Two RHIC puzzles: Early thermalization and the HBT problem

TL;DR

The paper addresses two RHIC puzzles: rapid thermalization and the HBT radii discrepancy. Using ideal-hydrodynamic simulations with boost-invariant expansion and a mixed initial condition, it shows that elliptic flow and bulk spectra imply thermalization on a timescale $<1$ fm/$c$ and partonic pressure at energy densities well above deconfinement, yet the same framework fails to reproduce the HBT radii, pointing to incomplete freeze-out kinetics. It explores pre-equilibrium flow and alternative freeze-out scenarios, finding partial improvements but no complete resolution of the HBT problem, while azimuthal HBT patterns suggest the evolution captures some geometry and opacity effects. Overall, the work highlights the success of hydrodynamics in describing momentum-space observables at RHIC and underscores the need for a more complete understanding of the freeze-out process to fully explain space-time emission features.

Abstract

Hadron spectra from the first year RHIC run are shown to be excellently reproduced by hydrodynamic calculations. We argue that in particular the elliptic flow data provide strong evidence for early thermalization at RHIC, at energy densities well above deconfinement, but that the phenomenologically extracted short thermalization time scale of less than 1 fm/c provides a serious challenge for theory. The HBT radii from the hydrodynamic calculations agree only qualitatively with the data, showing significant quantitative discrepancies. It is argued that this points to a still incomplete understanding of the freeze-out process at RHIC.

Figures (6)

• Figure 1: Charged pion, antiproton and positive kaon spectra from central (upper left panel) and semi-central to peripheral (other three panels) Au+Au collisions at $\sqrt{s}{\,=\,}130\,A$ GeV. The data were taken by the PHENIX PHENIX_spec and STAR STAR_spec collaborations (the STAR data have slightly different centralities than the indicated values from PHENIX). The curves show hydrodynamical calculations (see text).
• Figure 2: The elliptic flow coefficient ${\rm v}_2(p_\perp)$ for all charged particles (left) and for identified pions and protons (right) from 130 $A$ GeV minimum bias Au+Au collisions Ackermann:2001trLacey:2001vaSnellings:2001nfAdler:2001nb. The curves are hydrodynamic calculations corresponding to equations of state with (Q) and without (H) a phase transition and (in the right panel) three different freeze-out temperatures ($T_{\rm f}{\,=\,}128$ MeV (dash-dotted), 130 MeV (solid) and 134 MeV (dashed)).
• Figure 3: HBT radii from a hydrodynamic source compared to RHIC data Adler:2001zdAdcox:2002uc. The solid lines show hydrodynamic results with standard initialization and freeze-out (see text). The dotted lines assume freeze-out directly after hadronization at $e_{\rm dec}{\,=\,}{e}_{\rm crit}$. The other lines correspond to modified initial conditions as described in the text.
• Figure 4: The $K_\perp$-integrated emission function from hydrodynamics, for directly emitted pions with rapidity $Y=0$ from semicentral Au+Au collisions ($b{\,=\,}7$ fm). The emission function is integrated over time and longitudinal coordinate $z$. The left panel shows contours of constant particle density in the transverse plane, the right panel presents cuts through this distribution along the $x$ and $y$ axes, showing that particle emission is strongly concentrated at the surface, especially for emission into the reaction plane ($y{\,=\,}0$).
• Figure 5: Time- and $z$-integrated emission function for $b{\,=\,}7$ fm Au+Au collisions at RHIC for directly emitted pions with rapidity $Y{\,=\,}0$ and fixed transverse momentum $K_\perp$. Shown are contours of constant particle density at freeze-out in the transverse plane, for $K_\perp{\,=\,}0$ in the upper left panel, and for $K_\perp{\,=\,}0.5$ GeV and three azimuthal emission angles ($0^\circ$, $45^\circ$, and $90^\circ$ relative to the reaction plane) in the remaining three panels.