Low-energy chiral two-pion exchange potential with statistical uncertainties

Abstract

We present a new phenomenological nucleon-nucleon $(NN)$ 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 ${c}_{1},\phantom{\rule{0.16em}{0ex}}{c}_{3}$, and ${c}_{4}$ with ${\ensuremath{\chi}}^{2}/\ensuremath{\nu}=1.02$. 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 counterterms. This fit allows for a new determination of the chiral constants ${c}_{1},\phantom{\rule{0.16em}{0ex}}{c}_{3}$, and ${c}_{4}$ compatible with previous determinations from $NN$ data. This new interaction 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 two-pion exchange (TPE) chiral potential fulfilling all necessary statistical requirements up to 125 MeV and shows unequivocal nonvanishing $D$-wave short-distance pieces.