Posterior predictive distributions of neutron-deuteron cross sections

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 ($\ensuremath{\chi}\mathrm{EFT}$) up to and including next-to-next-to-next-to-leading order ($\mathrm{N}^{3}\mathrm{LO}$). 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 $\ensuremath{\chi}\mathrm{EFT}$ truncation error, at least below $\mathrm{N}^{3}\mathrm{LO}$. 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.