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

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.

💡 Research Summary

The manuscript presents a comprehensive, data‑driven framework for analyzing azimuthal anisotropy (v₂) of identified hadrons and their antiparticles across a wide range of collision energies—from LHC Pb+Pb at √sₙₙ = 2.76 and 5.02 TeV to RHIC Au+Au at √sₙₙ = 7.7–200 GeV. Building on earlier work on anisotropy scaling functions (ASF), the authors extend the method to resolve species‑dependent effects, allowing a simultaneous extraction of viscous attenuation, radial‑flow response, and hadronic rescattering contributions.

Key methodological steps:

1. An ultra‑central (20–30 % centrality) Pb+Pb collision at 5.02 TeV is used as a reference system. Charged kaons, because of their intermediate mass and small hadronic cross‑section, define the baseline attenuation parameter β₀.
2. For each particle species the measured v₂(p_T) is first scaled by the initial eccentricity ε₂ and a size proxy R ∝ ⟨N_chg⟩¹ᐟ³. A viscous correction δf = κ p_T² (κ = 0.17 (GeV/c)⁻²) is applied uniformly.
3. The transverse kinetic energy KE_T = m_T − m₀ is used as the scaling variable; plotting v₂/ε₂ versus 1/√KE_T largely removes trivial mass ordering.
4. Remaining species‑specific offsets are captured by two response coefficients: ζ_hs (hadronic rescattering) for mesons and ζ_rf (radial‑flow) for baryons. The baryon response is explicitly written as ζ_b = (1 − ζ_rf) |n_B|, enforcing a linear dependence on baryon number.
5. Particle–antiparticle differences are isolated through a charge‑odd radial‑flow term Δζ_rf = ζ̄_rf − ζ_rf.

The authors fit these parameters to a large set of experimental data from ALICE, PHENIX, and STAR, covering pions, kaons, φ mesons, protons, Λ, Ξ, Ω, deuterons, and ³He, together with their antiparticles. The extracted scaling parameters are summarized in Table I.

Principal findings:

• Viscous attenuation (k_β): At LHC energies k_β ≈ 0.95–1.00, indicating near‑minimal shear viscosity. At lower RHIC energies k_β drops to ≈ 0.63 (√sₙₙ = 200 GeV) and further to ≈ 0.55 at 11.5 GeV, reflecting stronger viscous damping as the system cools.

• Hadronic rescattering (ζ_hs): Negligible (≈ 0) at the LHC, but rises to 0.10–0.20 for √sₙₙ ≲ 20 GeV, consistent with an increasing role of late‑stage hadronic interactions at lower beam energies.

• Radial‑flow response (ζ_rf): Increases logarithmically with charged‑particle multiplicity, i.e., with centrality and energy density, confirming stronger collective expansion in more central, higher‑energy collisions.

• Baryon‑number scaling: The deuteron (|n_B| = 2) exhibits a blue‑shift exactly twice that of single baryons (|n_B| = 1). This precise scaling validates the functional form ζ_b = (1 − ζ_rf) |n_B| and supports the hypothesis that a common radial‑flow field acts proportionally to baryon number.

• Charge‑odd effect (Δζ_rf): At the LHC Δζ_rf is consistent with zero; at √sₙₙ = 11.5 GeV it reaches ≈ 0.10, indicating that antibaryons acquire a larger radial boost than baryons. The magnitude of Δζ_rf grows as √sₙₙ decreases, mirroring the expected increase of net‑baryon density (μ_B) and suggesting a baryon‑number‑dependent contribution to the flow field.

Interpretation: The observed uniform baryon‑antibaryon separation across all |n_B| = 1 species, together with the |n_B| scaling seen in the deuteron, is naturally explained by a baryon‑junction mechanism. In this picture, topological QCD configurations (junctions) transport net baryon number from beam rapidities toward mid‑rapidity, enhancing the pressure gradients experienced by baryons. The resulting additional radial push scales with baryon number and diminishes with increasing collision energy as μ_B → 0.

Alternative explanations based solely on hadronic annihilation would predict species‑dependent, strangeness‑ordered distortions and a stronger correlation with ζ_hs. The data, however, show that the charge‑odd shift tracks ζ_rf rather than ζ_hs, disfavoring a purely hadronic origin.

Finally, the ASF approach demonstrates that a compact set of scaling parameters can simultaneously describe viscous attenuation, partonic energy loss (via the link β ∝ η/s ∝ T³/ĥq), radial flow, and hadronic rescattering. This unified description provides a powerful tool for future investigations of QCD critical dynamics, especially in the finite‑μ_B regime where baryon stopping and junction effects become prominent.