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

Abstract

We utilize the experimentally known difference of the $\Lambda$ separation energies of the mirror hypernuclei ${}_{\Lambda }^4\mathrm{He}$ and ${}_{\Lambda }^4\mathrm{H}$ 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 ${}_{\Lambda }^4\mathrm{He}$-${}_{\Lambda }^4\mathrm{H}$ accurately. This allows us to provide first predictions for the $\Lambda$n scattering lengths, based solely on available hypernuclear data.

Comments: 19 pages, 2 figures, to be submitted to special issue of few-body systems "Celebrating 30 years of Steven Weinberg's papers on Nuclear Forces from Chiral Lagrangians"