# Renormalization of a Finite Range Inverse Cube Potential

## TL;DR

This paper investigates the regularization and renormalization of a finite range inverse cube potential, comparing different schemes and demonstrating the effectiveness of a two-body contact interaction in renormalizing few-body observables.

## Contribution

It provides a comparative analysis of regulation schemes and shows that a simple two-body contact interaction suffices for renormalization in this context.

## Key findings

- Different regulation schemes yield consistent renormalization results.
- A two-body contact interaction effectively renormalizes two- and three-body observables.
- Residual cutoff dependence is quantitatively analyzed.

## Abstract

We study the regularization and renormalization of a finite range inverse cube potential in the two- and three-body sectors. Specifically, we compare and contrast three different regulation schemes frequently used to study few-body systems as well as the associated renormalization group flows. We also calculate bound state and scattering observables over a wide range of cutoffs, demonstrating the sufficiency of a two-body contact interaction to renormalize two- and three-body observables. We supplement these plots with quantified analyses of the observables' residual cutoff dependence.