Estimation of the shear viscosity at finite net-baryon density from $A+A$ collision data at $\sqrt{s_\mathrm{NN}} = 7.7-200$ GeV

Hybrid approaches based on relativistic hydrodynamics and transport theory have been successfully applied for many years for the dynamical description of heavy ion collisions at ultrarelativistic energies. In this work a new viscous hybrid model employing the hadron transport approach UrQMD for the early and late non-equilibrium stages of the reaction, and 3+1 dimensional viscous hydrodynamics for the hot and dense quark-gluon plasma stage is introduced. This approach includes the equation of motion for finite baryon number, and employs an equation of state with finite net-baryon density to allow for calculations in a large range of beam energies. The parameter space of the model is explored, and constrained by comparison with the experimental data for bulk observables from SPS and the phase I beam energy scan at RHIC. The favored parameter values depend on energy, but allow to extract the effective value of the shear viscosity coefficient over entropy density ratio $\eta/s$ in the fluid phase for the whole energy region under investigation. The estimated value of $\eta/s$ increases with decreasing collision energy, which may indicate that $\eta/s$ of the quark-gluon plasma depends on baryochemical potential $\mu_B$.