Dispersion Relations and Pole-Skipping in a Holographic Charmonium Model with Rotating Plasma

TL;DR

This work studies charmonium in a rotating quark-gluon plasma using a bottom-up holographic QCD model. By computing quasinormal modes, retarded Green’s functions, and spectral functions in longitudinal and transverse sectors, it uncovers how rotation (through the Lorentz factor γ) and system size (radius l) modify meson masses, widths, and diffusion, with pole-skipping points linked to hydrodynamic modes in the longitudinal channel and to Matsubara-like structures in the transverse channel. A key result is the rotation-induced suppression of charmonium stability, especially in the transverse direction, and a rotation- and geometry-dependent spin alignment that qualitatively tracks experimental data. The study provides a holographic framework to connect microscopic spectral features to macroscopic transport and spin observables in non-central heavy-ion collisions, laying groundwork for incorporating magnetic fields and more realistic QGP dynamics.

Abstract

In this paper, we employ a bottom-up holographic QCD model to investigate the dissociation of charmonium states moving in a rotating medium by calculating their quasinormal modes. We begin by reviewing the holographic quarkonium spectrum at zero temperature. Then, we derive the equations of motion for heavy vector mesons propagating in a rotating plasma, separating the analysis into longitudinal and transverse directions relative to the wave vector. Additionally, we compute the charge diffusion constant in the rotating background and analyze the pole-skipping phenomenon, which emerges in the retarded Green's function. Finally, we investigate the impact of rotation on the spin alignment of the J/psi state in the helicity frame, utilizing the spectral function obtained from the holographic framework.

Figures (13)

• Figure 1: We display the spectral function for various values of linear momentum at $T = 200$ MeV, $\Omega = 20$ MeV, and $l = 3$ fm: the left panel corresponds to the longitudinal direction, while the right panel shows the transverse direction.
• Figure 2: On the left, we show the spectral function in the longitudinal direction for various values of the radius $l$ at $q = 1$ GeV, $T = 200$ MeV, and $\Omega = 20$ MeV. On the right, the spectral function in the transverse direction is presented for the same set of parameters.
• Figure 3: The frequencies of the first three quarkonium modes in the direction longitudinal to the wave vector, computed as a function of momentum using the shooting method at $T = 200$ MeV, $\Omega = 20$ MeV, and $l = 3$ fm, are presented.
• Figure 4: The quasinormal frequencies for the ground state are displayed as a function of $\bar{\Omega}$ for different values of momentum. The temperature is fixed at $T = 200$ MeV.
• Figure 5: 3D plots of the quasinormal frequencies for the ground state at $200$ MeV. The right panel shows the real part of the frequency as a function of momentum and angular velocity, while the left panel shows the imaginary part.