Possible generation of anomalously soft quark excitations at nonzero temperature: Nonhyperbolic dispersion of parapion and van Hove singularity

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.