Hypernuclear constraints on $\Lambda N$ and $\Lambda NN$ interactions

Recent work on using density dependent $\Lambda$-nuclear optical potentials in calculations of $\Lambda$-hypernuclear binding energies is reviewed. It is found that all known $\Lambda$ binding energies in the mass range $16 \leq A \leq 208$ are well fitted in terms of two interaction parameters: one, attractive, for the spin-averaged $\Lambda N$ interaction and another one, repulsive, for the $\Lambda NN$ interaction. The $\Lambda N$ interaction term by itself overbinds $\Lambda$ hypernuclei, in quantitative agreement with recent findings obtained in EFT and Femtoscopy studies. The strength of the $\Lambda NN$ interaction term is compatible with values required to resolve the hyperon puzzle.