Nonperturbative $^3S_1$-$^3D_1$ NN scattering in pionless EFT

TL;DR

This paper presents a nonperturbative analysis of neutron-proton scattering in coupled channels within pionless effective field theory, highlighting renormalization features and proposing a simplified power counting scheme.

Contribution

It introduces a nonperturbative framework for $^3S_1$-$^3D_1$ NN scattering in pionless EFT with contact potentials truncated at order 4, emphasizing renormalization and power counting.

Findings

On-shell $T$-matrices derived for coupled channels

Analysis of nonperturbative renormalization features

Proposed simplified EFT power counting scheme

Abstract

The rigorous on-shell $T$-matrices for $NN$ scattering in the coupled channels $^3S_1$$-$$^3D_1$ are briefly presented in the context of EFT($\not\pi$) with the contact potentials truncated at order $\Delta=4$. The nonperturbative features of renormalization are highlighted and elaborated. A simple scenario for EFT power counting's and renormalization prescriptions is also presented with its consequences being roughly analyzed and discussed.