Probing Quarkonium Diffusion in a Magnetized Quark-Gluon Plasma

TL;DR

This work develops a self-consistent EBID holographic model to study heavy-quark diffusion in a magnetized QGP, capturing anisotropic transport under a background magnetic field. It combines spectral-function analysis and hydrodynamic expansion to compute the quark-number susceptibility $\chi$, and employs both hydrodynamic and hanging-string formalisms to derive closed-form diffusion coefficients for diffusion parallel and perpendicular to $\mathbf{B}$, revealing distinct magnetic-field and temperature dependencies. The results show $\chi$ increasing with both $B$ and $T$, while $D^{\parallel}$ is enhanced by $B$ and $D^{\perp}$ is suppressed, with nontrivial temperature trends and a near-Tc sensitivity. The hanging-string approach yields results that qualitatively align with the spectral-function findings at finite $B$ but differ at $B=0$, illustrating the influence of frame choices and scale hierarchies in holographic implementations. Overall, the EBID framework provides a coherent, nonperturbative lens to probe anisotropic quarkonium diffusion in magnetized QGP with potential connections to lattice results and heavy-ion phenomenology.

Abstract

Motivated by the potential experimental relevance of magnetically affected heavy-quark diffusion, we consider here a five-dimensional nonlinear Einstein-Born-Infeld-dilaton model to not only holographically model the QCD thermodynamics in a magnetic background, but also to probe the charged inner structure of a heavy quarkonium. The dual model's gravitational equations of motion can be solved in analytical form via the potential reconstruction method. Using a variety of tools -- spectral functions, hydrodynamic expansions or hanging strings -- we study the anisotropic diffusion constants and heavy-quark number susceptibility, each time reporting closed form expressions.

Figures (12)

• Figure 1: The variation of the deconfined transition temperature $T_c$ with magnetic field. In units of GeV.
• Figure 2: Quark number susceptibility $\chi$ as a function of magnetic fields.
• Figure 3: The rescaled quark number susceptibility $\chi/T^2$ as a function of temperature for different values of the magnetic field. In units GeV.
• Figure 4: Heavy quark diffusion coefficient as a function of magnetic field for different temperatures in parallel directions to the magnetic field. In GeV units.
• Figure 5: Heavy quark diffusion coefficient as a function of magnetic field for different temperatures in perpendicular directions to the magnetic field. In GeV units.