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

TL;DR

This paper investigates how the spectral function and pole structure of quarks, both massless and massive, coupled with bosons at finite temperature, change with temperature and quark mass, revealing a critical point where collective excitations undergo a drastic transformation.

Contribution

It provides a detailed analysis of the spectral and pole structures of quarks in Yukawa models at finite temperature, highlighting the impact of quark mass on collective excitations and identifying a critical mass for structural changes.

Findings

Three-peak spectral structure persists at high temperature for finite quark mass.

Pole trajectories undergo a structural rearrangement at a critical quark mass.

Level mixing explains the collective excitation behavior.

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 anti-quarks.