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.
Categories: nucl-th hep-ph nucl-ex