Resolving the $Λ$ hypernuclear overbinding problem in pionless effective field theory

Abstract

We address the $Λ$-hypernuclear `overbinding problem' in light hypernuclei which stands for a 1--3 MeV excessive $Λ$ separation energy calculated in $_Λ^5$He. This problem arises in most few-body calculations that reproduce ground-state $Λ$ separation energies in the lighter $Λ$ hypernuclei within various hyperon-nucleon interaction models. Recent pionless effective field theory nuclear few-body calculations are extended in this work to $Λ$ hypernuclei. At leading order, the $ΛN$ low-energy constants are associated with $ΛN$ scattering lengths and the $ΛNN$ low-energy constants are fitted to $Λ$ separation energies ($B_Λ^{\rm exp}$) for $A\leq 4$. The resulting pionless-EFT interaction reproduces in few-body stochastic variational method calculations the reported value $B_Λ^{\rm exp}(_Λ^5 $He)=3.12$\pm$0.02 MeV within a fraction of MeV over a broad range of momentum-space cut-off parameters. Possible consequences and extensions to heavier hypernuclei and to neutron-star matter are discussed.