Resolving the $\Lambda$ hypernuclear overbinding problem in pionless effective field theory

Abstract

We address the $\Lambda$-hypernuclear `overbinding problem' in light hypernuclei which stands for a 1--3 MeV excessive $\Lambda$ separation energy calculated in ${}_{\Lambda }^5$He. This problem arises in most few-body calculations that reproduce ground-state $\Lambda$ separation energies in the lighter $\Lambda$ hypernuclei within various hyperon-nucleon interaction models. Recent pionless effective field theory nuclear few-body calculations are extended in this work to $\Lambda$ hypernuclei. At leading order, the $\Lambda N$ low-energy constants are associated with $\Lambda N$ scattering lengths and the $\Lambda NN$ low-energy constants are fitted to $\Lambda$ separation energies ($B_{\Lambda }^{\exp }$) for $A\le 4$. The resulting pionless-EFT interaction reproduces in few-body stochastic variational method calculations the reported value $B_{\Lambda }^{\exp }{(}_{\Lambda }^5$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.

Comments: matches published PRL 121 (2018) 102502 with one minor correction: the number of nuclear plus hypernuclear LECs at LO is eight, not seven