Separation energies of light $\Lambda$ hypernuclei and their theoretical uncertainties

Separation energies of light $\Lambda$ hypernuclei ($A\leq 5$) and their theoretical uncertainties are investigated. Few-body calculations are performed within the Faddeev-Yakubovsky scheme and the no-core shell model. Thereby, modern and up-to-date $N\!N$ and $Y\!N$ potentials derived within chiral effective field theory are employed. % It is found that the numerical uncertainties of the few-body methods are well under control and an accuracy of around $1$ keV for the hypertriton and of less than $20$ keV for the separation energies of the $^4_{\Lambda}\mathrm{He}$ and $^5_{\Lambda}\mathrm{He}$ hypernuclei can be achieved. Variations caused by differences in the $N\!N$ interaction are in the order of $10$ keV for $^3_{\Lambda}\mathrm{H}$ and no more than $110$ keV for $A=4,\,5$ $\Lambda$ hypernuclei, when recent high-precision potentials up to fifth order in the chiral expansion are employed. The variations are smaller than expected contributions from chiral $Y\!N\!N$ three-body forces (3BFs) which arise at the chiral order of state-of-the-art $Y\!N$ potentials. Estimates for those 3BFs are deduced from a study of the truncation uncertainties in the chiral expansion.