Acoustic scaling of linear and mode-coupled anisotropic flow; implications for precision extraction of the specific shear viscosity

TL;DR

This study reveals an acoustic scaling pattern in linear and nonlinear flow coefficients in Pb+Pb collisions, providing new constraints for precise extraction of the matter's shear viscosity and initial-state eccentricity spectrum.

Contribution

It demonstrates a universal acoustic scaling pattern in flow coefficients, enabling more accurate determination of the shear viscosity to entropy ratio in heavy-ion collisions.

Findings

Flow coefficients follow exponential viscous modulation scaling.

Scaling parameters constrain shear viscosity and initial eccentricity.

Pattern applies to both linear and mode-coupled flow coefficients.

Abstract

The $\mathrm{n^{th}}$-order linear flow coefficients $\mathrm{v^L_n \, (n=2,3,4,5)}$, and the corresponding nonlinear mode-coupled ($\mathrm{mc}$) coefficients $\mathrm{v^{mc}_{4,(2,2)}}$, $\mathrm{v^{mc}_{5,(2,3)}}$, $\mathrm{v^{mc}_{6,(3,3)}}$ and $\mathrm{v^{mc}_{6,(2,2,2)}}$, are studied for Pb+Pb collisions at $\sqrt{s_{_{\rm NN}}} = 2.76$ TeV. Both sets of coefficients indicate a common acoustic scaling pattern of exponential viscous modulation, with a rate proportional to the square of the harmonic numbers and the mean transverse momenta (respectively), and inversely proportional to the cube root of the charged particle multiplicity ($\mathrm{(N_{ch})^{1/3}}$), that characterizes the dimensionless size of the systems produced in the collisions. These patterns and their associated scaling parameters, provide new stringent constraints for eccentricity independent estimates of the specific shear viscosity ($\eta/s$) and the viscous correction to the thermal distribution function for the matter produced in the collisions. They also give crucial constraints for extraction of the initial-state eccentricity spectrum.