# The onset of $\Lambda\Lambda$ hypernuclear binding

## TL;DR

This study uses pionless EFT and stochastic variational methods to analyze the binding energies of light $ ext{Lambda} ext{Lambda}$ hypernuclei, assessing the conditions for their formation and stability in the strangeness S=-2 sector.

## Contribution

It provides a systematic EFT-based calculation of light $ ext{Lambda} ext{Lambda}$ hypernuclei binding energies, clarifying the onset of binding and stability in this sector.

## Key findings

- $^{3}_{ ext{Lambda} ext{Lambda}}$n and $^{4}_{ ext{Lambda} ext{Lambda}}$n are unbound.
- Large $|a_{ ext{Lambda} ext{Lambda}}| extgreater 1.5$ fm needed for $^{4}_{ ext{Lambda} ext{Lambda}}$H binding.
- $^{5}_{ ext{Lambda} ext{Lambda}}$H--$^{5}_{ ext{Lambda} ext{Lambda}}$He are stable with $ ext{Lambda}$ separation energy around 1 MeV.

## Abstract

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.