# Renormalization of chiral nuclear forces with multiple subtractions in peripheral channels

## TL;DR

This paper investigates the renormalization process of two-nucleon interactions in peripheral channels using multiple subtractions at N3LO, demonstrating scale independence in most cases and identifying some convergence issues.

## Contribution

It introduces a method for renormalizing chiral nuclear forces with multiple subtractions and analyzes their effects on phase shifts across different scales.

## Key findings

- Phase shifts are largely scale-independent in most peripheral waves.
- Some waves show slow convergence as the renormalization scale decreases.
- Oscillations in phase shifts occur at certain subtraction points.

## Abstract

We analyse the renormalization of the of two-nucleon interaction with multiple subtractions in peripheral waves considering two chiral forces at N3LO. Phase shifts at low energies are then computed with several subtraction points below \mu = 10 / fm. We show that for most peripheral waves the phase shifts have nearly no dependence on the renormalization scale. In two cases the phase shifts converge slowly as the renormalization scale approaches \mu = 1 / fm and in one case the phase shifts presented oscillations with respect to the subtraction point \mu.