[Paper Review] An estimate for the location of QCD critical end point

R. Lacey, N. N. Ajitanand+5 more|ArXiv.org|Aug 27, 2007

Particle physics theoretical and experimental studies4 citations

TL;DR

This paper proposes using the ratio of shear viscosity to entropy density (η/s) as a dynamic probe to estimate the location of the QCD critical end point (CEP) in the T–μB plane. Based on elliptic flow excitation functions from RHIC data, it estimates the CEP at Tcep ≈ 165–170 MeV and μB^cep ≈ 150–180 MeV, placing it within reach of immediate experimental validation via energy scans at RHIC.

ABSTRACT

It is proposed that a study of the ratio of shear viscosity to entropy density $\fracη{s}$ as a function of the baryon chemical potential $μ_B$, and temperature T, provides a dynamic probe for the critical end point (CEP) in hot and dense QCD matter. An initial estimate from an elliptic flow excitation function gives $μ^{ ext{cep}}_B \sim 150-180$ MeV and $T_{ ext{cep}} \sim 165 - 170$ MeV for the location of the the CEP. These values place the CEP in the range for "immediate" validation at RHIC.

Motivation & Objective

• To identify a dynamic observable sensitive to the QCD critical end point (CEP) in hot and dense nuclear matter.
• To estimate the CEP location in the T–μB plane using experimental data from heavy-ion collisions.
• To validate the CEP hypothesis via the behavior of η/s as a function of μB and T, leveraging universality with the 3D Ising model.
• To provide a quantitative estimate for the CEP that aligns with lattice QCD predictions and is accessible via existing RHIC energy scan programs.

Proposed method

• Utilizes the ratio of shear viscosity to entropy density (η/s) as a dynamic probe for the CEP, based on its universal behavior near critical points.
• Applies the universality class of the 3D Ising model to connect QCD matter behavior to known critical phenomena in atomic and molecular systems.
• Analyzes elliptic flow (v2) excitation functions from RHIC data (Au+Au collisions at √sNN = 17–200 GeV) to infer μB and T dependence of ⟨η/s⟩.
• Interpolates the observed v2 behavior across collision energies to estimate the onset of increased η/s, signaling proximity to the CEP.
• Uses the 'knee' in the v2 excitation function at √sNN ≈ 18–62 GeV as a signature of rising η/s, indicating μB ≈ μB^cep.
• Compares the estimated η/s behavior with theoretical models (e.g., Landau-Lifshitz, Eckart) and lattice QCD predictions to validate the estimate.

Experimental results

Research questions

• RQ1 Can the ratio of shear viscosity to entropy density (η/s) serve as a dynamic probe for the QCD critical end point?
• RQ2 Where is the critical end point located in the T–μB plane, based on existing RHIC data?
• RQ3 Does the observed behavior of elliptic flow (v2) across beam energies indicate a transition in transport properties consistent with the CEP?
• RQ4 How does the estimated CEP location compare with lattice QCD simulations and experimental energy scan programs?

Key findings

• The critical end point (CEP) is estimated at Tcep ≈ 165–170 MeV and μB^cep ≈ 150–180 MeV based on the v2 excitation function.
• A significant drop in elliptic flow (v2) from √sNN ≈ 62 GeV to 18 GeV correlates with increasing μB and rising η/s, signaling proximity to the CEP.
• The estimated μB^cep range is consistent with lattice QCD predictions using realistic pion masses and large volumes (Gavai and Gupta, 2005).
• The CEP is located within the accessible range of RHIC energy scans, making it a prime target for immediate experimental validation.
• The behavior of ⟨4π(η/s)⟩ as a function of reduced temperature and pressure shows a cusp-like minimum at the critical point, analogous to liquid-gas systems.
• Measurements at √sNN ≈ 40 and 30 GeV are expected to show significantly larger ⟨η/s⟩ and deviations from universal scaling, confirming the CEP proximity.