Structure of single-$\Lambda$ hypernuclei with chiral hyperon-nucleon potentials

The structure of single-$\Lambda$ hypernuclei is studied using the chiral hyperon-nucleon potentials derived at leading order (LO) and next-to-leading order (NLO) by the J\"{u}lich--Bonn--Munich group. Results for the separation energies of $\Lambda$ single-particle states for various hypernuclei from $^5_{\Lambda}$He to $^{209}_{\,\,\,\,\,\Lambda}$Pb are presented for the LO interaction and the 2013 (NLO13) and 2019 (NLO19) versions of the NLO potentials. It is found that the results based on the LO potential show a clear tendency for overbinding while those for the NLO13 interaction underbind most of the considered hypernuclei. A qualitatively good agreement with the data is obtained for the NLO19 interaction over a fairly large range of mass number values when considering the uncertainty due to the regulator dependence. A small spin-orbit splitting of the $p$-, $d$-, $f$-, and $g$-wave states is predicted by all interactions, in line with the rather small values observed in pertinent experiments.