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Heavy Quark Diffusion from the Lattice

Peter Petreczky, Derek Teaney

TL;DR

The paper analyzes how heavy quark diffusion in the quark-gluon plasma contributes to Euclidean vector current correlators and assesses the feasibility of constraining transport coefficients from lattice data. It combines Langevin dynamics with linear-response theory to relate a low-frequency transport peak in the spectral density to the Euclidean correlator, and models the high-frequency sector with a resonance plus continuum. The main finding is that the Euclidean correlator at τ ≈ β/2 is largely insensitive to the diffusion coefficient at leading order, while the transport peak width affects higher τ derivatives and could be detectable if the diffusion is sufficiently small; a two-component spectral ansatz and a heavy-quark chemical-potential difference are proposed as practical lattice strategies to isolate and measure the transport signal. The work provides a concrete framework and methodology for lattice QCD studies to constrain heavy quark transport properties in the QGP.

Abstract

We study the diffusion of heavy quarks in the Quark Gluon Plasma using the Langevin equations of motion and estimate the contribution of the transport peak to the Euclidean current-current correlator. We show that the Euclidean correlator is remarkably insensitive to the heavy quark diffusion coefficient and give a simple physical interpretation of this result using the free streaming Boltzmann equation. However if the diffusion coefficient is smaller than $\sim 1/(πT)$, as favored by RHIC phenomenology, the transport contribution should be visible in the Euclidean correlator. We outline a procedure to isolate this contribution.

Heavy Quark Diffusion from the Lattice

TL;DR

The paper analyzes how heavy quark diffusion in the quark-gluon plasma contributes to Euclidean vector current correlators and assesses the feasibility of constraining transport coefficients from lattice data. It combines Langevin dynamics with linear-response theory to relate a low-frequency transport peak in the spectral density to the Euclidean correlator, and models the high-frequency sector with a resonance plus continuum. The main finding is that the Euclidean correlator at τ ≈ β/2 is largely insensitive to the diffusion coefficient at leading order, while the transport peak width affects higher τ derivatives and could be detectable if the diffusion is sufficiently small; a two-component spectral ansatz and a heavy-quark chemical-potential difference are proposed as practical lattice strategies to isolate and measure the transport signal. The work provides a concrete framework and methodology for lattice QCD studies to constrain heavy quark transport properties in the QGP.

Abstract

We study the diffusion of heavy quarks in the Quark Gluon Plasma using the Langevin equations of motion and estimate the contribution of the transport peak to the Euclidean current-current correlator. We show that the Euclidean correlator is remarkably insensitive to the heavy quark diffusion coefficient and give a simple physical interpretation of this result using the free streaming Boltzmann equation. However if the diffusion coefficient is smaller than , as favored by RHIC phenomenology, the transport contribution should be visible in the Euclidean correlator. We outline a procedure to isolate this contribution.

Paper Structure

This paper contains 9 sections, 106 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Linear Response and the Spectral Density
  3. Transport in Euclidean Correlators
  4. Heavy Quark Diffusion in the Langevin Effective Theory
  5. Numerical Estimate of the Euclidean Correlator
  6. Brief Summary and Discussion
  7. Diffusion of a Brownian Particle
  8. The Free Spectral Function
  9. Resonance Spectral Function

Figures (4)

  • Figure 2: The ratio $G_{JJ}(\tau,T)/G_{JJ}^{\rm rec}(\tau,T)$ for different temperatures and ${\bf k}=0$.
  • Figure 3: The difference of correlators at $\mu_c=M_c/5$ and $\mu=0$ for the (a) Lorentzian and (b) Gaussian ansätze and various values of the diffusion coefficient, D.
  • Figure 4: The relative transport contribution to the correlator as a function of quark mass, Eq. (\ref{['massratio']}), for the (a) Lorentzian and (b) Gaussian ansätze to the low frequency spectral function. The numbers indicate the diffusion coefficient for each ansatz.
  • Figure 5: Feynman graph contributing to the free spectral function