Constraints on the $\Lambda$-neutron interaction from charge symmetry breaking in the $\mathbf{^4_\Lambda \rm \bf He}$--$\mathbf{^4_\Lambda \rm \bf H}$ hypernuclei

TL;DR

This paper constrains the $ ext{Λ}$-neutron interaction by analyzing charge symmetry breaking in mirror hypernuclei, using chiral effective field theory and hypernuclear data to predict scattering lengths.

Contribution

It introduces a method to determine the $ ext{Λ}$-neutron interaction strength from hypernuclear charge symmetry breaking data within chiral EFT.

Findings

Accurately describes hyperon-nucleon scattering data and hypernuclear charge symmetry breaking.

Provides first predictions for $ ext{Λ}$-neutron scattering lengths from hypernuclear data.

Determines the strength of charge-symmetry breaking contact terms in the interaction.

Abstract

We utilize the experimentally known difference of the $\Lambda$ separation energies of the mirror hypernuclei ${^4_\Lambda \rm He}$ and ${^4_\Lambda \rm H}$ to constrain the $\Lambda$-neutron interaction. We include the leading charge-symmetry breaking (CSB) interaction into our hyperon-nucleon interaction derived within chiral effective field theory at next-to-leading order. In particular, we determine the strength of the two arising CSB contact terms by a fit to the differences of the separation energies of these hypernuclei in the $0^+$ and $1^+$ states, respectively. By construction, the resulting interaction describes all low energy hyperon-nucleon scattering data, the hypertriton and the CSB in ${^4_\Lambda \rm He}$-${^4_\Lambda \rm H}$ accurately. This allows us to provide first predictions for the $\Lambda$n scattering lengths, based solely on available hypernuclear data.