Pion dynamics in a soft-wall AdS-QCD model

TL;DR

This paper uses a soft-wall AdS-QCD model to analyze pion pseudo-Goldstone modes, exploring their dispersion, dissipation, and temperature-dependent properties, providing quantitative holographic predictions and revealing deviations from chiral perturbation theory.

Contribution

It offers a detailed holographic study of pion dynamics, including dispersion relations and temperature effects, with new quantitative predictions for effective coefficients.

Findings

Pion dispersion relations are characterized in a holographic model.

Finite temperature effects on pion parameters are quantitatively estimated.

Deviations from chiral perturbation theory predictions are observed.

Abstract

Pseudo-Goldstone modes appear in many physical systems and display robust universal features. First, their mass $m$ obeys the so-called Gell-Mann-Oakes-Renner (GMOR) relation $f^2\,m^2=H\,\bar{\sigma}$, with $f$ the Goldstone stiffness, $H$ the explicit breaking scale and $\bar{\sigma}$ the spontaneous condensate. More recently, it has been shown that their damping $\Omega$ is constrained to follow the relation $\Omega=m^2 D_\varphi$, where $D_\varphi$ is the Goldstone diffusivity in the purely spontaneous phase. Pions are the most paradigmatic example of pseudo-Goldstone modes and they are related to chiral symmetry breaking in QCD. In this work, we consider a bottom-up soft-wall AdS-QCD model with broken ${\rm{SU}}(2)_L \times {\rm{SU}}(2)_R$ symmetry and we study the nature of the associated pseudo-Goldstone modes -- the pions. In particular, we perform a detailed investigation of their dispersion relation in presence of dissipation, of the role of the explicit breaking induced by the quark masses and of the dynamics near the critical point. Taking advantage of the microscopic information provided by the holographic model, we give quantitative predictions for all the coefficients appearing in the effective description. In particular, we estimate the finite temperature behavior of the kinetic parameter $\mathfrak{r^2}$ defined as the ration between the Goldstone diffusivity $D_\varphi$ and the pion attenuation constant $D_A$. Interestingly, we observe important deviations from the value $\mathfrak{r^2}=3/4$ computed in chiral perturbation theory in the limit of zero temperature.