Non-perturbative quarkonium dissociation rates in strongly coupled quark-gluon plasma

TL;DR

The paper develops a nonperturbative, lattice-QCD-constrained $T$-matrix framework to compute heavy-quarkonium dissociation rates in a strongly coupled QGP. By self-consistently treating in-medium HQ binding, HL interactions, and off-shell parton spectral functions, it reveals large nonperturbative enhancements of dissociation rates, especially for excited states, and highlights interference effects that suppress ground-state rates at low temperatures. The work systematically contrasts quasifree, on-shell, and off-shell treatments and compares to dipole EFT expectations, identifying regimes where the dipole approximation holds. The findings have direct implications for heavy-ion phenomenology, suggesting altered suppression and regeneration patterns and underscoring the need to incorporate these nonperturbative rates into transport simulations of URHICs.

Abstract

Heavy quarks and quarkonia are versatile probes of the transport properties of the hot QCD medium produced in ultra-relativistic heavy-ion collisions (URHICs). A robust description of heavy-flavor transport coefficients requires a microscopic approach that treats the open and hidden heavy-flavor sectors on the same footing. Here, we employ the quantum many-body $T$-matrix formalism to evaluate the dissociation rates of heavy quarkonia in the quark-gluon plasma (QGP). The basic ingredient is the heavy-light $T$-matrix, which utilizes a nonperturbative driving kernel constrained by lattice-QCD data. Its resummation in a ladder series provides a much enhanced interaction strength compared to previously used perturbative coupling to the quasiparticle partons in the QGP. The in-medium quarkonium properties, particularly their temperature-dependent binding energies, are evaluated self-consistently using the same interaction kernel, including interference effects (also referred to as the imaginary part of the heavy-quark potential) as well as off-shell parton spectral functions. We systematically investigate the interplay of these effects and elaborate on the connections to the dipole approximation used in effective field theory.

Figures (20)

• Figure 1: Scattering of heavy quarks with heavy antiquarks (left), gluons (middle) and light quarks or antiquarks ($u$, $d$, $s$, right).
• Figure 2: Feynman diagrams for the selfenergies of partons ($j=Q,i$) in the QGP calculated by closing the in-medium $T$-matrix with a thermal gluon (left) or light quark/antiquark (right) propagator in the heat bath.
• Figure 3: The in-medium potentials $\widetilde{V}(r)$ between a heavy quark and antiquark as a function of distance $r$ at different temperatures in a strongly coupled scenario (SCS), constrained by HQ free energies (left) and in a scenario constrained by WLCs (right).
• Figure 4: The negative imaginary (solid) part and real part (dashed) of the charm-gluon $T\text{-matrix}$ in the color-triplet channel, $T_{cg}$ (left), and the charm-light-quark $T\text{-matrix}$ in the color-singlet channel, $T_{c \bar{q}}$ (right), as functions of energy at various temperatures and zero relative momentum ($p=0$). The upper (lower) panels correspond to the SCS (WLC) constraints.
• Figure 5: Spectral functions of heavy quarks and light partons at $p=0$ in the QGP for increasing temperature from top to bottom, in the SCS (left panels) and WLC scenario (right panels).