Strangeness in neutron star matter: a challenging puzzle

The onset of strange baryons in the core of neutron stars and the consequent softening of the equation of state have been questioned for a long time. Controversial theoretical predictions about the predicted maximum mass and the recent astrophysical observations are the grounds of the so called \emph{hyperon puzzle}. We attempt to give our contribution to the discussion by studying the general problem of the hyperon-nucleon interaction by means of Auxiliary Field Diffusion Monte Carlo calculations. We employ a phenomenological approach showing that a three-body hyperon-nucleon force provides the strong repulsive contribution needed to correctly describe the systematics of medium-light $\Lambda$~hypernuclei. The same potential has been used to determine the equation of state and the mass-radius relation of an infinite systems of neutrons and $\Lambda$~particles. We find that the three-body hyperon-nucleon force has a dramatic effect on the equation of state and the predicted maximum mass. Our results suggest that more constraints on the nature of hyperon-neutron forces are needed before drawing any conclusion on the role played by hyperons in neutron stars.