Spectral Signatures of Heavy Quarkonia in a Rotating and Anisotropic Quark-Gluon Plasma: A Holographic Study

TL;DR

This work builds a holographic model of a rotating and anisotropic quark-gluon plasma to compute in-medium spectral functions and effective masses of heavy quarkonia ($J/\Psi$ and $\Upsilon(1S)$). Rotation and anisotropy are implemented in a five-dimensional Einstein–dilaton–two-Maxwell setup with warp factor $c$ and anisotropy parameter $\nu$, and rotation is incorporated via a Lorentz boost with angular velocity $\omega$ and radius $l$, leading to temperature $T=\tilde{T}(\tilde{z}_h,\tilde{\mu},c,\nu)\sqrt{1-\omega^2 l^2}$ and chemical potential $\mu=\tilde{\mu}\sqrt{1-\omega^2 l^2}$. Spectral functions, obtained from a bulk vector field using the membrane paradigm, reveal that increasing $T$, $\mu$, $c$, $\omega$, or $\nu$ suppresses peaks and broadens widths, with distinct polarization-dependent dissociation: anisotropy primarily dissociates longitudinally polarized states, while rotation more strongly disrupts transversely polarized ones. A competitive interplay emerges: for small $\nu$, rotation dominates at high $\omega l$, whereas for large $\nu$, anisotropy governs regardless of rotation; the effective mass exhibits non-monotonic temperature dependence in a polarization-specific manner, notably for $J/\Psi$. These results provide a non-perturbative basis for interpreting polarization-dependent quarkonium suppression in non-central heavy-ion collisions and motivate time-dependent or field-inclusive extensions.

Abstract

We investigate the in-medium spectral functions and effective masses of heavy quarkonia charmonium ($J/Ψ$) and bottomonium ($Υ(1S)$) in a quark-gluon plasma (QGP) possessing both global rotation and spatial anisotropy. Using a gauge/gravity holographic model incorporating finite temperature, chemical potential, and warp factor, we compute the spectral signatures non-perturbatively. Our results show that both rotation and anisotropy enhance quarkonium dissociation, manifesting as peak suppression and width broadening in the spectral functions. Crucially, their effects are directional: anisotropy primarily dissociates longitudinally polarized states, while rotation more strongly disrupts transversely polarized ones. A competitive interplay exists: for small anisotropy, rotational effects dominate at high angular velocity, whereas for large anisotropy, anisotropy governs the dissociation regardless of rotation strength. Furthermore, rotation induces a non-monotonic temperature dependence in the transverse effective mass of $J/Ψ$, while strong anisotropy causes similar non-monotonicity in the longitudinal effective mass of $J/Ψ$. These findings reveal how the distinct symmetry breaking patterns induced by QGP rotation and anisotropy reshape the heavy quarkonium spectrum, providing new insights into polarization-dependent suppression in non-central heavy-ion collisions.

Figures (7)

• Figure 1: Spectral functions of $J/\Psi$ and $\Upsilon (1S)$ at different temperatures, with fixed anisotropy parameter $\nu = 1.05$, $\mu = 0.1\,{\rm{GeV}},c = - 0.3\;{\rm{Ge}}{{\rm{V}}^2}$ and $\omega = 0.3~{\rm{GeV}}$. Panels (a) and (b) correspond to $J/\Psi$, while (c) and (d) correspond to $\Upsilon (1S)$. The left panels (a, c) show the spectral function parallel to the anisotropic direction (i.e., the direction of the rotational angular velocity), and the right panels (b, d) show the spectral function perpendicular to it.
• Figure 2: Spectral functions of $J/\Psi$ and $\Upsilon (1S)$ at different chemical potentials ($\mu$), with fixed temperature $T$ = 0.4 GeV and $c = -0.3\;{\text{Ge}}{{\text{V}}^2}$. Panels (a) and (b) correspond to $J/\Psi$ , while (c) and (d) correspond to $\Upsilon (1S)$. The left panels (a, c) show the spectral function parallel to the anisotropic direction, and the right panels (b, d) show the spectral function perpendicular to it.
• Figure 3: Spectral functions of $J/\Psi$ and $\Upsilon (1S)$ with varying warp factor coefficient, at fixed temperature, $T$ = 0.4 GeV, chemical potential $\mu = 0.1 ~\textrm{GeV}$. Panels (a) and (b) correspond to $J/\Psi$, (c) and (d) correspond to $\Upsilon (1S)$. For each meson, left/right panels show longitudinal/transverse polarizations relative to the anisotropic direction respectively.
• Figure 4: Spectral functions of $J/\Psi$ and $\Upsilon (1S)$ at $\mu = 0.1\,{\rm{GeV}},c = - 0.3\;{\rm{Ge}}{{\rm{V}}^2}$ and $T$ = 0.4 GeV under varying angular velocities, comparing two anisotropy strengths: (a, c) correspond to smaller anisotropy ($\nu = 1.025$); (b, d) correspond to larger anisotropy ($\nu = 1.1$). Panels (a, b) show $J/\Psi$, and panels (c, d) show $\Upsilon (1S)$. Left/right sides within each meson correspond to longitudinal/transverse polarizations relative to the anisotropic direction.
• Figure 5: The effective mass of $J/\Psi$ and $\Upsilon (1S)$ as a function of temperature with different angular velocities at $\mu = 0.1\, {\rm{GeV}}, c = - 0.3\;{\rm{Ge}}{{\rm{V}}^2}$ and $\nu = 1.1$. Panels (a) and (b) are the effective mass of $J/\Psi$, and panels (c) and (d) are the effective mass of $\Upsilon (1S)$. (a) and (c) are parallel to the anisotropic direction, and (b) and (d) are perpendicular to the anisotropic direction.