Weinberg eigenvalues for chiral nucleon-nucleon interactions

TL;DR

This paper analyzes modern chiral nucleon-nucleon interactions using Weinberg eigenvalues, revealing similarities in attractive eigenvalues and regulator-dependent differences in repulsive ones, offering insights for potential development.

Contribution

It provides a comprehensive Weinberg eigenvalue analysis across various chiral potentials, highlighting regulator effects and guiding future interaction construction.

Findings

Attractive eigenvalues are similar across interactions.

Repulsive eigenvalues depend on regularization schemes.

Comparison of cutoff values across different interactions can be misleading.

Abstract

We perform a comprehensive Weinberg eigenvalue analysis of a representative set of modern nucleon-nucleon interactions derived within chiral effective field theory. Our set contains local, semilocal, and nonlocal potentials, developed by Gezerlis, Tews et al. (2013); Epelbaum, Krebs, and Mei{\ss}ner (2015); and Entem, Machleidt, and Nosyk (2017) as well as Carlsson, Ekstr\"om et al. (2016), respectively. The attractive eigenvalues show a very similar behavior for all investigated interactions, whereas the magnitudes of the repulsive eigenvalues sensitively depend on the details of the regularization scheme of the short- and long-range parts of the interactions. We demonstrate that a direct comparison of numerical cutoff values of different interactions is in general misleading due to the different analytic form of regulators; for example, a cutoff value of $R=0.8$ fm for the semilocal interactions corresponds to about $R=1.2$ fm for the local interactions. Our detailed comparison of Weinberg eigenvalues provides various insights into idiosyncrasies of chiral potentials for different orders and partial waves. This shows that Weinberg eigenvalues could be used as a helpful monitoring scheme when constructing new interactions.