Transport-model investigation of scaling of the number of constituent quarks and the hadronic-partonic transition in Au + Au collisions

Abstract

We investigate the elliptic flow ($v_2$) in Au+Au collisions at $\sqrt{s_{\text{NN}}} = 3.0$ and 4.5 GeV using both hadronic and partonic transport models, including JAM, SMASH, AMPT-Hadronic Cascade, and AMPT-String Melting. At 3.0 GeV, the JAM model reproduces the number-of-constituent-quark (NCQ) scaling violation observed by STAR, as well as the particle ordering ($K^0_S > p > \pi^+$). Model calculations of the centrality dependence indicate that the scaling violation mainly originates from hadronic interactions rather than spectator effects, while the rapidity dependence further constrains the mechanism of the scaling breaking and the underlying longitudinal dynamics. 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 increasing role of partonic degrees of freedom. The energy dependence of the $p_T$-integrated $v_2$ is also examined within these models.