Towards Hypernuclei from Nuclear Lattice Effective Field Theory

Understanding the strong interactions within baryonic systems beyond the up and down quark sector is pivotal for a comprehensive description of nuclear forces. This study explores the interactions involving hyperons, particularly the $\mathrm{\Lambda }$ particle, within the framework of nuclear lattice effective field theory (NLEFT). By incorporating $\mathrm{\Lambda }$ hyperons into the NLEFT framework, we extend our investigation into the $S=-1$ sector, allowing us to probe the third dimension of the nuclear chart. We calculate the $\mathrm{\Lambda }$ separation energies ($B_{\mathrm{\Lambda }}$) of hypernuclei up to the medium-mass region, providing valuable insights into hyperon-nucleon ($YN$) and hyperon-nucleon-nucleon ($YNN$) interactions. Our calculations employ high-fidelity chiral interactions at N${}^3$LO for nucleons and extend it to $\mathrm{\Lambda }$ hyperons with leading-order S-wave $YN$ interactions as well as $YNN$ forces constrained only by the $A=4,5$ systems. Our results contribute to a deeper understanding of the SU(3) symmetry breaking and establish a foundation for future improvements in hypernuclear calculations.