Acoustic scaling of linear and mode-coupled anisotropic flow; implications for precision extraction of the specific shear viscosity
The n th -order linear flow coefficients v n L ( n = 2 , 3 , 4 , 5 ) , and the corresponding nonlinear mode-coupled ( mc ) coefficients v 4 , ( 2 , 2 ) mc , v 5 , ( 2 , 3 ) mc , v 6 , ( 3 , 3 ) mc , and v 6 , ( 2 , 2 , 2 ) mc , are studied for Pb+Pb collisions at s N N = 2.76 TeV. Both sets of coefficients suggest 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 [ ( N ch ) 1 / 3 ] , which characterizes the dimensionless size of the systems produced in the collisions. These patterns and their associated scaling parameters offer new stringent constraints for eccentricity-independent estimates of the specific shear viscosity η s ( T ) 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.