Quarkonium in a QCD medium with momentum-dependent relaxation time

TL;DR

This work studies quarkonium behavior in a hot QCD medium by incorporating momentum-dependent relaxation times via the extended relaxation time approximation (ERTA). It combines HTL-based non-equilibrium corrections to the gluon self-energy and dielectric screening with ERTA-driven kinetic theory and a Bjorken expansion to track time-dependent screening and quarkonium properties. The study finds that non-equilibrium effects, especially those enhanced by larger momentum dependence ℓ, significantly modify both the real and imaginary parts of the in-medium potential, leading to stronger screening and larger thermal widths for quarkonia (notably J/ψ) at early times, with effects diminishing as the system cools. These results highlight the critical role of microscopic relaxation dynamics in quarkonium phenomenology and motivate future extensions to temperature-dependent ℓ and 3D hydrodynamic evolutions for more realistic heavy-ion collision modeling.

Abstract

In this study, we explore the properties of quarkonia in a hot QCD medium using a newly proposed collision kernel that consistently incorporates the particle's momentum dependence into the relaxation time scale of the medium. The longitudinal component of the gluon self-energy, along with the Debye screening mass, is computed within the one-loop hard thermal loop framework by incorporating non-equilibrium corrections. A modified kinetic theory with an extended relaxation time approximation is employed to model the non-equilibrium dynamics of the QCD medium. The sensitivity of the heavy quarkonia potential to the momentum dependence of the relaxation time is studied. Further, we studied the binding energy and thermal width of quarkonia states within this new kinetic theory. Sizable variations in the temperature behavior of these quantities are observed in comparison with the standard relaxation time approximation method due to the particle momentum dependence on the relaxation timescale of the QCD medium. Our findings highlight that accounting for the microscopic nature of the collision timescale is crucial for understanding the quarkonium behavior in a QCD medium.

Figures (6)

• Figure 1: Temperature evolution of the medium as a function of its proper time ($\tau$) for equilibrium and non-equilibrium scenarios within the ERTA for different values of the momentum-dependence parameter $\ell$.
• Figure 2: The ratio of $\delta m_D$ to the total screening mass $m_D$ is plotted against the proper time $\tau$ for different values of $\ell$ (left panel). In the right panel, this ratio is plotted against $\ell$ at $\tau= 2$ fm/c which corresponds to $T\sim 235$ MeV in the equilibrium scenario.
• Figure 3: The real part of a quarkonia potential is plotted against the distance, $r$ between the heavy quarks, for various values of $\ell$ at proper times, $\tau=0.6$ fm/c corresponding to $T \sim 350$ MeV (left panel) and $\tau=2$ fm/c corresponding to $T \sim 235$ MeV (right panel).
• Figure 4: The imaginary part of a quarkonia potential is plotted against the distance $r$ between the quark anti-quark pair for various values of $\ell$ at $\tau=0.6$ fm/c. The left panel shows both the contributions from coulomb and string parts to the imaginary potential for each $\ell$ along with the equilibrium case, and the right panel shows the total value of the imaginary potential for both the equilibrium and non-equilibrium scenarios.
• Figure 5: The imaginary part of a quarkonia potential is plotted against the distance $r$ between the quark antiquark pair for various values of $\ell$ at $\tau=2$ fm/c. The left panel shows both the contributions from coulomb and string parts to the imaginary potential for each $\ell$ along with the equilibrium case, and the right panel shows the total value of the imaginary potential for both the equilibrium and non-equilibrium scenarios.