Proper time evolution of magnetic susceptibility in a magnetized quark-gluon plasma

TL;DR

This paper investigates how magnetic susceptibility evolves over time in a magnetized quark-gluon plasma created in heavy-ion collisions, using anisotropic kinetic theory and magnetohydrodynamics, including effects of dissipation.

Contribution

It introduces a method to determine the time-dependent magnetic susceptibility in a quark-gluon plasma using anisotropic kinetic theory and ideal transverse magnetohydrodynamics.

Findings

Magnetic susceptibility depends on magnetic field and temperature.

Proper time evolution of $hi_m$ is derived in ideal magnetohydrodynamics.

Dissipation influences the evolution of magnetic susceptibility.

Abstract

In ultrarelativistic heavy-ion collisions, enormous magnetic fields are generated because of fast-moving charged particles. In the presence of these magnetic fields, the spin of particles is aligned either in the parallel or in the antiparallel direction with respect to the direction of the magnetic field. A finite magnetization is thus produced. It is known that a finite magnetic susceptibility, $\chi_{m}$, changes the evolution of the energy density of the quark-gluon plasma (QGP), which is believed to be created in these collisions. Depending on whether the system under consideration is a paramagnetic ($\chi_{m}>0$) or diamagnetic ($\chi_{m}<0$) fluid, it slows down or speeds up the decay of the energy density, and affects other thermodynamic quantities. In general, one expects that the magnetic susceptibility depends on the magnetic field and temperature. Bearing in mind that these parameters evolve with the evolution of the fluid, a nonuniform magnetic susceptibility in this system is thus expected. In this work, we first determine $\chi_{m}$ by using a certain analogy to the standard anisotropic kinetic theory, where the one-particle distribution function is replaced by the corresponding anisotropic distribution function. We then determine the proper time dependence of the magnetic susceptibility in the framework of the ideal transverse magnetohydrodynamics. We also study the effect of dissipation on the evolution of $\chi_{m}$.