The onset of hyperons 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 and recent astrophysical observations of neutron stars are the grounds for the so-called hyperon puzzle. We calculate the equation of state and the neutron star mass-radius relation of an infinite systems of neutrons and Λ particles by using the auxiliary field diffusion Monte Carlo algorithm. We find that the three-body hyperon-nucleon interaction plays a fundamental role in the softening of the equation of state and for the consequent reduction of the predicted maximum mass. We have considered two different models of three-body force that successfully describe the binding energy of medium mass hypernuclei. Our results indicate that they give dramatically different results on the maximum mass of neutron stars, not necessarily incompatible with the recent observation of very massive neutron stars. We conclude that stronger constraints on the hyperon-neutron force are necessary in order to properly assess the role of hyperons in neutron stars.

Quantum Monte Carlo methods have recently been employed to study properties of nuclei and infinite matter using local chiral effective field theory interactions. In this work, we present a detailed description of the auxiliary field diffusion Monte Carlo algorithm for nuclei in combination with local chiral two-and three-nucleon interactions up to next-to-next-to-leading order. We show results for the binding energy, charge radius, charge form factor, and Coulomb sum rule in nuclei with 3 ≤ A ≤ 16. Particular attention is devoted to the effect of different operator structures in the three-body force for different cutoffs. The outcomes suggest that local chiral interactions fit to few-body observables give a very good description of the ground-state properties of nuclei up to 16 O, with the exception of one fit for the softer cutoff which predicts overbinding in larger nuclei. arXiv:1802.08932v1 [nucl-th]

Background: An accurate assessment of the hyperon-nucleon interaction is of great interest in view of recent observations of very massive neutron stars. The challenge is to build a realistic interaction that can be used over a wide range of masses and in infinite matter starting from the available experimental data on the binding energy of light hypernuclei. To this end, accurate calculations of the hyperon binding energy in a hypernucleus are necessary.Purpose: We present a quantum Monte Carlo study of Λ and ΛΛ hypernuclei up to A = 91. We investigate the contribution of two-and three-body Λ-nucleon forces to the Λ binding energy.Method: Ground state energies are computed solving the Schrödinger equation for non-relativistic baryons by means of the auxiliary field diffusion Monte Carlo algorithm extended to the hypernuclear sector. Results:We show that a simple adjustment of the parameters of the ΛN N three-body force yields a very good agreement with available experimental data over a wide range of hypernuclear masses. In some cases no experiments have been performed yet, and we give new predictions.Conclusions: The newly fitted ΛN N force properly describes the physics of medium-heavy Λ hypernuclei, correctly reproducing the saturation property of the hyperon separation energy.