Abstract
We study the influence of a background magnetic field on the $J/\ensuremath{\psi}$ vector meson in a Dirac-Born-Infeld-extension of the soft wall model, building upon our earlier work [Phys. Rev. D 91, 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.
Highlights
Brownian diffusion of a charged particle of mass m and charge q in a background magnetic field B can be modeled using the Langevin equation, dp 1⁄4 −γp þ qv × B þ RðtÞ; ð1Þ dt where the first term describes friction, the second one the Lorentz force and the third one white Gaussian random noise, hRiðtÞi 1⁄4 0; hRiðt1ÞRjðt2Þi 1⁄4 κδijδðt1 − t2Þ: ð2ÞThis has been studied extensively in the nonequilibrium statistical mechanics literature, see e.g. [1,2] for some classical works on the subject and [3,4] for some more recent studies
Not many models would be capable of studying heavy quarks in QCD in magnetic fields in the strongly coupled thermal medium, and we are naturally led to see what our model does, and how it gives different results compared to the superconformal N 1⁄4 4 supersymmetric Yang-Mills (SYM) case
It is interesting to note that we find evidence for the inverse magnetic catalysis for Tc using the original soft wall model, i.e. without taking into account the backreaction of the magnetic field on the metric, which would correspond on the QCD side to the charged quarks coupling the magnetic field indirectly to the uncharged glue
Summary
Brownian diffusion of a charged particle of mass m and charge q in a background magnetic field B can be modeled using the Langevin equation, dp 1⁄4 −γp þ qv × B þ RðtÞ; ð1Þ dt where the first term describes friction, the second one the Lorentz force and the third one white Gaussian random noise, hRiðtÞi 1⁄4 0; hRiðt1ÞRjðt2Þi 1⁄4 κδijδðt1 − t2Þ: ð2Þ. We expect the magnetic field to influence the thermal background, whichinturncaninfluencethediffusionofthecharged particle This effect is indirect, and as a first order approximation, we may imagine we can neglect this part. QCD supplemented with a classical magnetic background attracted a great deal of interest over the past decade, given the expectation that such a field is generated during a noncentral heavy ion collision and persists long enough to influence the generated quark-gluon plasma [7,8,9,10,11,12,13]. Not many models would be capable of studying heavy quarks in QCD in magnetic fields in the strongly coupled thermal medium, and we are naturally led to see what our model does, and how it gives different results compared to the superconformal N 1⁄4 4 supersymmetric Yang-Mills (SYM) case.
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