and to what extent a microscopic description of hyperon-nucleon two- and three-body forces is capable of providing the necessary repulsion in dense baryonic matter. The key quantities to be calculated are the hyperon ($\Lambda$ and $\Sigma$) single-particle potentials $U_{\Lambda,\Sigma}(\rho)$ in nuclear and neutron matter. The density dependence of the resulting chemical potential $\mu_\Lambda(\rho)= M_\Lambda +U_{\Lambda}(\rho)$ of a $\Lambda$ in neutron matter indicates whether it is favourable to replace neutrons by $\Lambda$ hyperons in the core of neutron stars.

Our starting point is the hyperon-nucleon interaction derived from SU(3) chiral effective field theory (ChEFT) at next-to-leading order (NLO) [@Haidenbauer2013]. This interaction includes exchanges of one and two pseudoscalar octet mesons and four-baryon contact terms with SU(3)-symmetric low-energy constants fitted to the (admittedly scarce) hyperon-nucleon scattering data. Three-body forces enter first at next-to-next-to-leading order (NNLO) in this scheme [@Petschauer2016]. Estimating the strength of contact terms in these forces through the contributions of explicit baryon decuplet resonances in intermediate states, these three-body interactions are promoted from NNLO to NLO [@Petschauer2017] due to the small decuplet-octet baryon mass-splitting. We shall adopt here the same strategy. Previous calculations of hyperon-nuclear potentials using Brueckner theory with these interactions as input have been reported in refs.[@Kohno2018; @Petschauer2016b; 