Low energy chiral two pion exchange potential with statistical uncertainties

TL;DR

This paper introduces a new low-energy chiral two-pion exchange nucleon-nucleon potential fitted to extensive scattering data, emphasizing statistical validation and uncertainty propagation, resulting in a softer interaction consistent with previous chiral constant determinations.

Contribution

The paper develops a statistically validated chiral NN potential with uncertainty analysis, providing a new determination of chiral constants and demonstrating a softer interaction than existing models.

Findings

Successful fit to scattering data with chi-squared per degree of freedom close to 1.

Determination of chiral constants c1, c3, c4 consistent with previous studies.

Identification of non-vanishing D-wave short distance components.

Abstract

We present a new phenomenological Nucleon-Nucleon chiral potential fitted to 925 pp and 1743 np scattering data selected from the Granada-2013 NN-database up to a laboratory energy of $125$ MeV with 20 short distance parameters and three chiral constants $c_1$, $c_3$ and $c_4$ with $\chi^2/\nu = 1.02$. Special attention is given to testing the normality of the residuals which allows for a sound propagation of statistical errors from the experimental data to the potential parameters, phase-shifts, scattering amplitudes and counter-terms. This fit allows for a new determination of the chiral constants $c_1$, $c_3$ and $c_4$ compatible with previous determinations from NN data. This new interactions is found to be softer than other high quality potentials by undertaking a Weinberg eigenvalue analysis. We further explore the interplay between the error analysis and the assumed form of the short distance interaction. The present work shows that it is possible to fit NN scattering with a TPE chiral potential fulfilling all necessary statistical requirements up to 125 MeV and shows unequivocal non-vanishing D-wave short distance pieces.