The onset of $\mathrm{\Lambda }\mathrm{\Lambda }$ hypernuclear binding

Binding energies of light, $A\le 6$, $\mathrm{\Lambda }\mathrm{\Lambda }$ 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 $\mathrm{\Lambda }\mathrm{\Lambda }$ contact term constrained by the $\mathrm{\Lambda }\mathrm{\Lambda }$ scattering length $a_{\mathrm{\Lambda }\mathrm{\Lambda }}$, using a range of values compatible with $\mathrm{\Lambda }\mathrm{\Lambda }$ correlations observed in relativistic heavy ion collisions, and (ii) a $\mathrm{\Lambda }\mathrm{\Lambda }N$ contact term constrained by the only available $A\le 6$ $\mathrm{\Lambda }\mathrm{\Lambda }$ hypernucler binding energy datum of ${}_{\mathrm{\Lambda }\mathrm{\Lambda }}^6$He. The recently debated neutral three-body and four-body systems ${}_{\mathrm{\Lambda }\mathrm{\Lambda }}^3$n and ${}_{\mathrm{\Lambda }\mathrm{\Lambda }}^4$n are found unbound by a wide margin. A relatively large value of $\mathrm{\mid }{a}_{\mathrm{\Lambda }\mathrm{\Lambda }}\mathrm{\mid }\gtrsim 1.5$ fm is needed to bind ${}_{\mathrm{\Lambda }\mathrm{\Lambda }}^4$H, thereby questioning its particle stability. In contrast, the particle stability of the $A=5$ $\mathrm{\Lambda }\mathrm{\Lambda }$ hypernuclear isodoublet ${}_{\mathrm{\Lambda }\mathrm{\Lambda }}^5$H–${}_{\mathrm{\Lambda }\mathrm{\Lambda }}^5$He is robust, with $\mathrm{\Lambda }$ separation energy of order 1 MeV.