High-density symmetry energy from subthreshold hyperon production in heavy-ion collisions

The hyperon dynamics in heavy-ion collisions near threshold energy has been investigated within the quantum molecular dynamics transport model. The isospin and momentum dependent hyperon-nucleon potential and the threshold energy correction on the hyperon elementary cross section are included in the model. It is found that the high-density symmetry energy is dependent on the isospin ratios $\Sigma^{-}/\Sigma^{+}$ and $\Xi^{-}/\Xi^{0}$, in particular in the domain of high kinetic energies. The isospin diffusion in heavy-ion collisions influences the neutron/proton ratio in the high-density region. The $\Sigma^{-}/\Sigma^{+}$ ratio depends on the stiffness of symmetry energy, in particular at the beam energy below the threshold value (E$_{th}$=1.58 GeV), i.e., the kinetic energy spectra of the single ratios, excitation functions and energy spectra of the double ratios in the isotopic reactions of $^{108}$Sn + $^{112}$Sn, $^{112}$Sn + $^{112}$Sn, $^{124}$Sn + $^{124}$Sn and $^{132}$Sn + $^{124}$Sn. The double strangeness ratio $\Xi^{-}/\Xi^{0}$ weakly depends on the symmetry energy because of the hyperon-hyperon collision mainly contributing the $\Xi$ production below the threshold energy (E$_{th}$ = 3.72 GeV).