in the $\Lambda N$ interaction at high momenta have their direct impact on the $\Lambda$ single-particle potentials in nuclear and neutron matter which change from attraction to repulsion at densities around or below $2\,\rho_0$, a feature not matched by any of the phenomenological potentials. However, as we shall see, such two-body repulsion is still not strong enough to prevent $\Lambda$ hyperons from occuring at baryon densities encountered in neutron stars and thereby softening the EoS to an unwanted degree.

Three-body interactions of hyperons with nucleons
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Three-nucleon forces are an important element in the quantitative understanding of nuclear few- and many-body systems. Likewise, the $\Lambda NN$ three-body interactions is expected to play a significant role in hypernuclear systems. Our interest in the present work is directed, in particular, to the behaviour of $\Lambda NN$ and $\Sigma NN$ three-body forces (3BF) in dense baryonic matter, where their influence is expected to grow continuously with increasing density.

In the systematic expansion of SU(3) chiral EFT, baryonic three-body forces appear at NNLO. Their detailed derivation is given in ref.[@Petschauer2016] on which we shall build. The leading 3BF diagrams are shown in fig.\[fig:3BF\]. They fall into three classes: six-baryon contact terms, one-meson exchange pieces, 