1,520 research outputs found
Thermal Abundances of Heavy Particles
Matsumoto and Yoshimura [hep-ph/9910393] have argued that there are loop
corrections to the number density of heavy particles (in thermal equilibrium
with a gas of light particles) that are not Boltzmann suppressed by a factor of
e^(-M/T) at temperatures T well below the mass M of the heavy particle. We
argue, however, that their definition of the number density does not correspond
to a quantity that could be measured in a realistic experiment. We consider a
model where the heavy particles carry a conserved U(1) charge, and the light
particles do not. The fluctuations of the net charge in a given volume then
provide a measure of the total number of heavy particles in that same volume.
We show that these charge fluctuations are Boltzmann suppressed (to all orders
in perturbation theory). Therefore, we argue, the number density of heavy
particles is also Boltzmann suppressed.Comment: 9 pages, 1 figure; minor improvements in revised versio
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.Comment: 19 pages, LATEX file with 2 PS figure
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.Comment: 12 pages, LATEX file with 6 PS figure
Boltzmann Suppression of Interacting Heavy Particles
Matsumoto and Yoshimura have recently argued that the number density of heavy
particles in a thermal bath is not necessarily Boltzmann-suppressed for T << M,
as power law corrections may emerge at higher orders in perturbation theory.
This fact might have important implications on the determination of WIMP relic
densities. On the other hand, the definition of number densities in a
interacting theory is not a straightforward procedure. It usually requires
renormalization of composite operators and operator mixing, which obscure the
physical interpretation of the computed thermal average. We propose a new
definition for the thermal average of a composite operator, which does not
require any new renormalization counterterm and is thus free from such
ambiguities. Applying this definition to the model of Matsumoto and Yoshimura
we find that it gives number densities which are Boltzmann-suppressed at any
order in perturbation theory. We discuss also heavy particles which are
unstable already at T=0, showing that power law corrections do in general
emerge in this case.Comment: 7 pages, 5 figures. New section added, with the discussion of the
case of an unstable heavy particle. Version to appear on Phys. Rev.
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.Comment: 12 pages, LATEX file with 5 PS figure
Time evolution in linear response: Boltzmann equations and beyond
In this work a perturbative linear response analysis is performed for the
time evolution of the quasi-conserved charge of a scalar field. One can find
two regimes, one follows exponential damping, where the damping rate is shown
to come from quantum Boltzmann equations. The other regime (coming from
multiparticle cuts and products of them) decays as power law. The most
important, non-oscillating contribution in our model comes from a 4-particle
intermediate state and decays as 1/t^3. These results may have relevance for
instance in the context of lepton number violation in the Early Universe.Comment: 19 page
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).Comment: 30 pages, LATEX file with 11 PS figure
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.Comment: 19 pages, LATEX file. Substantially expanded and revised for
publication, including more complete description of application to unstable
particle decay in thermal medium. Some minor mistake of numerical factors
correcte
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