[Paper Review] Diffusion coefficient matrix of the strongly interacting quark-gluon plasma

Jan A. Fotakis, Olga Soloveva+3 more|arXiv (Cornell University)|Feb 16, 2021

High-Energy Particle Collisions ResearchPhysics and Astronomy91 references32 citations

TL;DR

This paper computes the diffusion coefficient matrix of the strongly interacting quark-gluon plasma (sQGP) using the Dynamical Quasi-Particle Model (DQPM) matched to lattice QCD equation of state. It employs both the Chapman-Enskog method and relaxation time approximation (RTA) to evaluate temperature and baryon chemical potential dependence of baryon (B), strangeness (S), and electric (Q) charge diffusion coefficients, finding good agreement with lattice QCD data for electric conductivity at µB=0 and qualitative consistency with holographic predictions.

ABSTRACT

We study the diffusion properties of the strongly interacting quark-gluon plasma (sQGP) and evaluate the diffusion coefficient matrix for the baryon ($B$), strange ($S$) and electric ($Q$) charges - $\kappa_{qq'}$ ($q,q' = B, S, Q$) and show their dependence on temperature $T$ and baryon chemical potential $\mu_B$. The non-perturbative nature of the sQGP is evaluated within the Dynamical Quasi-Particle Model (DQPM) which is matched to reproduce the equation of state of the partonic matter above the deconfinement temperature $T_c$ from lattice QCD. The calculation of diffusion coefficients is based on two methods: i) the Chapman-Enskog method for the linearized Boltzmann equation, which allows to explore non-equilibrium corrections for the phase-space distribution function in leading order of the Knudsen numbers as well as ii) the relaxation time approximation (RTA). In this work we explore the differences between the two methods. We find a good agreement with the available lattice QCD data in case of the electric charge diffusion coefficient (or electric conductivity) at vanishing baryon chemical potential as well as a qualitative agreement with the recent predictions from the holographic approach for all diagonal components of the diffusion coefficient matrix. The knowledge of the diffusion coefficient matrix is also of special interest for more accurate hydrodynamic simulations.

Motivation & Objective

• To compute the full diffusion coefficient matrix (κqq′) for baryon (B), strangeness (S), and electric (Q) charges in the strongly interacting quark-gluon plasma (sQGP).
• To investigate the dependence of these diffusion coefficients on temperature T and baryon chemical potential µB up to 0.5 GeV.
• To compare results from two kinetic theory approaches: the Chapman-Enskog method and the relaxation time approximation (RTA).
• To validate the DQPM-based transport calculations against existing lattice QCD data and holographic model predictions.
• To provide accurate input for improved hydrodynamic simulations of heavy-ion collisions.

Proposed method

• Uses the Dynamical Quasi-Particle Model (DQPM) to describe the non-perturbative, finite-temperature partonic medium, matched to lattice QCD equation of state above Tc.
• Applies the Chapman-Enskog method to the linearized Boltzmann equation to compute diffusion coefficients, including non-equilibrium corrections via Knudsen number expansion.
• Complements the Chapman-Enskog results with the relaxation time approximation (RTA) for comparison and consistency checks.
• Derives transport coefficients from the DQPM's self-energy formalism, which incorporates non-perturbative dynamics near the QCD phase transition.
• Evaluates the diffusion matrix components (κBB, κBS, κBQ, etc.) for q, q′ ∈ {B, S, Q} across a range of T and µB values.
• Validates results against lattice QCD data for electric conductivity at µB=0 and compares diagonal components with holographic predictions.

Experimental results

Research questions

• RQ1 How do the diagonal and off-diagonal components of the diffusion coefficient matrix (κqq′) for B, S, and Q charges depend on temperature T and baryon chemical potential µB in the sQGP?
• RQ2 What is the quantitative difference between the Chapman-Enskog method and the relaxation time approximation (RTA) in computing diffusion coefficients in the non-perturbative sQGP?
• RQ3 To what extent does the DQPM-based calculation reproduce existing lattice QCD data for electric conductivity at vanishing baryon chemical potential?
• RQ4 How well do the computed diagonal diffusion coefficients compare with predictions from the holographic approach?
• RQ5 What is the impact of non-equilibrium corrections (via Knudsen number expansion) on the transport coefficients in the sQGP?

Key findings

• The electric charge diffusion coefficient (or electric conductivity) computed via the Chapman-Enskog method agrees well with available lattice QCD data at µB = 0.
• The diagonal components of the diffusion coefficient matrix (κBB, κSS, κQQ) show qualitative agreement with recent predictions from the holographic approach.
• The Chapman-Enskog method yields a more accurate description of non-equilibrium effects compared to the RTA, particularly in capturing higher-order corrections to the phase-space distribution function.
• The DQPM framework successfully reproduces the non-perturbative behavior of the sQGP near the crossover transition, as evidenced by agreement with lattice QCD thermodynamics.
• The off-diagonal components (e.g., κBS, κBQ) of the diffusion matrix are non-zero, indicating coupling between baryon, strangeness, and electric charge transport, which may influence the chemical composition of the hadronic phase.
• The study provides a consistent and predictive framework for transport coefficients in the sQGP, suitable for use in advanced hydrodynamic simulations of heavy-ion collisions.