Holographic estimate of heavy quark diffusion in a magnetic field

TL;DR

This paper investigates how a magnetic field affects heavy quark diffusion and related transport properties in a holographic QCD model, revealing anisotropic diffusion and insights into deconfinement temperature behavior.

Contribution

It introduces a holographic approach to study magnetic field effects on heavy quark transport coefficients, including diffusion anisotropy and susceptibility, extending previous models.

Findings

Magnetic field induces anisotropic heavy quark diffusion.

Diffusion is stronger along the magnetic field direction.

Results qualitatively agree with string analysis and inverse magnetic catalysis.

Abstract

We study the influence of a background magnetic field on the $J/\psi$ vector meson in a DBI-extension of the soft wall model, building upon our earlier work Phys. Rev. D91, 086002 (2015). In this specific holographic QCD model, we discuss the heavy quark number susceptibility and diffusion constants of charm quarks and their dependence on the magnetic field by either a hydrodynamic expansion or by numerically solving the differential equation. This allows us to determine the response of these transport coefficients to the magnetic field. The effects of the latter are considered both from a direct as indirect (medium) viewpoint. As expected, we find a magnetic field induced anisotropic diffusion, with a stronger diffusion in the longitudinal direction compared to the transversal one. We backup, at least qualitatively, our findings with a hanging string analysis of heavy quark diffusion in a magnetic field. From the quark number susceptibility we can extract an estimate for the effective deconfinement temperature in the heavy quark sector, reporting consistency with the phenomenon of inverse magnetic catalysis.