Transport Model Investigation of NCQ Scaling and the Hadronic-Partonic Transition in Au+Au Collisions

Abstract: We investigate elliptic flow ($v_2$) in Au+Au collisions at $\sqrt{s_{\text{NN}}} = 3.0$ and 4.5 GeV using hadronic and partonic transport models, including JAM, SMASH, AMPT-Hadronic Cascade, and AMPT-String Melting. At 3.0 GeV, hadronic models reproduce the centrality dependence of $v_2$ and the particle ordering ($K^0_S > p > \pi^+$), while violating number-of-constituent-quark (NCQ) scaling, indicating that collectivity is primarily driven by hadronic interactions and influenced by spectator shadowing. Forward rapidity shows weaker spectator effects, yielding more positive $v_2$ for heavier hadrons, whereas pions remain largely unaffected. At 4.5 GeV, partonic interactions in the AMPT-String Melting mode significantly enhance NCQ scaling, and turning off final-state hadronic rescattering further clarifies the scaling pattern, highlighting the growing role of partonic degrees of freedom. The energy dependence of $p_T$-integrated $v_2$ reflects the transition from hadronic-dominated dynamics at lower energies to increasing partonic collectivity at higher energies. These results demonstrate that the breakdown of NCQ scaling at 3.0 GeV arises from hadronic interactions, whereas the emergence of scaling at higher energies signals partonic contributions in heavy-ion collisions.