Abstract
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.
Highlights
Effective field theory (EFT) has become a widely used tool to construct interactions for few-body problems in atomic and nuclear physics
Halo EFT uses the ratio of the valence-nucleon separation energy and the binding of the core as the expansion parameter for the low-energy EFT expansion
Numerically we are limited to lower cutoffs in the expansion prescription (EP), than in the unitarity piece removal prescription (UP) or subtraction prescription (SP), since the three-body amplitudes will consist of differences of very large numbers when the cutoff is large
Summary
Effective field theory (EFT) has become a widely used tool to construct interactions for few-body problems in atomic and nuclear physics. [24] this interaction is needed already at LO for the theory to be renormalized Another problem that can occur in few-body systems is the appearance of spurious bound states in the two-body subsystem at cutoffs larger than the breakdown scale. This happens for example in the deuteron system when a chiral potential with a large momentum-space cutoff is employed, and in Halo EFT when systems that interact resonantly in a relative P-wave are considered. We compare the three different prescriptions of how to treat the unphysical P-wave poles in the two-body sector This manuscript is organized as follows: In Sect.
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