A model comparison of resonance lifetime modifications, a soft equation of state and non-Gaussian effects on $\pi-\pi$ correlations at FAIR/AGS energies

TL;DR

This study uses transport models to analyze pion-pion correlations at FAIR/AGS energies, exploring resonance lifetimes, equation of state, and non-Gaussian effects to understand HBT measurements.

Contribution

It systematically investigates three different sources affecting HBT correlations, providing insights into their roles and limitations in explaining experimental data.

Findings

Resonance decay time treatment does not resolve the HBT puzzle but slightly modifies radii.

A soft, momentum-dependent equation of state describes the data well.

Non-Gaussian effects are significant, especially longitudinally, affecting correlation functions.

Abstract

HBT correlations of $\pi^--\pi^-$ pairs at FAIR/AGS energies are investigated by using the UrQMD transport model and the CRAB analyzing program. Three different possible sources (treatment of resonance lifetimes, a soft equation of state and non-Gaussian effects) to understand the HBT $R_O/R_S$ puzzle are investigated. Firstly, we find that different treatments of the resonance decay time can not resolve the HBT time-related puzzle, however it can modify the HBT radii at low transverse momenta to some extent to explain the data slightly. Secondly, with a soft equation of state with momentum dependence, the measured transverse momentum dependent HBT radii and $R_O/R_S$ ratio can be described fairly well. Thirdly, non-Gaussian effects are visible in the calculated correlation function. Using the Edgeworth expansion, one finds that the non-Gaussian effect is strongest in the longitudinal direction and weakest in the sideward direction.