics - Theory, 2013
    Co-Authors: Louis Lello, D. Boyanovsky, R Holman
    Abstract:

    The Decay of a parent Particle into two or more daughter Particles results in an entangled quantum state as a consequence of conservation laws in the Decay process. Recent experiments at Belle and BaBar take advantage of quantum entanglement and the correlations in the time evolution of the product Particles to study CP and T violations. If one (or more) of the product Particles are not observed, their degrees of freedom are traced out of the pure state density matrix resulting from the Decay, leading to a mixed state density matrix and an entanglement entropy. This entropy is a measure of the loss of information present in the original quantum correlations of the entangled state. We use the Wigner-Weisskopf method to construct an approximation to this state that evolves in time in a {\em manifestly unitary} way. We then obtain the entanglement entropy from the reduced density matrix of one of the daughter Particles obtained by tracing out the unobserved states, and follow its time evolution. We find that it grows over a time scale determined by the lifetime of the parent Particle to a maximum, which when the width of the parent Particle is narrow, describes the phase space distribution of maximally entangled Bell-like states. The method is generalized to the case in which the parent Particle is described by a wave packet localized in space. Possible experimental avenues to measure the entanglement entropy in the Decay of mesons at rest are discussed.

N. G. Sanchez - One of the best experts on this subject based on the ideXlab platform.

  • Particle Decay during inflation self Decay of inflaton quantum fluctuations during slow roll
    Physical Review D, 2005
    Co-Authors: D. Boyanovsky, H. J. De Vega, N. G. Sanchez
    Abstract:

    Particle Decay during inflation is studied by implementing a dynamical renormalization group resummation combined with a small $\ensuremath{\Delta}$ expansion. $\ensuremath{\Delta}$ measures the deviation from the scale invariant power spectrum and regulates the infrared. In slow-roll inflation, $\ensuremath{\Delta}$ is a simple function of the slow-roll parameters ${ϵ}_{V},{\ensuremath{\eta}}_{V}$. We find that quantum fluctuations can self-Decay as a consequence of the inflationary expansion through processes which are forbidden in Minkowski space-time. We compute the self-Decay of the inflaton quantum fluctuations during slow-roll inflation. For wavelengths deep inside the Hubble radius the Decay is enhanced by the emission of ultrasoft collinear quanta, i.e., bremsstrahlung radiation of superhorizon quanta which becomes the leading Decay channel for physical wavelengths $H\ensuremath{\ll}{k}_{\mathrm{p}\mathrm{h}}(\ensuremath{\eta})\ensuremath{\ll}H/({\ensuremath{\eta}}_{V}\ensuremath{-}{ϵ}_{V})$. The Decay of short wavelength fluctuations hastens as the physical wave vector approaches the horizon. Superhorizon fluctuations Decay with a power law ${\ensuremath{\eta}}^{\ensuremath{\Gamma}}$ in conformal time where in terms of the amplitude of curvature perturbations ${△}_{\mathcal{R}}^{2}$, the scalar spectral index ${n}_{s}$, the tensor to scalar ratio $r$ and slow-roll parameters: $\ensuremath{\Gamma}\ensuremath{\simeq}[32{\ensuremath{\xi}}_{V}^{2}{△}_{\mathcal{R}}^{2}/({n}_{s}\ensuremath{-}1+\frac{r}{4}{)}^{2}][1+\mathcal{O}({ϵ}_{V},{\ensuremath{\eta}}_{V})]$. The behavior of the growing mode ${\ensuremath{\eta}}^{{\ensuremath{\eta}}_{V}\ensuremath{-}{ϵ}_{V}+\ensuremath{\Gamma}}/\ensuremath{\eta}$ features an anomalous scaling dimension $\ensuremath{\Gamma}$. We discuss the implications of these results for scalar and tensor perturbations as well as for non-Gaussianities in the power spectrum. The recent Wilkinson Map Anisotropy Probe data suggests $\ensuremath{\Gamma}\ensuremath{\gtrsim}3.6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}$.

  • Particle Decay during inflation: self-Decay of inflaton quantum fluctuations during slow roll
    Physical Review D, 2005
    Co-Authors: D. Boyanovsky, H. J. De Vega, N. G. Sanchez
    Abstract:

    Particle Decay during inflation is studied by implementing a dynamical renormalization group resummation combined with a small Delta expansion. Delta measures the deviation from the scale invariant power spectrum and regulates the infrared. In slow roll inflation, Delta is a simple function of the slow roll parameters epsilon_V, eta_V.We find that quantum fluctuations can self-Decay as a consequence of the inflationary expansion through processes which are forbidden in Minkowski space-time. We compute the self-Decay of the inflaton quantum fluctuations during slow roll inflation.For wavelengths deep inside the Hubble radius the Decay is enhanced by the emission of ultrasoft collinear quanta, i.e. bremsstrahlung radiation of superhorizon quanta which becomes the leading Decay channel for physical wavelengths H

Louis Lello - One of the best experts on this subject based on the ideXlab platform.

  • superhorizon entanglement entropy from Particle Decay in inflation
    Journal of High Energy Physics, 2014
    Co-Authors: Louis Lello, D. Boyanovsky, R Holman
    Abstract:

    In inflationary cosmology all Particle states Decay as a consequence of the lack of kinematic thresholds. The Decay of an initial single Particle state yields an entangled quantum state of the product Particles. We generalize and extend a manifestly unitary field theoretical method to obtain the time evolution of the quantum state. We consider the Decay of a light scalar field with mass M ≪ H with a cubic coupling in de Sitter space-time. Radiative corrections feature an infrared enhancement manifest as poles in � = M 2 /3H 2 and we obtain the quantum state

  • entanglement entropy in Particle Decay
    Journal of High Energy Physics, 2013
    Co-Authors: Louis Lello, D. Boyanovsky, R Holman
    Abstract:

    The Decay of a parent Particle into two or more daughter Particles results in an entangled quantum state as a consequence of conservation laws in the Decay process. Recent experiments at Belle and BaBar take advantage of quantum entanglement and the correlations in the time evolution of the product Particles to study CP and T violations. If one (or more) of the product Particles are not observed, their degrees of freedom are traced out of the pure state density matrix resulting from the Decay, leading to a mixed state density matrix and an entanglement entropy. This entropy is a measure of the loss of information present in the original quantum correlations of the entangled state. We use the Wigner-Weisskopf method to construct an approximation to this state that evolves in time in a manifestly unitary way. We then obtain the entanglement entropy from the reduced density matrix of one of the daughter Particles obtained by tracing out the unobserved states, and follow its time evolution. We find that it grows over a time scale determined by the lifetime of the parent Particle to a maximum, which when the width of the parent Particle is narrow, describes the phase space distribution of maximally entangled Bell-like states. The method is generalized to the case in which the parent Particle is described by a wave packet localized in space. Possible experimental avenues to measure the entanglement entropy in the Decay of mesons at rest are discussed.

  • superhorizon entanglement entropy from Particle Decay in inflation
    arXiv: Cosmology and Nongalactic Astrophysics, 2013
    Co-Authors: Louis Lello, D. Boyanovsky, R Holman
    Abstract:

    In inflationary cosmology all Particle states Decay as a consequence of the lack of kinematic thresholds. The Decay of an initial single Particle state yields an \emph{entangled quantum state of the product Particles}. We generalize and extend a manifestly unitary field theoretical method to obtain the time evolution of the quantum state. We consider the Decay of a light scalar field with mass $M\ll H$ with a cubic coupling in de Sitter space-time. Radiative corrections feature an infrared enhancement manifest as poles in $\Delta=M^2/3H^2$ and we obtain the quantum state in an expansion in $\Delta$. To leading order in $\Delta$ the pure state density matrix describing the Decay of a Particle with sub-horizon wavevector is dominated by the emission of superhorizon quanta, describing \emph{entanglement between superhorizon and subhorizon fluctuations and correlations across the horizon}. Tracing over the superhorizon degrees of freedom yields a mixed state density matrix from which we obtain the entanglement entropy. Asymptotically this entropy grows with the \emph{physical} volume as a consequence of more modes of the Decay products crossing the Hubble radius. A generalization to localized wave packets is provided. The cascade Decay of single Particle states into many Particle states is discussed. We conjecture on \emph{possible} impact of these results on non-gaussianity and on the ``low multipole anomalies'' of the CMB.

  • entanglement entropy in Particle Decay
    arXiv: High Energy Physics - Theory, 2013
    Co-Authors: Louis Lello, D. Boyanovsky, R Holman
    Abstract:

    The Decay of a parent Particle into two or more daughter Particles results in an entangled quantum state as a consequence of conservation laws in the Decay process. Recent experiments at Belle and BaBar take advantage of quantum entanglement and the correlations in the time evolution of the product Particles to study CP and T violations. If one (or more) of the product Particles are not observed, their degrees of freedom are traced out of the pure state density matrix resulting from the Decay, leading to a mixed state density matrix and an entanglement entropy. This entropy is a measure of the loss of information present in the original quantum correlations of the entangled state. We use the Wigner-Weisskopf method to construct an approximation to this state that evolves in time in a {\em manifestly unitary} way. We then obtain the entanglement entropy from the reduced density matrix of one of the daughter Particles obtained by tracing out the unobserved states, and follow its time evolution. We find that it grows over a time scale determined by the lifetime of the parent Particle to a maximum, which when the width of the parent Particle is narrow, describes the phase space distribution of maximally entangled Bell-like states. The method is generalized to the case in which the parent Particle is described by a wave packet localized in space. Possible experimental avenues to measure the entanglement entropy in the Decay of mesons at rest are discussed.