[Paper Review] Hydrodynamic Flow from Fast Particles

Jorge Casalderrey-Solana, Edward Shuryak+1 more|ArXiv.org|Feb 20, 2006

High-Energy Particle Collisions Research20 citations

TL;DR

This paper investigates hydrodynamic flow induced by fast partons in a quark-gluon plasma using linearized hydrodynamics. It identifies two modes—sound and diffusion—where the relative strength of the diffusion mode to the sound mode is directly proportional to entropy produced by the jet-medium interaction. The key result is that observable Mach cone-like peaks in di-hadron correlations only emerge if jet energy loss occurs with minimal entropy production, making such signals highly sensitive to medium transport properties.

ABSTRACT

We study the interaction of a fast moving particle in the Quark Gluon Plasma with linearized hydrodynamics. We derive the linearized hydrodynamic equations on top of an expanding fireball, and detail the solutions for a static medium. There are two modes far from the jet -- a sound mode and a diffusion mode. The diffusion mode is localized in a narrow wake behind the jet while the sound mode propagates at the Mach angle, $\cos(θ_M) = c_s/c$. A general argument shows that the strength of the diffusion mode relative to the sound mode is directly proportional to the entropy produced by the jet-medium interaction. This argument does not rely on the linearized approximation and the assumption of local thermal equilibrium close to the jet. With this insight we calculate the spectrum of secondaries associated with the fast moving particle. If the energy loss is large and the jet-medium interaction does not produce significant entropy, the flow at the Mach angle can be observed in the associated spectrum. However, the shape of associated spectra is quite fragile and sensitive to many of the inputs of the calculation.

Motivation & Objective

• To understand the hydrodynamic response of quark-gluon plasma to fast partons using linearized hydrodynamics.
• To clarify the origin and relative strength of two hydrodynamic modes—sound and diffusion—excited by a jet.
• To link the entropy produced during jet-medium interaction to the amplitude of the diffusion mode relative to the sound mode.
• To assess the viability of conical flow as an explanation for large-angle azimuthal correlations observed in RHIC experiments.
• To evaluate the sensitivity of observable flow patterns to microscopic parameters like viscosity, source size, and jet-medium interaction time.

Proposed method

• Derive linearized hydrodynamic equations on top of an expanding fireball background, using relativistic potential flow formalism.
• Solve the equations for a static, homogeneous medium to identify two distinct modes: a sound wave propagating at the Mach angle and a diffusion mode localized in a narrow wake.
• Use a general argument based on energy and momentum conservation to relate the strength of the diffusion mode to the entropy produced by the jet-medium interaction.
• Apply the formalism to calculate the spectrum of secondary particles associated with the fast parton, linking energy loss and entropy production to final-state observables.
• Systematically vary parameters such as viscosity, jet-medium interaction time, source size, and freeze-out time to assess robustness of conical flow predictions.
• Use Eqs. (16), (39), (40), and (49) to compute flow fields and their dependence on momentum transfer and entropy production.

Experimental results

Research questions

• RQ1 What hydrodynamic modes are excited by a fast-moving parton in a quark-gluon plasma, and how do they depend on the medium's properties?
• RQ2 How is the relative amplitude of the sound wave and diffusion mode determined by the entropy produced during jet-medium interaction?
• RQ3 Under what conditions can conical flow lead to observable peaks in di-hadron azimuthal correlations at the Mach angle?
• RQ4 How sensitive are the predictions of hydrodynamic flow to variations in viscosity, source size, and jet-medium interaction time?
• RQ5 Can the observed large-angle correlations in RHIC data be explained by hydrodynamic flow from jets with minimal entropy production?

Key findings

• The strength of the diffusion mode relative to the sound mode is directly proportional to the entropy produced by the jet-medium interaction, a result valid beyond the linearized approximation.
• For a jet with energy loss of approximately 12 GeV/fm in a static medium, the resulting hydrodynamic flow produces azimuthal correlation amplitudes comparable to those observed by PHENIX and STAR.
• At moderate energy loss (2 GeV/fm), the model fails to reproduce the qualitative features of experimental data, indicating a need for additional effects like medium expansion.
• The expansion of the fireball can amplify the sound wave, reducing the required energy loss to observe Mach cone-like structures, suggesting a possible resolution to the discrepancy at lower energy loss.
• The prediction of conical flow is highly fragile: small changes in viscosity, source size, interaction time, or freeze-out time drastically alter the shape and strength of the correlation function.
• Observation of Mach cone peaks is only possible if the jet-medium interaction produces minimal entropy; otherwise, the wake obscures the conical signal.