B$_\Lambda$($^5_\Lambda$He) from short range effective field theory

Abstract

We present an effective field theory (EFT) at leading order to describe light single-$\Lambda$ hypernuclei. Owing to the weak $\Lambda$ binding and to the $\Lambda N$ short interaction range, meson exchange forces are approximated by contact interactions within a pionless EFT where the only degrees of freedom are baryons. At leading order, the $\Lambda$-nuclear interaction contains two 2-body (singlet and triplet) and three 3-body interaction terms, a total of 5 terms associated with 5 coupling strengths or low energy constants (LECs). We adopt the 2-body LECs from hyperon-nucleon scattering data and interaction models that constrain the $\Lambda N$ scattering lengths, while the 3-body LECs are adjusted using both 3-body and 4-body hypernuclear binding energies. To calculate the binding energies for A-body systems with A$>$2, we expand the wavefunctions using a correlated Gaussian basis. The stochastic variational method is employed to select the non-linear parameters. The resulting \nopieft~is then applied to calculate the $\Lambda$ separation energy in $_\Lambda^5$He, where the adjusted 3-body interactions largely resolve the known overbinding problem of $_\Lambda^5$He.