arXiv subjects

Sh. Matsumoto

Publications and source records attributed to Sh. Matsumoto.

14 recordsLinked to original sources

arXiv2003

Time Evolution of Tunneling in Thermal Medium -- Environment-driven Excited Tunneling --

Time evolution of tunneling phenomena proceeding in thermal medium is studied using a standard model of environment interaction. A semiclassical probability formula for the particle motion in a metastable state of one dimensional system put in thermal medium is combined with the formula of quantum penetration factor through a potential barrier, to derive the tunneling rate in medium. Effect of environment, its influence on time evolution in particular, is clarified in a real-time formalism. A nonlinear resonance effect is shown to enhance the tunneling rate at finite times of order $2/η$, with $η$ the friction coefficient. In the linear approximation this effect has relevance to the parametric resonance. This effect enhances the possibility of early termination of the cosmological phase transition much prior to the typical Hubble time.

hep-ph↗

arXiv2003

Unitarity and Higher-Order Corrections in Neutralino Dark Matter Annihilation into Two Photons

The neutralino pair annihilation into two photons in our galactic halo gives a robust dark matter signal, since it would give a quasi-monotonic gamma ray. This process is radiatively-induced, and the full-one loop calculation was done previously. However, for the heavy wino-like or Higgsino-like neutralino, the one-loop cross section violates unitarity, therefore the higher-order corrections may be important. We construct a non-relativistic theory for chargino and neutralino two-body states, and estimate all-order QED corrections and two-loop corrections by $Z$ and/or $W$ exchange. We find that the critical mass, above that the two-loop contribution is larger than one-loop one, is about 8 TeV (O(10) TeV) in the limit where neutralino is wino (Higgsino)-like, respectively. Around and above the critical mass, the all-order Z and/or W exchange must be included to estimate the cross section. On the other hand, the QED corrections depend on the mass difference between the neutralino and chargino. In the wino-like limit where neutralino is highly degenerate with chargino in mass, we find that QED corrections enhance the pair annihilation cross section by 1.5-2.

hep-ph↗

arXiv2000

Resonance Enhanced Tunneling

Time evolution of tunneling in thermal medium is examined using the real-time semiclassical formalism previously developed. Effect of anharmonic terms in the potential well is shown to give a new mechanism of resonance enhanced tunneling. If the friction from environment is small enough, this mechanism may give a very large enhancement for the tunneling rate. The case of the asymmetric wine bottle potential is worked out in detail.

hep-ph↗

arXiv2000

Quantum tunneling in thermal medium

Time evolution of tunneling phenomena in medium is studied using a standard model of environment interaction. A semiclassical formula valid at low, but finite temperatures is derived in the form of integral transform for the reduced Wigner function, and the tunneling probability in thermal medium is calculated for a general tunneling potential of one dimensional system. Effect of dissipation, its time evolution in particular, depends on the behavior of the potential far beyond the barrier.

hep-ph↗

arXiv2000

Dynamics of barrier penetration in thermal medium: exact result for inverted harmonic oscillator

Time evolution of quantum tunneling is studied when the tunneling system is immersed in thermal medium. We analyze in detail the behavior of the system after integrating out the environment. Exact result for the inverted harmonic oscillator of the tunneling potential is derived and the barrier penetration factor is explicitly worked out as a function of time. Quantum mechanical formula without environment is modifed both by the potential renormalization effect and by a dynamical factor which may appreciably differ from the previously obtained one in the time range of 1/(curvature at the top of potential barrier).

hep-ph↗

arXiv1999

New Kinetic Equation for Pair-annihilating Particles: Generalization of the Boltzmann Equation

A convenient form of kinetic equation is derived for pair annihilation of heavy stable particles relevant to the dark matter problem in cosmology. The kinetic equation thus derived extends the on-shell Boltzmann equation in a most straightforward way, including the off-shell effect. A detailed balance equation for the equilibrium abundance is further analyzed. Perturbative analysis of this equation supports a previous result for the equilibrium abundance using the thermal field theory, and gives the temperature power dependence of equilibrium value at low temperatures. Estimate of the relic abundance is possible using this new equilibrium abundance in the sudden freeze-out approximation.

hep-ph↗

arXiv1999

Temperature Power Law of Equilibrium Heavy Particle Density

A standard calculation of the energy density of heavy stable particles that may pair-annihilate into light particles making up thermal medium is performed to second order of coupling, using the technique of thermal field theory. At very low temperatures a power law of temperature is derived for the energy density of the heavy particle. This is in sharp contrast to the exponentially suppressed contribution estimated from the ideal gas distribution function. The result supports a previous dynamical calculation based on the Hartree approximation, and implies that the relic abundance of dark matter particles is enhanced compared to that based on the Boltzmann equation.

hep-ph↗

arXiv1998

Quantum Kinetic Equation and Cosmic Pair Annihilation

Pair annihilation of heavy stable particle that occurs in the early universe is investigated, and quantum kinetic equation for the momentum distribution of the annihilating particle is derived, using the influence functional method. A bosonic field theory model is used to describe the pair annihilation in the presence of decay product particles making up a thermal environment. A crossing symmetric Hartree approximation that determines self-consistently the equilibrium distribution is developed for an otherwise intractable theory. The time evolution equation and its Markovian approximation is derived, to give a generalized Boltzmann equation including off-shell effects. The narrow width approximation to an energy integral in this equation gives the usual Boltzmann equation in a thermal bath of light particles. The off-shell effect is a correction to the Boltzmann equation at high temperatures, but is dominant at low temperatures. The effect changes the equilibrium distribution from the familiar $1/(e^{ω_{k}/T} - 1)$ to a modified one given by a Gibbs formula. Integrated over momenta, the particle number density becomes roughly of order (coupling) $\times \sqrt{T/M}\cdot T^{3}$ at low temperatures for the S-wave annihilation. The relic mass density in the present universe is insensitive to the coupling strength in a large range of the mass and the coupling parameters, and scales with the WIMP mass as (\approx 6 \times 10^{4} eV cm^{-3} (M/GeV)^{4/3}). The bound from the closure density gives an upper WIMP mass bound roughly of order 1 $GeV$ in the present model.

hep-ph↗

arXiv1998

Relic Abundance due to Cosmic Pair Annihilation

Pair annihilation of heavy stable particles that occurs in the early universe is reconsidered including the off-shell effect not properly taken into account by the conventional Boltzmann equation approach. Our new calculation of the time evolution shows that the off-shell effect prolongs the freeze-out, always with a larger final relic abundance. The final yield (number density/temperature^3) is insensitive to the effective coupling for the annihilation and of order (10^{- 8}\times (M/1 GeV)^{1/3}), with $M$ the heavy particle mass, if the coupling is not too small.

hep-ph↗

arXiv1998

Prolonged Decay and CP-asymmetry

Time evolution of unstable particles that occur in the expanding universe is investigated. The off-shell effect not included in the Boltzmann-like equation is important for the decay process when the temperature becomes much below the mass of unstable particle. When the off-shell effect is taken into account, the thermal abundance of unstable particles at low temperatures has a power law behavior of temperature $T$, $\fracΓ{M}(\frac{T}{M})^{α+ 1}$ unlike the Boltzmann suppressed $e^{-M/T}$, with the power $α$ related to the spectral rise near the threshold of the decay and with $Γ$ the decay rate. Moreover, the relaxation time towards the thermal value is not governed by the exponential law; instead, it is the power law of time. The evolution equation for the occupation number and the number density of the unstable particle is derived, when both of these effects, along with the cosmic expansion, are included. We also critically examine how the scattering off thermal particles may affect the off-shell effect to the unstable particle. As an application showing the importance of the off-shell effect we compute the time evolution of the baryon asymmetry generated by the heavy $X$ boson decay. It is shown that the out-of equilibrium kinematics previously discussed is considerably changed.

hep-ph↗

arXiv1997

Time Evolution of Unstable Particle Decay Seen with Finite Resolution

Time evolution of the decay process of unstable particles is investigated in field theory models. We first formulate how to renormalize the non-decay amplitude beyond perturbation theory and then discuss short-time behavior of very long-lived particles. Two different formalisms, one that does and one that does not, assume existence of the asymptotic field of unstable particles are considered. The non-decay amplitude is then calculated by introducing a finite time resolution of measurement, which makes it possible to discuss both renormalizable and non-renormalizable decay interaction including the nucleon decay. In ordinary circumstances the onset of the exponential decay law starts at times as early as at roughly the resolution time, but with an enhanced amplitude which may be measurable. It is confirmed that the short-time formula $1 - Γt$ of the exponential decay law may be used to set limits on the nucleon decay rate in underground experiments. On the other hand, an exceptional example of S-wave decay of very small Q-value is found, which does not have the exponential period at all.

hep-ph↗

arXiv1997

Quantum Dissipation and Decay in Medium

Quantum dissipation in thermal environment is investigated, using the path integral approach. The reduced density matrix of the harmonic oscillator system coupled to thermal bath of oscillators is derived for arbitrary spectrum of bath oscillators. Time evolution and the end point of two-body decay of unstable particles is then elucidated: After early transient times unstable particles undergo the exponential decay, followed by the power law decay and finally ending in a mixed state of residual particles containing contributions from both on and off the mass shell, whose abundance does not suffer from the Boltzmann suppression.

hep-th↗

arXiv1997

Quantum System under Periodic Perturbation: Effect of Environment

In many physical situations the behavior of a quantum system is affected by interaction with a larger environment. We develop, using the method of influence functional, how to deduce the density matrix of the quantum system incorporating the effect of environment. After introducing characterization of the environment by spectral weight, we first devise schemes to approximate the spectral weight, and then a perturbation method in field theory models, in order to approximately describe the environment. All of these approximate models may be classified as extended Ohmic models of dissipation whose differences are in the high frequency part. The quantum system we deal with in the present work is a general class of harmonic oscillators with arbitrary time dependent frequency. The late time behavior of the system is well described by an approximation that employs a localized friction in the dissipative part of the correlation function appearing in the influence functional. The density matrix of the quantum system is then determined in terms of a single classical solution obtained with the time dependent frequency. With this one can compute the entropy, the energy distribution function, and other physical quantities of the system in a closed form. Specific application is made to the case of periodically varying frequency. This dynamical system has a remarkable property when the environmental interaction is switched off: Effect of the parametric resonance gives rise to an exponential growth of the populated number in higher excitation levels, or particle production in field theory models. The effect of the environment is investigated for this dynamical system and it is demonstrated that there exists

hep-ph↗

arXiv1996

Quantum Dissipation in Open Harmonic Systems: Operator Solution

A finite number of harmonic oscillators coupled to infinitely many environment oscillators is fundamental to the problem of understanding quantum dissipation of a small system immersed in a large environment. Exact operator solution as a function of time is given to this problem, by using diagonalized dynamical variable of the entire system, the small system plus the environment. The decay law of prepared initial configuration is worked out in greatest detail. A clear separation of the exponential- and the power-law decay period is made possible by our method. Behavior of physical quantities at asymptotically late times can be understood in terms of the overlap probability of the system variable with the diagonal variable of the entire system.

cond-mat.stat-mech↗