Pion quasiparticles and QCD phase transitions at finite temperature and isospin density from holography

TL;DR

This paper investigates pion spectra and chiral phase transitions at finite temperature and isospin density using holographic QCD, revealing Goldstone bosons, chiral symmetry restoration, and pion condensation phenomena.

Contribution

It provides a holographic analysis of pion behavior, including mass spectra and phase transitions, extending understanding of QCD at finite temperature and isospin chemical potential.

Findings

Pions are massless Goldstone bosons at finite temperature in chiral limit.

Chiral symmetry restoration occurs above critical temperature $T_c$.

Charged pion masses split and $ ext{π}^+$ approaches zero mass at critical isospin chemical potential.

Abstract

Spectra of pions, which are known as the pseudo-Goldstone bosons of spontaneous chiral symmetry breaking, as well as their relationship with chiral phase transition and pion superfluidity phase transition, have been investigated in the framework of soft-wall AdS/QCD. In chiral limit, it is proved both numerically and analytically that pions are massless Goldstone bosons even at finite temperature, which was usually considered as an assumption in soft-wall models. Above $T_c$, at which chiral condensate $\langle \bar{q}q\rangle$ vanishes, the spectra of pions and scalar mesons merge together, showing the evidence of the restored chiral symmetry in hadronic spectrum level. Extending to finite quark mass, pion masses increase with quark mass. Further, it is more interesting to observe that the pole masses of pions decrease with temperature below $T_c$, which agrees with the analysis in Phys.Rev.Lett.88(2002)202302. Meanwhile, symmetry restoration above $T_c$ could be seen in the spectra of scalar and pseudo-scalar mesons. With finite temperature and isospin chemical potential $\mu_I$, it is shown that the masses of charged pions would split. The mass of positive charged pion $\pi^+$ decreases almost linearly to zero when $\mu_I$ grows to $\mu_{I}^c$, where pion condensation starts to form. This reveals the Goldstone nature of $\pi^+$ after pion superfluidity transition, which are closely related to the experimental observation.