Assuming a tricritical point of the two-flavor QCD in the space of temperature, baryon number chemical potential and quark mass, we study the change of the associated soft mode along the critical line within the Ginzburg-Landau approach and the Nambu-Jona-Lasinio model. The ordering density along the chiral critical line is the scalar density whereas a linear combination of the scalar, baryon number and energy densities becomes the proper ordering density along the critical line with finite quark masses. It is shown that the critical eigenmode shifts from the sigma-like fluctuation of the scalar density to a hydrodynamic mode at the tricritical point, where we have two ordering densities, the scalar density and a linear combination of the baryon number and energy densities. We argue that appearance of the critical eigenmode with hydrodynamic character is a logical consequence of divergent susceptibilities of the conserved densities.12.38. -t, 24.85.+p, 05.70.-a, 64.70.-p

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We propose a chiral random matrix model which properly incorporates the flavor-number dependence of the phase transition owing to the UA(1) anomaly term. At finite temperature, the model shows the second-order phase transition with mean-field critical exponents for two massless flavors, while in the case of three massless flavors the transition turns out to be of the first order. The topological susceptibility satisfies the anomalous UA(1) Ward identity and decreases gradually with the temperature increased.

We study the effect of thermal width of π on the spectral function of σ applying a resummation technique called optimized perturbation theory at finite temperature (T ) to O(4) linear sigma model. In order to take into account finite thermal width of π, we replace the internal pion mass in the selfenergy of σ with that of complex pole found in a previous paper. The obtained spectral function for T > ∼ 100 MeV turns out to possess two broad peaks. Although a sharp peak at σ → ππ threshold was observed in the one-loop calculation without pion thermal width, the peak is proved to be smeared out. We also search for the poles of the σ propagator and analyze the behavior of the spectral function with these poles. It is now believed that the chiral symmetry is restored at finite temperature. As temperature increases to the critical temperature, σ is softened while light π becomes heavy, because their masses should degenerate after the symmetry restoration. At certain temperature, therefore, the mass of σ coincides with twice that of π. Accordingly, the spectrum of σ is expected to be enhanced near the threshold of σ → ππ, since the phase space available for the decay is squeezed to zero.Chiku and Hatsuda [1] showed that the threshold enhancement in the σ channel is observed as expected. They also calculated the spectral function of π and found that π has finite width due to the scattering with thermal pions in the heat bath: π + π thermal → σ. The width of π is ∼ 50 MeV at the temperature where the threshold in the σ spectrum is most strongly enhanced. In their analysis of the spectrum of σ, however, the effect of the pion thermal width is not included, since they calculated the self-energy only up to one-loop order. The purpose of this paper is to show that the threshold enhancement is smeared out by taking into account the effect of pion thermal width.Our strategy is as follows. We utilize the one-loop selfenergy for σ, but we replace the masses of internal pions with complex ones. This complex mass was obtained from the location of the pole of the pion propagator in a previous work [2]. Using the self-energy with the complex pion mass, we study the spectral function of σ. The poles of the σ propagator are also searched for to analyze the behavior of the spectral function.Along the lines mentioned above, here we employ the O(4) linear sigma model:with φ α = (φ 0 , π). As the chiral symmetry is taken to be dynamically broken at low temperature (T ), the quadratic term in the Lagrangian has negative sign, µ 2 < 0. Owing to this choice of the sign and the explicit breaking term of hφ 0 , the field φ 0 has a non-vanishing expectation value ξ. In this prospect, we decompose beforehand the field operator φ 0 into the classical condensate and the quantum fluctuation asIntegrating out the quadratic of the fluctuations σ and π around the condensate, we obtain the one-loop effective potential V eff (ξ). As a minimum of the effective potential, the condensate ξ(T ) is determined and this leads us to the gap equation, 0 = ∂VThe ...

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