[Paper Review] Quark Mass Dependence of Heavy Quark Diffusion Coefficient from Lattice QCD

Luis Altenkort, David de la Cruz+7 more|arXiv (Cornell University)|Nov 2, 2023

High-Energy Particle Collisions Research48 references4 citations

TL;DR

This study presents the first lattice QCD calculation of the quark mass dependence of the heavy quark spatial diffusion coefficient $D_s$ at finite temperature with dynamical light quarks (pion mass 320 MeV). Using continuum-extrapolated correlators and a quasi-particle model, it finds $D_s$ for charm and bottom quarks is significantly smaller than phenomenological estimates, resolving a long-standing discrepancy in heavy quark thermalization models.

ABSTRACT

We present the first study of the quark mass dependence of the heavy quark momentum and spatial diffusion coefficients using lattice QCD with light dynamical quarks corresponding to a pion mass of 320 MeV. We find that, for the temperature range 195 MeV $

Motivation & Objective

• To resolve the discrepancy between phenomenological transport models and lattice QCD results for heavy quark diffusion coefficients in the quark-gluon plasma.
• To investigate how the spatial diffusion coefficient $D_s$ of heavy quarks depends on their mass in a finite-temperature QCD medium with dynamical light quarks.
• To compute $D_s$ using lattice QCD with physical pion mass (320 MeV) and continuum extrapolation, enabling direct comparison with experimental data.
• To assess the role of quark mass dependence in explaining the underestimation of $D_s$ in previous infinite-mass lattice calculations compared to phenomenology.

Proposed method

• Lattice QCD simulations with 2+1 dynamical quarks using the Highly Improved Staggered Quark action and tree-level improved Lüscher-Weisz gauge action at five temperatures between 195 and 352 MeV.
• Continuum extrapolation of the chromo-magnetic field correlator $G_B( au, T)$ using three lattice spacings per temperature to extract the spectral function $\rho_B(\omega, T)$.
• Application of the Kubo formula to compute the momentum diffusion coefficient $\kappa$ from $\kappa_E$ and $\kappa_B$, with $\kappa_B$ governing the $M$-dependence.
• Use of a quasi-particle model to extract the charm quark mass from lattice data on the charm quark number susceptibility, enabling calculation of $\langle v^2 \rangle$ and $\langle p^2 \rangle$.
• Calculation of $D_s$ via the relation $D_s = \frac{2T^2}{\kappa} \frac{\langle p^2 \rangle}{3MT}$, with uncertainties propagated from $\kappa$ and charm mass.

Experimental results

Research questions

• RQ1 How does the spatial diffusion coefficient $D_s$ of heavy quarks depend on their mass in finite-temperature QCD with dynamical light quarks?
• RQ2 Does the quark mass dependence of $D_s$ explain the discrepancy between previous infinite-mass lattice QCD results and phenomenological estimates from heavy-ion data?
• RQ3 What is the value of $D_s$ for charm and bottom quarks at temperatures between 195 MeV and 352 MeV, and how does it compare to phenomenological models?
• RQ4 To what extent do thermal effects and mass shifts influence the computed $D_s$ values for heavy quarks in the QGP?

Key findings

• The spatial diffusion coefficient $D_s$ for charm quarks is $1.338(279)(12)$ in units of $2\pi T$ at $T = 195$ MeV, decreasing with increasing temperature.
• For bottom quarks with mass 4.5 GeV, $D_s = 1.242(267)$ at $T = 195$ MeV, showing a similar trend of decreasing $D_s$ with increasing $T$.
• The $D_s$ values for both charm and bottom quarks are significantly smaller than those used in phenomenological models that fit $p_T$ spectra and elliptic flow data.
• The uncertainty in $D_s$ due to charm quark mass is small, with $\sim$10% variation across the temperature range, indicating robustness of the result.
• The mass dependence of $\kappa_B$ is the dominant source of $M$-dependence in $\kappa$, and thus in $D_s$, confirming the theoretical expectation.
• The results show a smooth connection between the 2+1 flavor lattice results and the quenched limit at high temperatures, validating the extrapolation procedure.