Ab initio description of hypernuclei

Hypernuclei are bound states of neutrons, protons and one or two hyperons, thus extending the nuclear landscape to a third dimension. They also encode information about the baryon-baryon and three-baryon interactions. Here, we review recent work on chiral effective field theory for two- and three-baryon interactions and their application in nuclei based on ab initio methods. These include the Faddeev-Yakubovsky equations, the no-core-shell-model (NCSM) and nuclear lattice effective field theory (NLEFT). Besides of providing an overview of the formalisms explicit results for the separation energies of light $\Lambda$ hypernuclei are provided. Two-body and three-body forces are included consistently, in line with the underlying power counting. Calculations of $\Lambda$ hypernuclei within the NCSM, performed up to A=7 so far, suggest that agreement with the experimental binding energies can be achieved once appropriate three-body forces are taken into account. Similar conclusions are drawn from the study based on NLEFT, where even hypernuclei up to A=16 can be computed. Additionally, applications of ab initio approaches in calculations of $\Lambda \Lambda$ and $\Xi$ hypernuclei are discussed and possible candidates for the lightest systems that could be bound are identified, namely $^{\ \ 5}_{\Lambda \Lambda}{\rm He}$ and $^4_\Xi{\rm H}$.