Nucleon-nucleon scattering within a multiple subtractive renormalization approach

TL;DR

This paper introduces a recursive multiple subtraction renormalization method for nucleon-nucleon interactions, successfully fitting experimental data across various partial waves and linking the subtraction energy to the QCD scale.

Contribution

It presents a novel recursive subtraction approach for renormalizing nucleon-nucleon interactions, applicable at NLO and NNLO, with a consistent renormalization scale.

Findings

Effective fit to low-energy experimental data

Subtraction energy aligns with the QCD scale

Method applicable to multiple partial waves

Abstract

A methodology to renormalize the nucleon-nucleon interaction, using a recursive multiple subtraction approach to construct the kernel of the scattering equation, is presented. We solve the subtracted scattering equation with the next-leading-order (NLO) and next-to-next-leading-order (NNLO) interactions. The results are presented for all partial waves up to $j=2$, fitted to low-energy experimental data. In our renormalizaton group invariant method, when introducing the NLO and NNLO interactions, the subtraction energy emerges as a renormalization scale and the momentum associated with it comes to be about the QCD scale ($\Lambda_{QCD}$), irrespectively to the partial wave.