The onset of ΛΛ hypernuclear binding

Abstract

Binding energies of light, $A\le 6$, ΛΛ hypernuclei are calculated using the stochastic variational method in a pionless effective field theory (π̸EFT) approach at leading order with the purpose of assessing critically the onset of binding in the strangeness $\mathcal{S}=-2$ hadronic sector. The π̸EFT input in this sector consists of (i) a ΛΛ contact term constrained by the ΛΛ scattering length $a_{\mathrm{\Lambda }\mathrm{\Lambda }}$, using a range of values compatible with ΛΛ correlations observed in relativistic heavy ion collisions, and (ii) a ΛΛN contact term constrained by the only available $A\le 6$ ΛΛ 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 $|a_{\mathrm{\Lambda }\mathrm{\Lambda }}|\gtrsim 1.5$ fm is needed to bind ${}_{\mathrm{\Lambda }\mathrm{\Lambda }}^4$H, thereby questioning its particle stability. In contrast, the particle stability of the $A=5$ ΛΛ hypernuclear isodoublet ${}_{\mathrm{\Lambda }\mathrm{\Lambda }}^5$H–${}_{\mathrm{\Lambda }\mathrm{\Lambda }}^5$He is robust, with Λ separation energy of order 1 MeV.