[Paper Review] Collision term dependence of the hadronic shear viscosity and diffusion coefficients

Jan Hammelmann, Jan Staudenmaier+1 more|arXiv (Cornell University)|Jul 28, 2023

High-Energy Particle Collisions ResearchPhysics and Astronomy3 citations

TL;DR

This study investigates the collision term dependence of hadronic shear viscosity (η) and diffusion coefficients (κ_ij) using the SMASH transport model and Green-Kubo formalism. It reveals that multi-particle reactions reduce η in a simplified hadron gas, while elastic cross sections and angular distributions significantly alter η and κ_ij—especially in the full hadron gas—highlighting strong sensitivity to microscopic interaction treatments.

ABSTRACT

In this work the shear viscosity $η$ and the diffusion coefficients of conserved charges $κ_{ij}$ with $i,j\in\{B,Q,S\}$ of hadronic matter are investigated within the hadronic transport approach SMASH. We systematically study the effect of multi-particle reactions, angular distributions and additional elastic cross sections via the additive quark model description, the numbers of degrees of freedom and the baryon density on the transport coefficients using the Green-Kubo formalism. We find that multi-particle reactions decrease the shear viscosity in a simplified hadron gas whereas the electric charge diffusion coefficient is not modified. Furthermore, additional elastic cross sections have a strong impact on both $η$ and $κ_{ij}$ whereas anisotropic scatterings enhance the shear viscosity in the full hadron gas. When increasing the number of degrees of freedom the shear viscosity is only slightly modified in comparison to the diffusion coefficients. Finally, the calculation within a finite baryon chemical potential reveals that the shear viscosity itself does not depend on $μ_B$ but on the ratio $η/ s$. The diffusion coefficients show a strong dependency which we compare to Chapman-Enskog calculations.

Motivation & Objective

• To understand how microscopically modeled interactions—such as multi-particle reactions, elastic cross sections, and angular distributions—affect transport coefficients in hadronic matter.
• To determine the sensitivity of shear viscosity (η) and diffusion coefficients (κ_ij) for conserved charges (B, Q, S) to the treatment of collision terms in the hadronic transport model SMASH.
• To assess the role of degrees of freedom, baryon density, and baryon chemical potential (μ_B) in shaping η and κ_ij.
• To compare simulation results with kinetic theory (Chapman-Enskog) and evaluate consistency with hydrodynamic expectations.

Proposed method

• Employed the SMASH transport model to simulate infinite matter under various hadronic interaction conditions.
• Applied the Green-Kubo formalism to extract η and κ_ij from time correlation functions of stress-energy and charge currents.
• Systematically switched on/off specific cross sections (e.g., multi-particle reactions, elastic processes, angular distributions) to isolate their contributions.
• Used three distinct systems: (1) stable hadrons with constant elastic cross sections; (2) extended resonances; (3) full SMASH hadron gas with all implemented degrees of freedom.
• Validated results against kinetic theory calculations, particularly Chapman-Enskog, for consistency.
• Performed simulations across temperatures and baryon chemical potentials to probe μ_B dependence.

Experimental results

Research questions

• RQ1 How do multi-particle reactions influence the shear viscosity η in a simplified hadron gas model?
• RQ2 To what extent do elastic cross sections and angular distributions affect η and the diffusion coefficients κ_ij in the full hadron gas?
• RQ3 How does increasing the number of degrees of freedom impact the scaling behavior of η and κ_ij?
• RQ4 What is the dependence of η and η/s on the baryon chemical potential μ_B, and how does it compare to thermodynamic expectations?
• RQ5 How do the diffusion coefficients κ_ij scale with temperature and μ_B, and do they follow the same trends as predicted by Chapman-Enskog theory?

Key findings

• Multi-particle reactions reduce the shear viscosity η in a simplified hadron gas at temperatures T ≳ 140 MeV, while the electric charge diffusion coefficient remains unchanged.
• Additional elastic cross sections significantly decrease both η and κ_ij in the full SMASH hadron gas, indicating strong sensitivity to elastic scattering rates.
• Anisotropic angular distributions increase the shear viscosity η but do not affect the diffusion coefficients κ_ij.
• Increasing the number of degrees of freedom has a minor effect on η but strongly modifies the diffusion coefficients, with the baryonic sector showing different scaling than the charge sector.
• Shear viscosity η is independent of μ_B, but η/s and ηT/w depend only on thermodynamic properties, contradicting earlier assumptions of μ_B dependence.
• The κ_ij/T² matrix exhibits a strong μ_B dependence and develops a plateau-like behavior at μ_B ≈ 600 MeV, consistent with Chapman-Enskog predictions.