Title: Correlation of the hyperon potential stiffness with hyperon constituents in neutron stars and heavy-ion collisions

Abstract: The breaking of SU(6) symmetry to a more general flavor SU(3) symmetry could serve as a potential explanation for the "hyperon puzzle" of neutron stars by adjusting the hyperon potentials. Specifically, when the soft relativistic mean-field (RMF) $\Lambda$ hyperon potentials fall within the domains of chiral SU(3) interactions NLO13 with two-body forces, the maximum mass of neutron stars is expected to be lower than 2.0 $M_\odot$, whereas it can exceed $2.0M_\odot$ if the RMF $\Lambda$ hyperon potentials are sufficiently stiff to be consistent with those from chiral SU(3) interactions NLO13 with three-body forces. In our investigation involving these two types of $\Lambda$ hyperon potentials, we explore how the hyperon yields and flows are affected in heavy-ion collisions. We find that the inclusion of hyperon potentials results in better agreement of the $\Lambda$ directed flows with data but without clear differentiation in the stiffness of the hyperon potentials. Similarly negligent is the disparity in the rapidity distributions of the $\Lambda$ collective flows predicted by the stiff and soft hyperon potentials. In contrast, the $\Lambda$ collective flows beyond the central rapidity region turn out to be sensitive to the stiffness of the RMF equation of state (EOS) with the preference of a soft RMF EOS to a stiff one. Notably, the transverse momentum distributions of $\Lambda$ hyperon production are sensitive to both the stiffness of the RMF EOS and $\Lambda$ hyperon potential at high transverse momenta.