Gaussian process error modeling for chiral effective-field-theory calculations of $np\leftrightarrow d\gamma$ at low energies

TL;DR

This paper employs Gaussian process modeling to quantify uncertainties in chiral effective field theory calculations of the neutron-proton to deuteron gamma process at low energies, relevant for astrophysics.

Contribution

It introduces a Bayesian Gaussian process error model to accurately estimate and correlate uncertainties in chiral EFT predictions of low-energy nuclear reaction cross sections.

Findings

Gaussian process model fits the convergence pattern well

Provides credible intervals for truncation errors

Estimates about 0.2% uncertainty from nuclear potential truncation

Abstract

We calculate the energy-dependent cross section of the $np\leftrightarrow d\gamma$ process in chiral effective field theory and apply state-of-the-art tools for quantification of theory uncertainty. We focus on the low-energy regime, where the magnetic dipole and the electric dipole transitions cross over, including the range relevant for big-bang nucleosynthesis. Working with the leading one- and two-body electromagnetic currents, we study the order-by-order convergence of this observable in the chiral expansion of the nuclear potential. We find that the Gaussian process error model describes the observed convergence very well, allowing us to present Bayesian credible intervals for the truncation error with correlations between the cross sections at different energies taken into account. We obtain a 1$\sigma$ estimate of about 0.2\% for the uncertainty from the truncation of the nuclear potential. This is an important step towards calculations with statistically interpretable uncertainties for astrophysical reactions involving light nuclei.