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

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.

References in corpus (11)

• How well do we know the neutron-matter equation of state at the densities inside neutron stars? A Bayesian approach with correlated uncertainties
• Quantifying uncertainties and correlations in the nuclear-matter equation of state
• Electromagnetic two-body currents of one- and two-pion range
• Get on the BAND Wagon: A Bayesian Framework for Quantifying Model Uncertainties in Nuclear Dynamics
• Light nuclei with semilocal momentum-space regularized chiral interactions up to third order
• Direct comparison between Bayesian and frequentist uncertainty quantification for nuclear reactions
• Precision determination of pion-nucleon coupling constants using effective field theory
• Dispersive evaluation of the Lamb shift in muonic deuterium from chiral effective field theory
• Effective field theory for dilute Fermi systems at fourth order
• Does Bayesian Model Averaging improve polynomial extrapolations? Two toy problems as tests
• Radiative pion photoproduction in covariant chiral perturbation theory