Hypernuclear constraints on $\mathrm{\Lambda }N$ and $\mathrm{\Lambda }NN$ interactions

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