Symmetry potential of $\Delta(1232)$ resonance and its effects on the $\pi^-/\pi^+$ ratio in heavy-ion collisions near the pion production threshold

TL;DR

This study investigates how the unknown symmetry potential of the 232 resonance affects the ar;/ar; ratio in heavy-ion collisions, finding it negligible at high energies but significant at sub-threshold energies for low-energy pions.

Contribution

It reveals the energy-dependent influence of the 232 resonance symmetry potential on pion ratios, highlighting its importance at sub-threshold energies for probing nuclear symmetry energy.

Findings

Negligible effect of 232 symmetry potential at energies above pion threshold.

Significant impact of 232 symmetry potential on low-energy pion ratios at sub-threshold energies.

High-energy pion ratios remain reliable probes of high-density symmetry energy despite 232 potential uncertainties.

Abstract

Effects of the completely unknown symmetry (isovector) potential of the \D on the total and differential \rpi in heavy-ion collisions at beam energies from 100 to 1000 MeV/A are explored within an isospin-dependent transport model IBUU. The effects are found to be negligible at beam energies above the pion production threshold due to the very short lifetimes of less than 2 fm/c for $\Delta$ resonances with masses around $m_{\Delta}=1232$ MeV, leaving the $\pi^-/\pi^+$ ratios of especially the energetic pions still a reliable probe of the high-density behavior of nuclear symmetry energy $E_{sym}(\rho)$. However, as the beam energy becomes deeply sub-threshold for pion production, effects of the $\Delta$ symmetry potential becomes appreciable especially on the \rpi of low-energy pions from the decays of low-mass $\Delta$ resonances which have lived long enough to be affected by their mean-field potentials, providing a useful tool to study the symmetry potential and spectroscopy of $\Delta$ resonances in neutron-rich nuclear matter. Interestingly though, even at the deeply sub-threshold beam energies, the differential \rpi of energetic pions remains sensitive to the \esym at supra saturation densities with little influence from the uncertain symmetry potential of the $\Delta$ resonance.