Power Counting For and Symmetries of the Effective Field Theory For NN Interactions

TL;DR

This paper reviews the power counting and symmetry properties of the effective field theory for nucleon-nucleon interactions, highlighting the role of a nontrivial fixed point and Wigner SU(4) symmetry in the limit of large scattering lengths.

Contribution

It clarifies the subtle power counting scheme and symmetry invariances in the EFT for NN interactions, especially near the nontrivial fixed point.

Findings

Leading two-body terms are scale invariant and Wigner symmetric.

Higher body terms without derivatives are automatically Wigner symmetric.

The power counting is more subtle due to the nontrivial fixed point.

Abstract

The appropriate power counting for the effective field theory of NN interactions is reviewed. It is more subtle than in most effective field theories since in the limit that the S-wave NN scattering lengths go to infinity it is governed by a nontrivial fixed point. The leading two body terms in the effective field theory for nucleon self interactions are scale invariant and invariant under Wigner SU(4) spin-isospin symmetry in this limit. Higher body terms with no derivatives (i.e., three and four body terms) are automatically invariant under Wigner symmetry.