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

TL;DR

This paper extends pionless effective field theory to hypernuclei, successfully resolving the overbinding problem by fitting low-energy constants to experimental separation energies, and reproduces the observed $ m _{\Lambda}^5$He binding energy.

Contribution

It introduces a pionless EFT approach for hypernuclei, fitting low-energy constants to experimental data, and accurately reproduces the $ m _{\Lambda}^5$He separation energy.

Findings

Reproduces $ m _{\Lambda}^5$He binding energy within a few hundred keV.

Addresses the overbinding problem in hypernuclear calculations.

Provides a framework for extending to heavier hypernuclei and neutron-star matter.

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 ($B_{\Lambda}^{\rm exp}$) for $A\leq 4$. The resulting pionless-EFT interaction reproduces in few-body stochastic variational method calculations the reported value $B_{\Lambda}^{\rm 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.