We study the quark spectrum at nonzero temperature and density near the critical point (CP) of the chiral phase transition incorporating effects of the scalar- and pseudoscalar-density fluctuations in a chiral effective model with a nonzero current q
uark mass. It is known that the soft mode associated with the second-order transition at the CP lies in the spacelike region of the scalar-density fluctuation. We find that the soft mode influences the quark spectrum significantly near the CP, resulting in the shift of the quasiquark peak. Effects of the composite stable pions on the quark spectrum near the CP are also discussed.
We study the quark spectrum at finite temperature near and above the pseudocritical temperature of the chiral phase transition incorporating the effects of the collective modes with the quantum number of the sigma (parasigma) and pion (parapion) in a
chiral effective model with a nonzero current quark mass. Below the pion zero-binding temperature where the pionic modes are bound, the quark self-energy has van Hove singularity induced by the scattering of quarks with the composite bound pions with a nonhyperbolic dispersion curve. This singularity is found to cause a drastic change in the quark spectrum from that in the mean field picture near the pseudocritical temperature: The quark spectrum has an unexpected sharp peak at an energy considerably lower than the constituent quark mass, while the spectrum approaches the mean field one at high temperatures. We clarify that the emergence of this anomalous structure of the quark spectral function originates from the composite nature of the pionic modes with a non-Lorentz invariant dispersion relation in the medium at finite temperature.
We investigate the effect of the electric-charge neutrality in $beta$ equilibrium on the chiral phase transition by solving the chiral and diquark condensates in the two-flavor Nambu--Jona-Lasinio model. We demonstrate that the electric-charge neut
rality plays a similar role as the repulsive vector interaction; they both weaken the first-order chiral phase transition in the high-density and low-temperature region. The first-order chiral phase transition is not affected, however, at finite temperatures where the diquark condensate melts. In this way the chiral phase transition could be second-order at intermediate temperatures if the diquark effects overwhelm the chiral dynamics, while the first-order transition may survive at lower and higher temperatures. The number of the critical points appearing on the phase diagram can vary from zero to three, which depends on the relative strength of the chiral and diquark couplings. We systematically study the possibility of the phase structure with multiple QCD critical points and evaluate the Meissner screening mass to confirm that our conclusion is not overturned by chromomagnetic instability.
This paper has been withdrawn by the authors, due to its incompleteness.
We investigate the quark spectrum near but above the critical temperature of the chiral transition, taking into account the precursory soft modes. It is found that there appear novel excitation spectra of quasi-quarks and quasi-antiquarks with a thre
e-peak structure. By a detailed analysis on the formation of the three-peak structure using Yukawa models, it is shown that the new quark spectra originate from the mixing between a quark (anti-quark) and an antiquark hole (quark hole) caused by a resonant scattering of the quasi-quark with the soft modes which have a small but finite excitation energy with a small width near the critical temperature.
