Insights on pion production mechanism and symmetry energy at high density

TL;DR

This study uses UrQMD simulations with improved cross sections to analyze pion production and its sensitivity to symmetry energy at high density, providing constraints consistent with neutron star observations.

Contribution

It introduces a Δ-mass dependent NΔ→NN cross section in UrQMD, enhancing pion multiplicity predictions and refining symmetry energy constraints at high density.

Findings

Pion multiplicity probes symmetry energy at 1-2 times normal density.

Sensitivity of π−/π+ ratio decreases after multiple N-Δ-π loops.

Symmetry energy at 2ρ₀ is constrained to 38-73 MeV, refined to 48-58 MeV with astrophysical constraints.

Abstract

The $N\Delta\to NN$ cross sections, which take into account the $\Delta$-mass dependence of M-matrix and momentum $p_{N\Delta}$, are applied on the calculation of pion production within the framework of the UrQMD model. Our study shows that UrQMD calculations with the $\Delta$-mass dependent $N\Delta\to NN$ cross sections enhance the pion multiplicities and decrease the $\pi^-/\pi^+$ ratios. By analyzing the time evolution of the pion production rate and the density in the overlapped region for Au+Au at the beam energy of 0.4A GeV, we find that the pion multiplicity probes the symmetry energy in the region of 1-2 times normal density. The process of pion production in the reaction is tracked including the loops of $NN\leftrightarrow N\Delta$ and $\Delta\leftrightarrow N\pi$, our calculations show that the sensitivity of $\pi^-/\pi^+$ to symmetry energy is weakened after 4-5 N-$\Delta$-$\pi$ loops in the pion production path, while the $\pi^{-}/\pi^{+}$ ratio in reactions at near threshold energies remains its sensitivity to the symmetry energy. By comparing the calculations to the FOPI data, we obtain a model dependent conclusion on the symmetry energy and the symmetry energy at two times normal density is $S(2\rho_0)$=38-73 MeV within $1\sigma$ uncertainties. Under the constraints of tidal deformability and maximum mass of neutron star, the symmetry energy at two times normal density is reduced to $48-58$ MeV and slope of symmetry energy $L=54-81$ MeV, and it is consistent with the constraints from ASY-EOS flow data.