Three-Body Halo States in Effective Field Theory: Renormalization and Three-Body Interactions in the Helium-6 System

In this paper we study the renormalization of Halo effective field theory applied to the Helium-6 halo nucleus seen as an alpha-neutron-neutron three-body state. We include the 0(+) dineutron channel together with both the 3/2(-) and 1/2(-) neutron-alpha channels into the field theory and study all of the six lowest-order three-body interactions that are present. Furthermore, we discuss three different prescriptions to handle the unphysical poles in the P-wave two-body sector. In the simpler field theory without the 1/2(-) channel present we find that the bound-state spectrum of the field theory is renormalized by the inclusion of a single three-body interaction. However, in the field theory with both the 3/2(-) and 1/2(-) included, the system can not be renormalized by only one three-body operator.