Chiral MHD description of a perfect magnetized QGP using the effective NJL model in a strong magnetic field

TL;DR

This paper develops a chiral magnetohydrodynamical model of a perfect, magnetized quark-gluon plasma using the NJL model, revealing anisotropic sound velocities influenced by magnetic fields and temperature near the chiral phase transition.

Contribution

It introduces a novel MHD framework incorporating chiral symmetry breaking effects in a strong magnetic field using the NJL model, analyzing sound velocity behavior in the QGP.

Findings

Sound velocity is anisotropic and depends on the angle with the magnetic field.

Maximum and minimum sound velocities occur near the critical temperature.

Sound velocity approaches a constant value at high temperatures.

Abstract

To study the effect of a strong magnetic field $B$ on the sound velocity $v_{s}$ of plane waves propagating in a strongly magnetized quark-gluon plasma (QGP), a chiral magnetohydrodynamical (MHD) description of a perfect (non-dissipative) QGP exhibiting dynamical chiral symmetry breaking (D$\chi$SB) is developed using the effective action of the Nambu-Jona-Lasinio (NJL) model of QCD at finite temperature, finite baryon chemical potential and in the presence of a strong magnetic field. Here, the D$\chi$SB arises due to the phenomenon of magnetic catalysis. Apart from an interesting frequency dependence, for plane waves propagating in the transverse or longitudinal direction with respect to the $B$ field, the sound velocity is anisotropic and depends on the angle between the corresponding wave vectors and the direction of the $B$ field. Moreover, for plane waves propagating in the transverse (longitudinal) direction to the external $B$ field, the sound velocity has a maximum (minimum) at $T<T_{c}$, reaches a local minimum (maximum) at $T\sim T_{c}$ and remains constant at $T\gtrsim T_{c}$. Here, $T_{c}$ is the critical temperature of the chiral phase transition. Thus, the constant value $v_{s}\sim 1.5 c_{s}$ at $T \gtrsim T_{c}$ turns out to be a lower (upper) bound for waves propagating in the transverse (longitudinal) direction with respect to the external $B$ field. Here, $c_{s}=1/\sqrt{3}$ is the sound velocity in an ideal gas.