Hydrodynamic Flow from Fast Particles

TL;DR

This work develops a linearized hydrodynamic framework for a fast jet traversing quark–gluon plasma atop an expanding fireball, revealing two far-field modes: a propagating sound wave and a near-field diffusion wake. The relative strength of these modes is governed by the entropy produced in jet–medium interactions, with isentropic (entropy-conserving) and non-isentropic (entropy-producing) scenarios yielding distinct flow patterns and observable spectra. The authors connect the jet energy–momentum loss to the emitted hydrodynamic disturbances and compute the resulting dihadron spectra, showing that Mach-cone signals are highly sensitive to transport properties, source size, and expansion dynamics; expansion can mitigate the required energy loss to produce observable conical features, while significant entropy production tends to mask them. Overall, conical flow predictions from linearized hydrodynamics are found to be delicate and strongly dependent on microscopic jet–medium coupling details, warranting further investigation with realistic expansion and dissipative effects.

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.

Figures (8)

• Figure 1: A schematic picture of the flow created by a jet moving through the fireball. The trigger jet is moving to the right away from the origination point (the black circle at point B). Sound waves start propagating as spherical waves (the dashed circle) from the origination point. The companion quenched jet is moving to the left creating a wake of matter (shaded area) and adding to the sound wave. The head of the jet is a non-equilibrium gluonic shower formed by the original hard parton (black dot A). The solid arrow indicates the flow velocity which is perpendicular to the shock cone at the angle $\theta_M$, $\cos(\theta_M) = c_s/c \simeq 0.55$.
• Figure 2: Sketch of the flow picture in the fluid jet rest frame. The non-hydro core (solid region) serves as a source for the hydrodynamic fields. The irrotational or potential component of the velocity field (wavy region) propagates out of the source and leads to a small disturbance at large distances. The irrotational part(circled region) remains concentrated along the jet axis within a transverse size that grows as $\sqrt{\chi}$.
• Figure 3: Left: Associate yield dependence on associate $p_T$ for fixed source size $\sigma=0.75/T$ , viscosity $\Gamma_s=0.1/T$, $t_j=8/T$, $t_f=10/T$, and energy loss, $dE/dx=10 T^2$ (top) and $dE/dx=63 T^2$ (bottom). The label values for $dE/dx$ correspond to $T=200~\hbox{MeV}$. The three curves are for $1 T<p_{t}<5 T$ (solid), $5 T<p_{t}<10 T$ (dotted), ($3\times$) $10 T<p_{t}<15 T$ (dashed), ($10\times$) $15 T<p_{t}<20 T$ (dashed-dotted). (in the upper panel all the curves are rescaled further up by a factor 10). No large angle correlation is observed for $dE/dx=10 T^2$. For $dE/dx=63 T^2$ the position of the peak shifts toward $\pi$ for lower $p_T$. Right: Experimental dihadron azimuthal distributions from STAR (top) star_peaks and PHENIX (bottom) phenix_peaks
• Figure 4: Spectrum of associated particles in the away side $\Delta \phi >1$ for $\sigma=0.75/T$, $dE/dx=142 T^2$, $\Gamma_s=0.1/T$ (solid). Spectrum of uncorrelated particles (rescaled down by a factor 100). The associated yield is much harder than the inclusive due to the boosted liquid induced by the jet.
• Figure 5: Associate yield dependence on energy loss for fixed source size $\sigma=0.75/T$, $\Gamma_s=0.1/T$, $t_j=8/T$, $t_f=10/T$ and $10 T<p_{t}<20 T$. The three curves are for $(1/20 \times) dE/dx=126 T^2$, $dE/dx=63 T^2$, $dE/dx=35.5 T^2$ for solid, dotted and dashed respectively.