Measuring the Rate of Isotropization of Quark-Gluon Plasma Using Rapidity Correlations

TL;DR

This paper proposes using rapidity-dependent momentum correlations to measure the shear relaxation time in quark-gluon plasma, linking initial anisotropy fluctuations to observable rapidity correlation patterns, and compares estimates with experimental data.

Contribution

It introduces a method to extract the shear relaxation time from rapidity correlations using a second order causal diffusion equation with Langevin noise.

Findings

Rapidity correlations are sensitive to the shear relaxation time.

Estimated ratio τ_π/ν ≈ 5-6 from comparison with RHIC data.

Initial anisotropy fluctuations influence freeze-out correlations.

Abstract

We propose that rapidity dependent momentum correlations can be used to extract the shear relaxation time $\tau_\pi$ of the medium formed in high energy nuclear collisions. The stress-energy tensor in an equilibrium quark-gluon plasma is isotropic, but in nuclear collisions it is likely very far from this state. The relaxation time $\tau_\pi$ characterizes the rate of isotropization and is a transport coefficient as fundamental as the shear viscosity. We show that fluctuations emerging from the initial anisotropy survive to freeze-out, in excess of thermal fluctuations, influencing rapidity correlation patterns. We show that these correlations can be used to extract $\tau_\pi$. We describe a method for calculating the rapidity dependence of two-particle momentum correlations with a second order, causal, diffusion equation that includes Langevin noise as a source of thermal fluctuations. The causality requirement introduces the relaxation time and we link the shape of the rapidity correlation pattern to its presence. Here we examine how different equations of state and temperature dependent transport coefficients in the presence of realistic hydrodynamic flow influence the estimate of $\tau_\pi$. In comparison to RHIC data, we find that the ratio $\tau_\pi/\nu \approx 5-6$ where $\nu=\eta/sT$ is the kinematic viscosity.