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A hybrid model that employs the hadron-string transport model UrQMD and the(3+1)D relativistic viscous hydrodynamic code vHLLE, is used to investigate thebeam energy dependence of the correlation coefficient $\rho(v^{2}_{2},[p_{T}])$between the average transverse momentum $[p_{T}]$ of hadrons emitted in anevent and the square of the anisotropic flow coefficient $v_2^2$. For Au+Aucollisions, the model predicts characteristic patterns for the energy andevent-shape dependence of the variances for $[p_{T}]$ and $v_n^2$ (${\rmVar}([p_T])$ and ${\rm Var}(v_2^2)$), and the covariance of $v_n^2$ and$[p_{T}]$ (${\rm cov}(v_{2}^{2},[p_T])$), consistent with the attenuationeffects of the specific shear viscosity $\eta/s$. In contrast,$\rho(v^{2}_{2},[p_{T}])$ is predicted to be insensitive to the beam energy butsensitive to the initial-state geometry of the collisions. These observationssuggest that a precise set of measurements for ${\rm Var}([p_T])$, ${\rmVar}(v_2^2)$, ${\rm cov}(v_{2}^{2},[p_T])$ and $\rho(v^{2}_{2},[p_{T}])$ as afunction of beam-energy and event-shape, could aid precision extraction of thetemperature and baryon chemical-potential dependence of $\eta/s$ from thewealth of Au+Au data obtained in the RHIC beam energy scan.

Model study of the energy dependence of the correlation between anisotropic flow and the mean transverse momentum in Au+Au collisions