Renormalization of chiral two pion exchange NN interactions with delta excitations: correlations in the partial wave expansion

TL;DR

This paper investigates the renormalization of chiral two-pion exchange NN interactions with delta excitations, revealing correlations across partial waves and reducing the number of necessary counterterms for consistent scattering phase calculations.

Contribution

It introduces a unified renormalization approach for singular attractive interactions across partial waves with delta excitations, decreasing counterterms from previous models.

Findings

Correlations between partial waves are established due to singular potentials.

A single counterterm can renormalize all partial waves with identical singularities.

The number of counterterms is reduced to eleven for NN scattering with delta excitations.

Abstract

In this work we consider the renormalization of the chiral two-pion exchange potential with explicit delta-excitations for nucleon-nucleon scattering at next-to-leading (NLO) and next-to-next-to-leading order (N2LO). Due to the singular nature of the chiral potentials, correlations between different partial waves are generated. In particular we show that two-body scattering by a short distance power like singular attractive interaction can be renormalized in all partial waves with a single counterterm, provided the singularities are identical. A parallel statement holds in the presence of tensor interactions when the eigenpotentials in the coupled channel problem also coincide. While this construction reduces the total number of counterterms to eleven in the case of nucleon-nucleon scattering with chiral two-pion exchange interactions with delta degrees of freedom, the differences in the scattering phases as compared to the case with the uncorrelated partial wave renormalization become smaller as the angular momentum is increased in the elastic scattering region.