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${}_{ΛΛ}^{4}$H in halo effective field theory

The ${}_{ΛΛ}^{\ \ 4}$H bound state and the $S$-wave hypertriton(${}_Λ^{ \, 3}$H)-$Λ$ scattering in spin singlet and triplet channels below the hypertriton breakup momentum scale are studied in halo/cluster effective field theory at leading order by treating the ${}_{ΛΛ}^{\ \ 4}$H system as a three-cluster ($Λ$-$Λ$-deuteron) system. In the spin singlet channel, the amplitude is insensitive to the cutoff parameter $Λ_c$ introduced in the integral equation, and we find that there is no bound state. In this case, the scattering length of the hypertriton-$Λ$ scattering is found to be $a_0^{} = 16.0\pm 3.0$ fm. In the spin triplet channel, however, the amplitude obtained by the coupled integral equations is sensitive to $Λ_c$, and we introduce the three-body contact interaction $g_1^{} (Λ_c)$. After phenomenologically fixing $g_1^{} (Λ_c)$, we find that the correlation between the two-$Λ$ separation energy $B_{ΛΛ}$ from the $_{ΛΛ}^{\ \ 4}$H bound state and the scattering length $a_{ΛΛ}^{}$ of the $S$-wave $Λ$-$Λ$ scattering is significantly sensitive to the value of $Λ_c$.