Azimuthal Anisotropy Scaling for Identified Mesons and Baryons: Insights into Medium Transport Properties, Equation of State and Hadronic Re-scattering

Abstract

Scaling functions for the centrality and transverse momentum dependence of \(v_2(p_T,\text{cent})\) and \(v_3(p_T,\text{cent})\) are constructed for identified mesons and baryons in Pb+Pb (\(\sqrt{s_{NN}}=2.76,\ 5.02\)~TeV), Xe+Xe (5.44~TeV), and Au+Au (0.2~TeV) collisions. These species-resolved functions capture the interplay of initial geometry, viscous attenuation, radial flow, partonic energy loss, and hadronic re-scattering across both flow- and quenching-dominated regimes. The systematic growth of the radial-flow parameter \(ζ_{\rm rf}\) with multiplicity and beam energy provides direct empirical constraints on the equation of state (EOS) of hot QCD matter. The extracted parameters also yield differential constraints on the specific shear viscosity \(η/s\), the jet-quenching parameter \(\hat{q}\), and late-stage hadronic dynamics. LHC systems exhibit low \(η/s\), strong radial flow, and negligible re-scattering at high energy density, whereas Au+Au at RHIC energy shows even lower \(η/s\), weaker radial flow, finite re-scattering, and reduced energy density. The coexistence of strong radial flow at low \(p_T\) and significant jet suppression at high \(p_T\) emerges as a defining hallmark of QGP formation, establishing the framework as a quantitative probe of QGP transport properties and EOS stiffness.

Figures (4)

• Figure 1: (Color online) Scaling of $v_2$ and $v_3$ in 5--10% central Pb+Pb collisions at $\sqrt{s_{NN}} = 5.02$ TeV. Panel (a): unscaled $v_2(p_T)$ and $v_3(p_T)$ for $\pi$, $K$, and $p$, showing mass and baryon-number ordering. Panels (b,c): eccentricity-scaled and fully scaled results vs. $1/\sqrt{KE_T}$. Eccentricity scaling reduces but does not remove species separation (b), while full scaling yields near-universal behavior across flow- (large $1/\sqrt{KE_T}$, low $p_T$) and quenching-dominated (small $1/\sqrt{KE_T}$, high $p_T$) regions. Data: ALICE Zhu:2019twzALICE:2022zks.
• Figure 2: (Color online) Scaling of $v_2$ in 30--40% central Pb+Pb collisions at $\sqrt{s_{NN}} = 5.02$ TeV. Panel (a): measured $v_2(p_T)$ for mesons ($\pi$, $K$, $K^0_S$, $\phi$) and baryons ($p$, $\Lambda^0$, $\Xi$, $^{3}$He). Panels (b,c): eccentricity-scaled and fully scaled results vs. $1/\sqrt{KE_T}$. Inset (c): multiplicity dependence of $\zeta_{\rm rf}$. Data: ALICE Zhu:2019twzALICE:2020chvALICE:2022zks.
• Figure 3: (Color online) Scaling of $v_2$ in 20--30% central Pb+Pb collisions at $\sqrt{s_{NN}} = 2.76$ TeV. Panel (a): measured $v_2(p_T)$. Panels (b,c): eccentricity-scaled and fully scaled results vs. $1/\sqrt{KE_T}$, following Fig. \ref{['fig2']}. Inset (c): multiplicity dependence of $\zeta_{\rm rf}$. Data: ALICE ALICE:2014waoALICE:2016ctiALICE:2017nufALICE:2018lao.
• Figure 4: (Color online) Scaling of $v_2$ in 0--30% central Au+Au collisions at $\sqrt{s_{NN}} = 0.20$ TeV. Panel (a): measured $v_2(p_T)$. Panels (b,c): eccentricity-scaled and fully scaled results vs. $1/\sqrt{KE_T}$. Full scaling (c) achieves near-universal behavior across mesons ($\pi$, $K$, $K^0_S$, $\phi$) and baryons ($p$, $\Lambda^0$, $\Omega$, $d$), spanning collective to quenching-dominated regimes. Inset (c): multiplicity dependence of $\zeta_{\rm rf}$. Data: PHENIX and STAR PHENIX:2014uikSTAR:2015ggeSTAR:2022ncy.