Azimuthal Anisotropy Scaling Functions for Identified Particle and Anti-Particle Species across Beam Energies: Insights into Baryon Junction Effects

Abstract

Azimuthal anisotropy scaling functions are constructed from species-resolved anisotropy measurements in Pb+Pb ($\sqrt{s_{NN}}=2.76$, $5.02$ TeV) and Au+Au ($\sqrt{s_{NN}}=7.7$-$200$~GeV) collisions to probe baryon transport and medium response at finite baryon chemical potential ($μ_B$). Within this data-driven framework, meson and baryon anisotropies spanning the collective-flow and quenching regimes collapse onto common scaling curves, enabling quantitative separation of viscous attenuation, radial flow, and hadronic re-scattering. The attenuation scale $k_β$ exhibits a non-monotonic beam-energy dependence, coincident with the low-energy rise of hadronic re-scattering, consistent with a temperature-dependent specific shear viscosity featuring a near-minimum near the QCD critical region. A charge-odd baryon-antibaryon separation in the effective radial-flow response is negligible at LHC energies but grows toward lower $\sqrt{s_{NN}}$. This species-uniform, baryon-number-scaling separation across $p,Λ,Ξ,Ω,$ and $d$ disfavors a purely hadronic origin and supports junction-driven net-baryon transport at finite $μ_B$, enhancing the experimental visibility of critical dynamics in finite, rapidly evolving systems. Together, these results establish species-resolved scaling functions as a compact and robust tool for constraining baryon stopping, medium opacity, and QGP transport properties.

Figures (6)

• Figure 1: (Color online) (a) Centrality dependence of the initial-state eccentricities $\varepsilon_2$ and $\varepsilon_3$ for Au+Au collisions at various beam energies. (b) The ratio $\varepsilon_3/\varepsilon_2$ for Au+Au at the same beam energies, with the Pb+Pb result at $\sqrt{s_{NN}}=5.02$ TeV included for reference.
• Figure 2: (Color online) Panel (a) compares $v_2(p_T)$ for mesons ($\pi^{\pm}, K^{\pm}, K^0_S, \phi$) and baryons ($d, p, \Lambda^{0}, \Xi^{\pm}, \Omega^{\pm}$), including antiparticles. Panel (b) shows the corresponding eccentricity-scaled values $v_2/\varepsilon_2$. Panel (c) presents the resulting species-resolved scaling function for 20--30% central Pb+Pb collisions at $\sqrt{s_{NN}}=2.76$ TeV. The scaling function is constructed using the kaon reference and the species-resolved anisotropy scaling relations described in the text. Data are from the ALICE Collaboration Zhu:2019twzALICE:2020chvALICE:2022zks.
• Figure 3: (Color online) Panels (a--c): $v_2(p_T)$, $v_2/\varepsilon_2$, and the scaling function for identified particles in 10--40% central Au+Au at $\sqrt{s_{NN}}=11.5$ GeV. Panels (d--f): corresponding antiparticle results. The 20--30% Pb+Pb baseline at 5.02 TeV is included for comparison. Data from STAR STAR:2013ayu and ALICE Zhu:2019twzALICE:2022zks.
• Figure 4: (Color Online) Same as Fig. \ref{['fig3']} but for $\sqrt{s_{NN}} = 27.0$ GeV.
• Figure 5: (Color online) Beam-energy dependence of (a) the meson re-scattering parameter $\zeta_{\rm hs}$ and (b) the attenuation scale $k_{\beta}\equiv\beta/\beta_{0}$, which serves as a proxy for the effective specific shear viscosity. The reference value $\beta_{0}$ is fixed by ultra-central charged kaons in Pb+Pb at $\sqrt{s_{NN}}=5.02$ TeV, corresponding to $k_{\beta}=1$. Results are shown for 20--30% Pb+Pb at $\sqrt{s_{NN}}=2.76$ and 5.02 TeV and 10--40% Au+Au over $\sqrt{s_{NN}}=7.7$--200 GeV. Data are from the ALICE, PHENIX, and STAR collaborations ALICE:2014waoALICE:2016ctiALICE:2017nufALICE:2018laoZhu:2019twzALICE:2020chvALICE:2022zksSTAR:2013ayuPHENIX:2014uikSTAR:2015ggeSTAR:2022ncy.