Posterior predictive distributions of neutron-deuteron cross sections

TL;DR

This paper quantifies the uncertainties in neutron-deuteron scattering cross sections using chiral effective field theory, finding that truncation errors dominate over LEC variability at low energies.

Contribution

It provides a detailed analysis of the posterior predictive distributions of $nd$ cross sections, highlighting the dominance of EFT truncation errors over LEC uncertainties at N$^3$LO.

Findings

Uncertainty in LECs from $NN$ data has minimal impact on $nd$ predictions.

EFT truncation errors are the main source of uncertainty below N$^3$LO.

Both the PPD credible interval and truncation error are small and comparable at N$^3$LO.

Abstract

We quantify the posterior predictive distributions (PPDs) of elastic neutron-deuteron ($nd$) scattering cross sections using nucleon-nucleon ($NN$) interactions from chiral effective field theory ($\chi$EFT) up to and including next-to-next-to-next-to-leading order (N$^3$LO). These PPDs quantify the spread in $nd$ predictions due to the variability of the low-energy constants (LECs) inferred from $NN$ scattering data. We use the wave-packet continuum discretization method to solve the Alt-Grassberger-Sandhas form of the Faddeev equations for elastic scattering. We draw 100 samples from the PPDs of $nd$ cross sections up to 67 MeV in scattering energy, i.e., in the energy region where the effects of three-nucleon forces are expected to be small. We find that the uncertainty about $NN$ LECs inferred from $NN$ scattering data, when assuming uncorrelated errors, does not translate to significant uncertainty in the low-energy $nd$ continuum. Based on our estimates, the uncertainty of $nd$ predictions are dominated by the $\chi$EFT truncation error, at least below N$^3$LO. At this order, the 90% credible interval of the PPD and the truncation error are comparable, although both are very small on an absolute scale.