Probing $\mathrm{\Lambda }$ potential at high and low densities via ${}_{\mathrm{\Lambda }}^3$H production in C+C reactions

The production of Lambda hyperons and light hypernuclei in heavy-ion collisions provides critical insights into the nuclear equation of state (EoS) and hyperon interactions in dense matter, addressing the longstanding ``hyperon puzzle’’ in neutron star physics. Using the INCL+ABLA and AMPT-HC models, we systematically investigate C+C collisions at beam energies of 1.1 and 1.9 GeV/nucleon to explore the sensitivity of hyperon and hypernuclei yields to the EoS and hyperon potential. Our results reveal that Lambda hyperon production is predominantly influenced by the nuclear EoS, while light hypernuclei formation (e.g., ${}_{\mathrm{\Lambda }}^3$H) exhibits stronger sensitivity to the hyperon potential at high/low densities with the incident beam energies of 1.1/1.9 GeV. The study provides a framework for future experiments at facilities like HIAF and FAIR/GSI to resolve the hyperon puzzle, thus advancing our understanding of quantum chromodynamics in high-density regimes.