Energy dependence of elliptic flow from heavy-ion collision models

We have compared the experimental data on charged-particle elliptic flow parameter (${v}_{2}$) in Au $+$ Au collisions at midrapidity for $\sqrt{{s}_{\mathrm{NN}}}=9.2$, $19.6$, $62.4$, and $200$ GeV with results from various models in heavy-ion collisions such as the ultrarelativistic quantum molecular dynamics (UrQMD) model, a multiphase transport model (AMPT), and heavy-ion jet interaction generator (HIJING). We observe that the average ${v}_{2}$ ($\ensuremath{\langle}{v}_{2}\ensuremath{\rangle}$) from the transport model UrQMD agrees well with the measurements at $\sqrt{{s}_{\mathrm{NN}}}=9.2$ GeV but increasingly falls short of the experimental $\ensuremath{\langle}{v}_{2}\ensuremath{\rangle}$ values as the beam energy increases. The difference in $\ensuremath{\langle}{v}_{2}\ensuremath{\rangle}$ is of the order of $60%$ at $\sqrt{{s}_{\mathrm{NN}}}=200$ GeV. The $\ensuremath{\langle}{v}_{2}\ensuremath{\rangle}$ results from HIJING are consistent with zero, while those from AMPT with default settings, a model based on HIJING with additional initial- and final-state rescattering effects included, give a $\ensuremath{\langle}{v}_{2}\ensuremath{\rangle}$ value of about $4%$ for all the beam energies studied. This is in contrast to an increase in $\ensuremath{\langle}{v}_{2}\ensuremath{\rangle}$ with beam energy for the experimental data. A different version of the AMPT model, which includes partonic effects and quark coalescence as a mechanism of hadronization, gives higher values of $\ensuremath{\langle}{v}_{2}\ensuremath{\rangle}$ among the models studied and is in agreement with the measured $\ensuremath{\langle}{v}_{2}\ensuremath{\rangle}$ values at $\sqrt{{s}_{\mathrm{NN}}}=200$ GeV. These studies show that the experimental $\ensuremath{\langle}{v}_{2}\ensuremath{\rangle}$ has substantial contribution from partonic interactions at $\sqrt{{s}_{\mathrm{NN}}}=200$ GeV, whose magnitude reduces with decrease in beam energy. We also compare the available data on the transverse momentum and pseudorapidity dependence of ${v}_{2}$ to those from these models.