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.
Highlights
Relativistic heavy-ion collisions (RHICs) provide an important approach to probe possible new states of nuclear matter in the laboratory [1]
For the quasiparticle masses at finite temperature, we introduce the spectral method for our study, which has been applied throughout the literature to investigate quantum chromodynamics (QCD) properties [77,78,79,80,81,82,83,84,85,86,87,88,89], and the masses are extracted from the locations of the peaks of the spectral functions
Since one of the main goals of this work is to investigate the relationship between the hadron spectrum and phase transitions, we focus on the isospin density effect, which provides a possibility to probe another kind of phase transition
Summary
Relativistic heavy-ion collisions (RHICs) provide an important approach to probe possible new states of nuclear matter in the laboratory [1]. For pion quasiparticles at finite temperature, a few investigations have been made using extended hard-wall and soft-wall models [72,73,74] Those studies showed that the pion mass decreases with temperature at a relatively low temperature. The mass splitting of mesons has been shown in the hard-wall model Since those studies focused on finite isospin density only and the mutual effect from temperature is unclear, we extend those studies to finite temperature in the soft-wall model and get the T − μI phase diagram [98,99].
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