Uncertainty of three-nucleon continuum observables arising from uncertainties of two-nucleon potential parameters

TL;DR

This study quantifies how uncertainties in two-nucleon potential parameters affect three-nucleon scattering observables, comparing chiral and semi-phenomenological forces, and assesses the relative importance of statistical, truncation, and cutoff errors across energies.

Contribution

It provides a detailed analysis of uncertainty propagation from two-nucleon potentials to three-nucleon observables using chiral interactions, including Bayesian estimates of truncation errors and cutoff dependence.

Findings

Statistical uncertainties are smaller than truncation errors at lower chiral orders.

At higher orders and low energies, statistical errors surpass truncation errors.

Overall uncertainties are within 0.5% to 4%, depending on observable and energy.

Abstract

Propagation of uncertainties from two-nucleon potential parameters to three-nucleon observables, that is statistical errors for the neutron-deuteron elastic scattering and the deuteron breakup reaction at neutron laboratory energies up to 200 MeV is investigated. To that end we use the chiral nucleon-nucleon interaction with the semi-local momentum-space regularization at various orders of the chiral expansion, exploiting knowledge of the covariance matrix of its parameters. For both reactions we compare statistical uncertainties for chiral predictions with the uncertainties obtained in the same way but for the semi-phenomenological One-Pion-Exchange two-nucleon force. In addition for the elastic scattering we show also the truncation errors arising from restriction to a given order of chiral predictions, estimated among others within the Bayesian method, and the cutoff dependence of chiral predictions. We find that the resulting statistical uncertainty is smaller than the truncation errors for the chiral force at lower orders of the chiral expansion. At the higher orders of the chiral expansion and at low energies the statistical errors exceed the truncation ones but at intermediate and higher energies truncation errors are more important. Overall, magnitudes of the theoretical uncertainties are small and amount up to 0.5\%-4\%, depending on the observable and energy. We also find that the magnitudes of statistical uncertainties for the chiral and semi-phenomenological potentials are similar and that the dependence of predictions on the regularization parameter values is important at all investigated energies.