The onset of $\Lambda \Lambda$ hypernuclear binding

Abstract

Binding energies of light, $A\le 6$, $\Lambda \Lambda$ 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 $A\le 6$ $\Lambda \Lambda$ hypernucler binding energy datum of ${}_{\Lambda \Lambda }^6$He. The recently debated neutral three-body and four-body systems ${}_{\Lambda \Lambda }^3$n and ${}_{\Lambda \Lambda }^4$n are found unbound by a wide margin. A relatively large value of $|a_{\Lambda \Lambda }|\gtrsim 1.5$ fm is needed to bind ${}_{\Lambda \Lambda }^4$H, thereby questioning its particle stability. In contrast, the particle stability of the $A=5$ $\Lambda \Lambda$ hypernuclear isodoublet ${}_{\Lambda \Lambda }^5$H--${}_{\Lambda \Lambda }^5$He is robust, with $\Lambda$ separation energy of order 1 MeV.

v2 -- 14 pages, 4 figures, 1 table, slightly revised, accepted for publication in PLB