Posterior predictive distributions of neutron-deuteron cross sections

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 (xEFT) up to and including next-to-next-to-next-to-leading order (N 3LO). 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 xEFT truncation error, at least below N 3LO. 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.

Automated summary

We quantify the uncertainty in nd predictions due to the variability of the low-energy constants (LECs) inferred from nucleon-nucleon (NN) scattering data using nucleon-nucleon (NN) interactions from chiral effective field theory (xEFT) up to next-to-next-to-next-to-leading order (N 3LO) and solve the Faddeev equation for elastic scattering using the wave-packet continuum discretization method. We find that the uncertainty of nd predictions is dominated by the xEFT truncation error below N 3LO, and the uncertainty about NN LECs does not significantly contribute to the uncertainty in the low-energy nd continuum, assuming uncorrelated errors.