Halo EFT treatment of 6He up to NLO

Halo nuclei exhibit separation of scales and are therefore amenable to an Effective Field Theory (EFT) description. In Halo EFT, $^6$He can be thought of as a tight $^4$He $(\alpha)$ core surrounded by two loosely bound neutrons ($n$), hence it constitutes an effective Borromean three-body system. The valence neutrons of $^6$He interact with the $\alpha$-core predominantly through a $p$-wave $(^2P_{3/2})$ resonance while the two neutrons are in relative $s$-wave $(^1S_0)$ resonance. The leading order (LO) Halo EFT calculations using momentum-space Faddeev equations pertinent to such a treatment of bound $^6$He were carried out by Ji et al. in Phys.\ Rev.\ C {\bf 90}, no. 4, 044004 (2014). As an extension to that work, we are investigating $^6$He up to NLO within Halo EFT. In this talk, I will demonstrate how the NLO piece of the $^1S_0$ $nn$ dimer propagator, the NLO piece of the $^2P_{3/2}$ $n\alpha$ dimer propagator and the contact $n\alpha$ vertex in the $^2S_{1/2}$ channel become important at NLO in the three-body problem. I will show the diagrams that contribute to the NLO three-body $t$-matrix and discuss their divergences and renormalization.