[Paper Review] HBT interferometry and the parton-hadron phase transition

S. Soff|ArXiv.org|Feb 25, 2002

High-Energy Particle Collisions Research3 citations

TL;DR

This paper investigates pion and kaon HBT interferometry in relativistic heavy-ion collisions using a hybrid transport model that couples hydrodynamics (for the quark-gluon plasma phase) with microscopic transport (for the hadronic phase), showing that the hadronic phase dominates interferometry radii and weakly probes the QGP phase transition. The key result is that model predictions for $ R_{\rm out}/R_{\rm side} $ ratios do not match RHIC data, especially at high transverse momentum, pointing to unresolved dynamics in the hadronic stage or alternative phase transition scenarios.

ABSTRACT

We discuss predictions for the pion and kaon interferometry measurements in relativistic heavy ion collisions at SPS and RHIC energies. In particular, we confront relativistic transport model calculations that include explicitly a first-order phase transition from a thermalized quark-gluon plasma to a hadron gas with recent data from the RHIC experiments. We critically examine the "HBT-puzzle" both from the theoretical as well as from the experimental point of view. Alternative scenarios are briefly explained.

Motivation & Objective

• To assess the sensitivity of HBT interferometry to a first-order quark-gluon plasma to hadron gas phase transition at RHIC and SPS energies.
• To resolve the HBT-puzzle by comparing theoretical predictions with experimental data, particularly focusing on the $ R_{\rm out}/R_{\rm side} $ ratio's $ K_T $-dependence.
• To evaluate the role of the hadronic phase in shaping interferometry radii and its impact on extracting QGP properties like $ T_c $ and latent heat.
• To test the robustness of phase transition signals using kaons as a cleaner probe due to lower density and resonance effects compared to pions.

Proposed method

• A hybrid transport model is employed, combining relativistic hydrodynamics for the dense, early QGP phase and microscopic transport for the dilute hadronic phase.
• The transition between models occurs at a hadronization hypersurface, with the equation of state based on the bag model featuring a first-order phase transition.
• Correlation functions are calculated and fitted to a 3D Gaussian form: $ C_2 = 1 + \lambda \exp(-R_{\rm o}^2 q_{\rm o}^2 - R_{\rm s}^2 q_{\rm s}^2 - R_{\rm l}^2 q_{\rm l}^2) $, yielding $ R_{\rm o}, R_{\rm s}, R_{\rm l} $, and $ \lambda $.
• The model includes hadronic rescattering and resonance production using vacuum cross sections, such as $ K^+\pi^- $, and accounts for finite momentum resolution effects.
• Sensitivity to $ T_c $, initial entropy density, and critical temperature is tested by varying model parameters and comparing results at SPS and RHIC energies.
• Alternative scenarios, including spinodal decomposition and supercooling, are considered to assess their impact on emission duration and interferometry radii.

Experimental results

Research questions

• RQ1 Why do model predictions for the $ R_{\rm out}/R_{\rm side} $ ratio in HBT interferometry fail to match RHIC data at high $ K_T $?
• RQ2 To what extent does the hadronic phase dominate the interferometry radii, obscuring signals of the QGP phase transition?
• RQ3 How does the $ K_T $-dependence of the $ R_{\rm out}/R_{\rm side} $ ratio differ between pions and kaons, and what does this imply for phase transition dynamics?
• RQ4 Can the observed HBT-puzzle be resolved by modifying assumptions about the hadronization process, such as nucleation mechanism or freeze-out conditions?
• RQ5 What role does the direct emission from the phase boundary play in shaping kaon interferometry parameters at high $ K_T $?

Key findings

• The interferometry radii $ R_{\rm o} $ and $ R_{\rm s} $ are less than 7 fm, indicating no unusually large source sizes despite a first-order phase transition.
• The $ R_{\rm out}/R_{\rm side} $ ratio increases with transverse momentum in the model, but experimental data show a stronger rise, indicating a mismatch in emission duration.
• The $ R_{\rm out} $ radius is overestimated in the model compared to data, while $ R_{\rm side} $ is reasonably reproduced, suggesting the out-radius is most sensitive to unresolved dynamics.
• Finite momentum resolution reduces the extracted radii and $ \lambda $, with stronger suppression at higher $ K_T $, indicating a need for correction in experimental analysis.
• Kaons show enhanced sensitivity to $ T_c $ and initial entropy density at $ K_T \sim 1 $ GeV/c, with up to 30% of kaons originating directly from the phase boundary at high $ K_T $.
• Even with strong first-order transitions or varying freeze-out temperatures, the model fails to reproduce the $ K_T $-dependence of the $ R_{\rm out}/R_{\rm side} $ ratio, suggesting the need for alternative mechanisms like spinodal decomposition or strong opacity effects.