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

Spectral functions in the sigma-channel near the critical end point

Spectral functions in the $\sigma$-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 $(\mu,T)$-plane of the QCD phase diagram. At that point the $\sigma$ 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 $\sigma$ 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 $\sigma$ meson. Experimentally, in such a low energy region below the threshold of two pions, photons from $\pi^0\to2\gamma$ are major sources of the background for the signal.Comment: 12 pages, 8 figures, 1 figure replaced, minor modification

Thermal and Nonthermal Pion Enhancements with Chiral Symmetry Restoration

The pion production by sigma decay and its relation with chiral symmetry restoration in a hot and dense matter are investigated in the framework of the Nambu-Jona-Lasinio model. The decay rate for the process sigma -> 2pion to the lowest order in a 1/N_c expansion is calculated as a function of temperature T and chemical potential mu. The thermal and nonthermal enhancements of pions generated by the decay before and after the freeze-out present only in the crossover region of the chiral symmetry transition. The strongest nonthermal enhancement is located in the vicinity of the endpoint of the first-order transition.Comment: Latex2e, 12 pages, 8 Postscript figures, submitted to Phys. Rev.

Linear sigma model and chiral symmetry at finite temperature

The chiral phase transition is investigated within the framework of the linear sigma model at finite temperature. We concentrate on the meson sector of the model and calculate the finite temperature effective potential in the Hartree approximation by using the Cornwall-Jackiw-Tomboulis formalism of composite operators. The effective potential is calculated for N=4 involving the usual sigma and three pions and in the large N approximation involving N-1 pion fields. In the N=4 case we have examined the theory both in the chiral limit and with the presence of a symmetry breaking term which generates the pion masses. In both cases we have solved the system of the resulting gap equations for the thermal effective masses of the particles numerically and we have investigated the evolution of the effective potential. In the N=4 case there is indication of a first order phase transition and the Goldstone theorem is not satisfied. The situation is different in the general case using the large $N$ approximation, the Goldstone theorem is satisfied and the phase transition is of the second order. For this analysis we have ignored quantum effects and we used the imaginary time formalism for calculations.Comment: 14 pages, 5 eps figures, RevTex, axodraw.st

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

Out of equilibrium O (N) linear-sigma system - Construction of perturbation theory with gap- and Boltzmann-equations

We establish from first principles a perturbative framework that allows us to compute reaction rates for processes taking place in nonequilibrium $O (N)$ linear-sigma systems in broken phase. The system of our concern is quasiuniform system near equilibrium or nonequilibrium quasistationary system. We employ the closed-time-path formalism and use the so-called gradient approximation. No further approximation is introduced. In the course of construction of the framework, we obtain the gap equation that determines the effective masses of $\pi$ and of $\sigma$, and the generalized Boltzmann equation that describes the evolution of the number-density functions of $\pi$ and of $\sigma$.Comment: 18 page

The Chiral Fermion Meson Model at Finite Temperature

We study the chiral fermion meson model which is the well known linear sigma model of Gell-Mann-and-Levy at finite temperature.A modified self-consistent resummation (MSCR) which resums higher order terms in the perturbative expansion is proposed. It is shown that with the MSCR the problem of tachyonic masses is solved, the renormalization of the gap equations is carried out and the Goldstone's theorem is verified. We also apply the method to investigate another known case at high temperature and compare with results found in the literature.Comment: 31 pages, 9 EPS figures. Final version with extended Concluding Remarks section, accepted for publication in Phys. Rev.

Screened Perturbation Theory to Three Loops

The thermal physics of a massless scalar field with a phi^4 interaction is studied within screened perturbation theory (SPT). In this method the perturbative expansion is reorganized by adding and subtracting a mass term in the lagrangian. We consider several different mass prescriptions that generalize the one-loop gap equation to two-loop order. We calculate the pressure and entropy to three-loop order and the screening mass to two-loop order. In contrast to the weak-coupling expansion, the SPT-improved approximations appear to converge even for rather large values of the coupling constant.Comment: 30 pages, 10 figure