Effective field theory for shallow P-wave states

TL;DR

This paper develops a non-relativistic effective field theory for shallow P-wave states, clarifying renormalization methods and their implications for two-body scattering analysis.

Contribution

It demonstrates the equivalence of different renormalization approaches and analyzes P-wave scattering using Wilsonian renormalization group techniques.

Findings

Consistent renormalization involves infinite counterterms in contact interaction models.

Auxiliary dimer field formalism simplifies renormalization with finite parameters.

Wilsonian RG analysis provides insights into P-wave scattering behavior.

Abstract

We discuss the formulation of a non-relativistic effective field theory for two-body P-wave scattering in the presence of shallow states and critically address various approaches to renormalization proposed in the literature. It is demonstrated that the consistent renormalization involving only a finite number of parameters in the well-established formalism with auxiliary dimer fields corresponds to the inclusion of an infinite number of counterterms in the formulation with contact interactions only. We also discuss the implications from the Wilsonian renormalization group analysis of P-wave scattering.