Relaxation-time approximation with pair production and annihilation processes

Amaresh Jaiswal,Radoslaw Ryblewski,Samapan Bhadury,Wojciech Florkowski

doi:10.1103/physrevc.102.064910

Abstract

We extend the Boltzmann equation in the relaxation time approximation to explicitly include transitions between particles forming an interacting mixture. Using the detailed balance condition as well as conditions of energy-momentum and current conservation, we show that only two independent relaxation time scales are allowed in such an interacting system. Dissipative hydrodynamic equations and the form of transport coefficients is subsequently derived for this case. We find that the shear and bulk viscosity coefficients, as well as the baryon charge conductivity are independent of the transition time scale. However, the bulk viscosity and conductivity coefficients that can be attributed to the individual components of the mixture depend on the transition time.

Highlights

Quantum chromodynamics (QCD) is the fundamental theory of strong interactions
Using the detailed balance condition as well as conditions of energy-momentum and current conservation, we show that only two independent relaxation time scales are allowed in such an interacting system
We showed that the coefficient of shear viscosity, η, is independent of γ and the transition time scale

Summary

Introduction

High energy heavy-ion collision experiments at the Relativistic Heavy Ion Collider (RHIC) at Brookhaven and the Large Hadron Collider (LHC) at CERN, Geneva, provide the opportunity to create hot and dense QCD matter and study its properties [1]. The phenomenological study of space-time evolution of QGP, by analyzing the experimental observables, helps us to understand its thermodynamic and transport properties [2,3]. Relativistic dissipative hydrodynamics has been quite successful in explaining the experimental results indicating that QGP behaves like a nearly thermalized fluid The value of shear viscosity to entropy density ratio, extracted from hydrodynamic analysis of flow data The value of shear viscosity to entropy density ratio, extracted from hydrodynamic analysis of flow data (for recent results see Ref. [9]), was found to be very close to the lower bound [10,11], which led to the claim that QGP is the most perfect fluid ever observed

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Conclusion