Hypernuclei in Halo/Cluster Effective Field Theory

Abstract

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