The impact of energy conservation in transport models on the $\pi^-/\pi^+$ multiplicity ratio in heavy-ion collisions and the symmetry energy

TL;DR

This study investigates how energy conservation in transport models affects the charged pion ratio in heavy-ion collisions, highlighting the sensitivity to the in-medium delta potential and the need for further model improvements.

Contribution

The paper introduces an upgraded transport model that conserves energy locally or globally, enabling more accurate constraints on the symmetry energy from pion observables.

Findings

Energy conservation impacts pion multiplicity predictions.

Pion multiplicities are highly sensitive to the in-medium delta potential.

Current uncertainties hinder definitive conclusions on symmetry energy.

Abstract

The charged pion multiplicity ratio in intermediate energy central heavy-ion collisions has been proposed as a suitable observable to constrain the high density dependence of the isovector part of the equation of state, with contradicting results. Using an upgraded version of the T\"ubingen QMD transport model, which allows the conservation of energy at a local or global level by accounting for the potential energy of hadrons in two-body collisions and leading thus to particle production threshold shifts, we demonstrate that compatible constraints for the symmetry energy stiffness can be extracted from pion multiplicity and elliptic flow observables. Nevertheless, pion multiplicities are proven to be highly sensitive to the yet unknown isovector part of the in-medium $\Delta$(1232) potential which hinders presently the extraction of meaningful information on the high density dependence of the symmetry energy. A solution to this problem together with the inclusion of contributions presently neglected, such as in-medium pion potentials and retardation effects, are needed for a final verdict on this topic.