106 research outputs found
Thermodynamics of O(N) sigma models: 1/N corrections
The thermodynamics of the O(N) linear and nonlinear sigma models in 3+1
dimensions is studied. We calculate the pressure to next-to-leading order in
the 1/N expansion and show that at this order, temperature-independent
renormalization is only possible at the minimum of the effective potential. The
1/N expansion is found to be a good expansion for N as low as 4, which is the
case relevant for low-energy QCD phenomenology. We consider the cases with and
without explicit symmetry breaking. We show that previous next-to-leading order
calculations of the pressure are either breaking down in the temperatures of
interest, or based on unjustifiable high-energy approximations.Comment: 11 pages, 5 figures, revte
On the thermal sunset diagram for scalar field theories
We study the so-called `` sunset diagram'', which is one of two-loop
self-energy diagrams, for scalar field theories at finite temperature.
For this purpose, we first find the complete expression of the bubble
diagram, the one-loop subdiagram of the sunset diagram, for arbitrary momentum.
We calculate the temperature independent part and dependent part of the
sunset diagram separately. For the former, we obtain the discontinuous part
first and the finite continuous part next using a twice-subtracted dispersion
relation. For the latter, we express it as a one-dimensional integral in terms
of the bubble diagram.
We also study the structure of the discontinuous part of the sunset diagram.
Physical processes, which are responsible for it, are identified. Processes due
to the scattering with particles in the heat bath exist only at finite
temperature and generate discontinuity for arbitrary momentum, which is a
remarkable feature of the two-loop diagrams at finite temperature.
As an application of our result, we study the effect of the diagram on the
spectral function of the sigma meson at finite temperature in the linear sigma
model, which was obtained at one-loop order previously. At high temperature
where the decay is forbidden, sigma acquires a finite width
of the order of while within the one-loop calculation its width
vanishes. At low temperature, the spectrum does not deviate much from that at
one-loop order. Possible consequences with including other two-loop diagrams
are discussed.Comment: 30 page
Low-momentum Pion Enhancement Induced by Chiral Symmetry Restoration
The thermal and nonthermal pion production by sigma decay and its relation
with chiral symmetry restoration in a hot and dense matter are investigated.
The nonthermal decay into pions of sigma mesons which are popularly produced in
chiral symmetric phase leads to a low-momentum pion enhancement as a possible
signature of chiral phase transition at finite temperature and density.Comment: 3 pages, 2 figure
In-medium pi-pi Correlation Induced by Partial Restoration of Chiral Symmetry
We show that both the linear and the non-linear chiral models give an
enhancement of the pi-pi cross section near the 2pi threshold in the
scalar-iso-scalar (I=J=0) channel in nuclear matter. The reduction of the
chiral condensate, i.e., the partial chiral restoration in nuclear matter, is
responsible for the enhancement in both cases. We extract an effective
4pi-nucleon vertex which is responsible for the enhancement but has not been
considered in the non-liear models for in-medium pi-pi interaction. Relation of
this vertex and a next-to-leading order terms in the heavy-baryon chiral
lagrangian, L_piN^(2), is also discussed.Comment: 5 pages, 5 eps figure, REVTe
The Fokker-Planck equation for bistable potential in the optimized expansion
The optimized expansion is used to formulate a systematic approximation
scheme to the probability distribution of a stochastic system. The first order
approximation for the one-dimensional system driven by noise in an anharmonic
potential is shown to agree well with the exact solution of the Fokker-Planck
equation. Even for a bistable system the whole period of evolution to
equilibrium is correctly described at various noise intensities.Comment: 12 pages, LATEX, 3 Postscript figures compressed an
A Precursor of Chiral Symmetry Restoration in the Nuclear Medium
Spectral enhancement near the 2m_{\pi} threshold in the I=J=0 channel in
nuclei is shown to be a distinct signal of the partial restoration of chiral
symmetry. The relevance of this phenomenon with the possible detection of
2\pi^{0} and 2\gamma in hadron-nucleus and photo-nucleus reactions is
discussed.Comment: Revtex, 4 pages, 3 eps figures, title and introduction changed, to
appear in Phys. Rev. Let
Spectral functions in the sigma-channel near the critical end point
Spectral functions in the -channel are investigated near the chiral
critical end point (CEP), that is, the point where the chiral phase transition
ceases to be first-ordered in the -plane of the QCD phase diagram. At
that point the meson becomes massless in spite of explicit breaking of
the chiral symmetry. It is expected that experimental signatures peculiar to
CEP can be observed through spectral changes in the presence of abnormally
light mesons. As a candidate, the invariant-mass spectrum for diphoton
emission is estimated with the chiral quark model incorporated. The results
show the characteristic shape with a peak in the low energy region, which may
serve as a signal for CEP. However, we find that the diphoton multiplicity is
highly suppressed by infrared behaviors of the meson. Experimentally,
in such a low energy region below the threshold of two pions, photons from
are major sources of the background for the signal.Comment: 12 pages, 8 figures, 1 figure replaced, minor modification
Investigation into O(N) Invariant Scalar Model Using Auxiliary-Mass Method at Finite Temperature
Using auxiliary-mass method, O(N) invariant scalar model is investigated at
finite temperature. This mass and an evolution equation allow us to calculate
an effective potential without an infrared divergence. Second order phase
transition is indicated by the effective potential. The critical exponents are
determined numerically.Comment: LaTex 8 pages with 3 eps figure
- …