Three-body halo states in effective field theory

TL;DR

This paper investigates the renormalization of Halo effective field theory for Helium-6, considering multiple channels and three-body interactions, revealing the complexity of renormalization when multiple channels are included.

Contribution

It introduces a comprehensive analysis of three-body interactions and unphysical poles in Halo EFT for Helium-6, highlighting the need for multiple operators for proper renormalization.

Findings

Single three-body interaction suffices in simpler models

Multiple channels complicate renormalization

Handling unphysical poles is crucial for accurate EFT

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.