  Adopting hyperon-nucleon and hyperon-nucleon-nucleon interactions
parametrized in chiral effective field theory, single-particle potentials of
the $\Lambda$ and $\Sigma$ hyperons are evaluated in symmetric nuclear matter
and in pure neutron matter within the framework of lowest order Bruckner
theory. The chiral NLO interaction bears strong $\Lambda$N-$\Sigma$N coupling.
Although the $\Lambda$ potential is repulsive if the coupling is switched off,
the $\Lambda$N-$\Sigma$N correlation brings about the attraction consistent
with empirical data. The $\Sigma$ potential is repulsive, which is also
consistent with empirical information. The interesting result is that the
$\Lambda$ potential becomes shallower beyond normal density. This provides the
possibility to solve the hyperon puzzle without introducing ad hoc assumptions.
The effects of the $\Lambda$NN-$\Lambda$NN and $\Lambda$NN-$\Sigma$NN
three-baryon forces are considered. These three-baryon forces are first reduced
to normal-ordered effective two-baryon interactions in nuclear matter and then
incorporated in the $G$-matrix equation. The repulsion from the
$\Lambda$NN-$\Lambda$NN interaction is of the order of 5 MeV at the normal
density, and becomes larger with increasing the density. The effects of the
$\Lambda$NN-$\Sigma$NN coupling compensate the repulsion at normal density. The
net effect of the three-baryon interactions to the $\Lambda$ single-particle
potential is repulsive at higher densities.
