Spectral properties of massless and massive quarks coupled with massive boson at finite temperature

Abstract

We study the properties of massless and massive quarks coupled with a scalar and pseudoscalar boson at finite temperature in Yukawa models at the one-loop order. The behavior of the spectral function and the pole structure of the propagator are analyzed as functions of temperature $T$ and the quark mass ${m}_{f}$. It is shown that the three-peak structure of the spectral function found in a previous work for massless quarks is formed at temperatures comparable to the boson mass even for finite ${m}_{f}$, but gradually ceases to exist as ${m}_{f}$ becomes larger. We identify the three poles of the quark propagator corresponding to the collective excitations of the quark in the complex-energy plane. It is shown that the three trajectories made by the poles along with a variation of $T$ undergo a structural rearrangement at a critical quark mass when ${m}_{f}$ is increased. This suggests that the physics content of the collective quark excitations is changed in a drastic way at this point. The results are nicely accounted for with the notion of the level mixing induced by a resonant scattering of the massive boson with quarks and holes of thermally excited antiquarks.