6ΛΛHe in cluster effective field theory

The hypernucleus He-6(Lambda Lambda) is studied as a three-body (Lambda Lambda alpha) cluster system in cluster effective field theory at leading order. We find that the three-body contact interaction exhibits the limit cycle when the cutoff in the integral equations is sent to the asymptotic limit and thus it should be promoted to leading order. We also derive a determination equation of the limit cycle which reproduces the numerically obtained limit cycle. We then study the correlations between the double Lambda separation energy B Lambda Lambda of He-6(Lambda Lambda) and the scattering length a Lambda Lambda of the S-wave Lambda Lambda scattering. The role of the scale in this approach is also discussed.