$\Lambda$ and $\Sigma$ potentials in neutron stars, hypernuclei, and heavy-ion collisions

With an appropriate $YNN$ force, the $\Lambda$ single-particle potential ($\Lambda$ potential) can be made strongly repulsive at high density, and one can solve the hyperon puzzle of neutron stars. We investigate the consistency of such a $\Lambda$ potential, evaluated recently from $YN$ and $YNN$ forces based on chiral effective field theory, with hypernuclear data and heavy-ion collision data. It is found that model calculations with such a $\Lambda$ potential can reproduce the data of the $\Lambda$ hypernuclear spectroscopy and the $\Lambda$ directed flow in heavy-ion collisions. Also, we evaluate the $\Sigma$ potential, which can be calculated by using the same hyperon forces as for the $\Lambda$ potential. Specifically, we show that the low-energy constants characterizing the strength of the $YNN$ force can be chosen to suppress the appearance of the $\Lambda$'s in neutron stars while at the same time the empirical value of the $\Sigma$ potential is reproduced.