Model study of the energy dependence of the correlation between anisotropic flow and the mean transverse momentum in Au + Au collisions
A hybrid model that employs the hadron-string transport model UrQMD and the (3+1)-dimensional relativistic viscous hydrodynamic code vHLLE, is used to investigate the beam energy dependence of the correlation coefficient ρ(v$^{2}_{2}$,[p T ]) between the average transverse momentum [p T ] of hadrons emitted in an event and the square of the anisotropic flow coefficient v$^{2}_{2}$. For Au+Au collisions, the model predicts characteristic patterns for the energy and event-shape dependence of the variances for [p T ] and v$^{2}_{n}$ [Var([p T ] and Var(v$^{2}_{2}$)], and the covariance of v$^{2}_{n}$ and [p T ][cov(v$^{2}_{2}$,[p T ])], consistent with the attenuation effects of the specific shear viscosity η/s. Here in contrast, ρ(v$^{2}_{2}$,[p T ]) is predicted to be insensitive to the beam energy but sensitive to the initial-state geometry of the collisions. These observations suggest that a precise set of measurements for Var([p T ]), Var(v$^{2}_{2}$), cov(v$^{2}_{2}$,[p T ]) and ρ(v$^{2}_{2}$,[p T ]) as a function of beam energy and event shape, could serve to constrain better the eccentricities and their fluctuations over the entire span of beam energies, and consequently aid precision extraction of the temperature and baryon chemical-potential dependence of η/s from the wealth of Au+Au data obtained in the RHIC beam energy scan.