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

TL;DR

The paper analyzes elliptic flow v2 and NCQ scaling in Au+Au collisions at 3.0 and 4.5 GeV using hadronic (JAM, SMASH, AMPT-HC) and partonic (AMPT-SM) transport models to disentangle hadronic versus partonic dynamics. It finds that at 3.0 GeV NCQ-scaling violations are driven primarily by hadronic interactions and spectator shadowing, while at 4.5 GeV partonic interactions and quark coalescence restore NCQ scaling, especially when final-state hadronic rescattering is suppressed. Centrality and rapidity dependencies reveal the role of spectator shadowing and longitudinal dynamics in shaping v2. The energy dependence of pT-integrated v2 suggests increasing partonic dominance with energy, highlighting NCQ scaling as a sensitive probe of partonic collectivity and motivating future high-baryon-density measurements and model improvements.

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 ($K^0_S > p > π^+$). 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.

Figures (4)

• Figure 1: The number-of-constituent-quark ($n_q$) scaled elliptic flow ($v_{2}/n_{q}$) as a function of $n_q$-scaled transverse momentum ($p_{T}/n_q$) for 0--10%, 10--40%, and 40--80% central Au+Au collisions at $\sqrt{s_{\text{NN}}} = 3.0$ GeV, obtained from model calculations with JAM, SMASH, and AMPT-HC, compared with the STAR publication (right panel) STAR:2021yiuSTAR:2025owm.
• Figure 2: Number-of-constituent-quark ($n_q$) scaled elliptic flow ($v_{2}/n_{q}$) as a function of $n_q$-scaled transverse momentum ($p_{T}/n_q$) in Au+Au collisions at $\sqrt{s_{\text{NN}}} = 3.0$ GeV, obtained from JAM, SMASH, and AMPT model calculations for 10–40% centrality at mid-rapidity ($0 < |y| < 0.5$) and forward rapidity ($0.5 < |y| < 1.0$).
• Figure 3: Number-of-constituent-quark ($n_q$) scaled elliptic flow ($v_{2}/n_{q}$) as a function of $n_q$-scaled transverse momentum ($p_{T}/n_q$) for Au+Au collisions at $\sqrt{s_{\text{NN}}} = 4.5$ GeV, obtained from AMPT model calculations in three configurations: Hadronic Cascade, String Melting, and String Melting without hadronic interactions.
• Figure 4: Integrated elliptic flow ($v_2$) of $\pi^{+}$, $K^{+}$, $K^{0}_{S}$, $p$, and $\Lambda$ in 10--40% central Au+Au collisions at $\sqrt{s_{\text{NN}}}$ = 3.0--4.5 GeV, extracted from various transport model calculations. Model results from JAM, AMPT-HC, AMPT-SM, and SMASH are shown as bands. Experimental data points are taken from STAR publications STAR:2021yiuSTAR:2025owm. For clarity, the x-axis values of integrated $v_2$ are shifted a little.