[Paper Review] Beam-energy dependence of the azimuthal anisotropic flow from RHIC

N. Magdy|arXiv (Cornell University)|Sep 20, 2019

High-Energy Particle Collisions Research19 references4 citations

TL;DR

This paper presents beam-energy-dependent measurements of azimuthal anisotropic flow coefficients (vₙ and v₁^{even}) in Au+Au collisions at RHIC across √sₙₙ = 7.7–200 GeV using the two-particle correlation method with pseudorapidity gaps and simultaneous fitting to disentangle global momentum conservation. The key result is a systematic observation of a transition from negative to positive v₁^{even} with increasing pₜ, confirming hydrodynamic-like response to initial-state geometric fluctuations, while vₙ show energy-dependent patterns consistent with temperature-driven viscosity effects.

ABSTRACT

Recent STAR measurements of the anisotropic flow coefficients (v$_{n}$) are presented for Au+Au collisions spanning the beam energy range $\sqrt{s_{NN}} = 7.7 - 200$ GeV. The measurements indicate dependences on the harmonic number ($n$), transverse momentum ($p_T$), pseudorapidity ($η$), collision centrality and beam energy ($\sqrt{s_{NN}}$) which could serve as important constraints to test different initial-state models and to aid precision extraction of the temperature dependence of the specific shear viscosity.

Motivation & Objective

• To constrain initial-state models of quark-gluon plasma (QGP) formation by measuring beam-energy-dependent anisotropic flow coefficients in Au+Au collisions.
• To reduce non-flow effects in flow measurements by applying a pseudorapidity gap (|Δη| > 0.7) and using a simultaneous fitting method to account for global momentum conservation (GMC).
• To extract the rapidity-even dipolar flow coefficient v₁^{even} via a two-particle correlation method and simultaneous fit to v₁,₁(pₜᵃ, pₜᵇ) to isolate hydrodynamic response.
• To provide new constraints on the temperature dependence of the specific shear viscosity η/s of the QGP by analyzing the energy and pₜ dependence of vₙ and v₁^{even}.
• To test hydrodynamic models by comparing measured vₙ and v₁^{even} patterns across beam energies and centralities.

Proposed method

• Two-particle correlation function Cr(Δϕ, Δη) is computed as the ratio of same-event to mixed-event azimuthal pair distributions to extract vₙ,ₙ coefficients.
• A pseudorapidity gap |Δη| > 0.7 is applied to suppress short-range non-flow correlations from resonance decays and jets.
• The vₙ,ₙ coefficients are extracted via Fourier decomposition of the correlation function: vₙ,ₙ = Σ[Cr·cos(nΔϕ)] / Σ[Cr].
• The rapidity-even dipolar flow v₁^{even} is extracted by simultaneously fitting v₁,₁(pₜᵃ, pₜᵇ) to the functional form v₁^{even}(pₜᵃ)v₁^{even}(pₜᵇ) – C·pₜᵃpₜᵇ, where C accounts for global momentum conservation.
• The fitting procedure uses N+1 parameters (N values of v₁^{even}(pₜ) and one C parameter) for each centrality and energy, enabling extraction of pₜ-dependent v₁^{even}.
• Systematic uncertainties are estimated and included as shaded bands in the final results, particularly for vₙ and v₁^{even} across different beam energies and centralities.

Experimental results

Research questions

• RQ1 How does the beam-energy dependence of vₙ (n ≥ 2) in Au+Au collisions reflect the temperature evolution of the quark-gluon plasma?
• RQ2 What is the behavior of the rapidity-even dipolar flow coefficient v₁^{even} as a function of transverse momentum and beam energy, and how does it constrain initial-state geometry and hydrodynamic response?
• RQ3 To what extent do non-flow effects, particularly global momentum conservation, distort the measured vₙ and v₁^{even} coefficients, and how can they be corrected?
• RQ4 How do the vₙ and v₁^{even} patterns across different centralities and beam energies help distinguish between competing initial-state models of QGP formation?
• RQ5 Can the measured vₙ and v₁^{even} trends provide improved constraints for the temperature dependence of the specific shear viscosity η/s in the QGP?

Key findings

• v₁^{even}(pₜ) exhibits a characteristic transition from negative to positive values as pₜ increases beyond ~1 GeV/c, consistent with hydrodynamic response to initial-state geometric fluctuations.
• The crossing point of v₁^{even}(pₜ) from negative to positive shifts slowly with beam energy, indicating a weak energy dependence of the underlying initial geometry and flow dynamics.
• vₙ (n ≥ 2) show a soft dependence on beam energy, with higher-order harmonics (v₃, v₄) decreasing in magnitude at lower √sₙₙ, suggesting increasing viscous attenuation at lower energies.
• The pₜ-integrated v₂, v₃, and v₄ exhibit monotonic increases with √sₙₙ, consistent with rising QGP temperature and enhanced collectivity at higher energies.
• The extracted C parameter for global momentum conservation shows a systematic dependence on centrality and multiplicity, with C ∝ 1/(⟨Mult⟩⟨pₜ²⟩), confirming its role in non-flow corrections.
• Hydrodynamic calculations with η/s = 0.16 describe v₁^{even}(pₜ) well at √sₙₙ = 200 GeV, supporting the hydrodynamic interpretation of the data.