Transport coefficients in Yang-Mills theory and QCD

Area of Science:

• High-energy physics
• Quantum field theory
• Thermodynamics

Background:

• The shear viscosity to entropy density ratio (η/s) is a crucial probe of the fluid properties of strongly interacting matter.
• Understanding η/s in Yang-Mills theory and Quantum Chromodynamics (QCD) is essential for interpreting heavy-ion collision experiments.

Purpose of the Study:

• To calculate the η/s ratio in Yang-Mills theory using a first-principles approach.
• To develop an analytic formula describing the temperature dependence of η/s.
• To provide an initial estimate of η/s in QCD.

Main Methods:

• Utilized the Kubo formula for viscosity calculation.
• Employed an exact diagrammatic representation with full propagators and vertices.
• Incorporated gluon spectral functions as input.
• Fitted the results to an analytic function across the temperature spectrum.

Main Results:

• An analytic fit formula for η/s in Yang-Mills theory was derived.
• The temperature dependence of η/s spans from a glueball resonance gas at low temperatures to a high-temperature regime.
• Results are consistent with perturbative QCD calculations at high temperatures.
• A first estimate for η/s in QCD was obtained.

Conclusions:

• The study provides a comprehensive calculation of η/s in Yang-Mills theory with broad temperature applicability.
• The derived analytic formula offers a valuable tool for theoretical and experimental studies.
• The findings contribute to a better understanding of the transport properties of strongly interacting matter.