The onset of \(\Lambda\Lambda\) hypernuclear binding

Binding energies of light, \(A\leq 6\), \(\Lambda\Lambda\) hypernuclei are calculated using the stochastic variational method in a pionless effective field theory (EFT) approach at leading order with the purpose of assessing critically the onset of binding in the strangeness S=-2 hadronic sector. The EFT input in this sector consists of (i) a \(\Lambda\Lambda\) contact term constrained by the \(\Lambda\Lambda\) scattering length \(a_{\Lambda\Lambda}\), using a range of values compatible with \(\Lambda\Lambda\) correlations observed in relativistic heavy ion collisions, and (ii) a \(\Lambda\Lambda N\) contact term constrained by the only available \(A\leq 6\) \(\Lambda\Lambda\) hypernucler binding energy datum of \(^{6}_{\Lambda\Lambda}\)He. The recently debated neutral three-body and four-body systems \(^{3}_{\Lambda\Lambda}\)n and \(^{4}_{\Lambda\Lambda}\)n are found unbound by a wide margin. A relatively large value of \(|a_{\Lambda\Lambda}| \gtrsim 1.5\) fm is needed to bind \(^{4}_{\Lambda\Lambda}\)H, thereby questioning its particle stability. In contrast, the particle stability of the \(A=5\) \(\Lambda\Lambda\) hypernuclear isodoublet \(^{5}_{\Lambda\Lambda} \)H--\(^{5}_{\Lambda\Lambda}\)He is robust, with \(\Lambda\) separation energy of order 1 MeV.