[Paper Review] Shear viscosity and spectral function of the quark matter

Masaharu Iwasaki, Hiromasa Ohnishi+1 more|ArXiv.org|Jun 19, 2006

High-Energy Particle Collisions Research2 references3 citations

TL;DR

This paper calculates the shear viscosity of quark matter using the Kubo-Mori formula, expressing it in terms of the quark spectral function. Assuming a modified Bright-Wigner form for the spectral function, it finds that viscosity decreases rapidly with increasing quark width Γ, indicating that strongly interacting quark matter behaves as a nearly perfect fluid, consistent with RHIC data on quark-gluon plasma.

ABSTRACT

We discuss the shear viscosity of the quark matter by using the Kubo-Mori formula. It is found that the shear viscosity is expressed in terms of the quark spectral function. If the spectral function is approximated by a modified Bright-Wigner type, the viscosity decreases as the width of the spectral function increases. We also discuss dependence of the shear viscosity on the temperature and the density.

Motivation & Objective

• To calculate the shear viscosity of quark matter in the quark-gluon plasma phase using a field-theoretic approach.
• To investigate how the viscosity depends on temperature, density, and the quark spectral function's width.
• To explore the connection between quark spectral properties and transport coefficients in hot, dense quark matter.
• To provide a phenomenological framework linking spectral functions to viscosity, relevant to RHIC experimental observations of low-viscosity matter.

Proposed method

• Uses the Kubo-Mori formula to express shear viscosity η(T) in terms of the retarded correlation function of the energy-momentum tensor component Jxy.
• Applies the Matsubara formalism and analytic continuation to compute the retarded Green’s function ΠR(ω) from the imaginary-time correlation function.
• Employs the Nambu-Jona-Lasinio (NJL) model to describe the quark sector, with the quark propagator represented via a spectral function.
• Assumes a modified Bright-Wigner spectral function ρ(p,ω) = 2Γ·sgn(p0)/[(p·γ−M)² + Γ²] to model quark excitations with finite width.
• Performs a contour integral over Matsubara frequencies and evaluates the trace involving γ² matrices and the spectral function to derive the viscosity integral.
• Numerically evaluates the resulting viscosity integral over momentum and energy, with parameters M (effective mass), Γ (width), T (temperature), and μ (chemical potential).

Experimental results

Research questions

• RQ1 How does the shear viscosity of quark matter depend on the width of the quark spectral function?
• RQ2 What is the role of the quark spectral function in determining transport properties like viscosity?
• RQ3 How does the viscosity vary with temperature and chemical potential in the quark matter phase?
• RQ4 To what extent does a finite spectral width lead to a strongly interacting, near-perfect fluid behavior in quark matter?

Key findings

• Shear viscosity decreases rapidly with increasing quark width Γ, indicating that stronger interactions (larger Γ) lead to lower viscosity.
• At Γ = 0, viscosity diverges, corresponding to a non-interacting ideal gas, while as Γ → ∞, viscosity vanishes, indicating perfect fluidity.
• Viscosity increases with temperature, consistent with classical gas viscosity scaling η ∝ ρvl/3.
• Viscosity shows only a weak dependence on density (chemical potential), increasing slowly with μ.
• The modified Bright-Wigner spectral function provides a phenomenological framework where viscosity is directly tied to the quark width, supporting near-perfect fluid behavior under strong interactions.
• The results are consistent with RHIC data suggesting a low-viscosity quark-gluon plasma, though quantitative comparison is not performed due to the phenomenological nature of the spectral function.