Hypernuclei in Halo/Cluster Effective Field Theory

The light double $Λ$ hypernuclei, ${}_{ΛΛ}^{\ \ 4}$H and ${}_{ΛΛ}^{\ \ 6}$He, are studied as three-body $ΛΛd$ and $ΛΛα$ cluster systems in halo/cluster effective field theory at leading order. We find that the $ΛΛd$ system in spin-0 channel does not exhibit a limit cycle whereas the $ΛΛd$ system in spin-1 channel and the $ΛΛα$ system in spin-0 channel do. The limit cycle is associated with the formation of bound states, known as Efimov states, in the unitary limit. For the $ΛΛd$ system in the spin-0 channel we estimate the scattering length $a_0$ for $S$-wave $Λ$ hyperon-hypertriton scattering as $a_0=16.0\pm 3.0$ fm. We also discuss that studying the cutoff dependences in the $ΛΛd$ and $ΛΛα$ systems, the bound state of ${}_{ΛΛ}^{\ \ 4}$H is not an Efimov state but formed due to a high energy mechanism whereas that of ${}_{ΛΛ}^{\ \ 6}$He may be regarded as an Efimov state.

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