Inference of the low-energy constants in $\Delta$-full chiral effective field theory including a correlated truncation error

Abstract

We sample the posterior probability distributions of the low-energy constants (LECs) in $\Delta$-full chiral effective field theory ($\chi$EFT) up to third order. We use eigenvector continuation for fast and accurate emulation of the likelihood and Hamiltonian Monte Carlo to draw effectively independent samples from the posteriors. Our Bayesian inference is conditioned on the Granada database of neutron-proton ($np$) cross sections and polarizations. We use priors grounded in $\chi$EFT assumptions and a Roy-Steiner analysis of pion-nucleon scattering data. We model correlated EFT truncation errors using a two-feature Gaussian process, and find correlation lengths for $np$ scattering energies and angles in the ranges 45--83 MeV and 24--39 degrees, respectively. These correlations yield a non-diagonal covariance matrix and reduce the number of independent scattering data with a factor of 8 and 4 at the second and third chiral orders, respectively. The relatively small difference between the second and third order predictions in $\Delta$-full $\chi$EFT suppresses the marginal variance of the truncation error and the effects of its correlation structure. Our results are particularly important for analyzing the predictive capabilities in \textit{ab initio} nuclear theory.

17 pages, 12 figures. Updated to match Phys. Rev. C version as closely as possible

References in corpus (14)

• Chiral effective field theory and nuclear forces
• Accurate nuclear radii and binding energies from a chiral interaction
• Improved chiral nucleon-nucleon potential up to next-to-next-to-next-to-leading order
• Ab initio predictions link the neutron skin of ${}^{208}$Pb to nuclear forces
• Minimally non-local nucleon-nucleon potentials with chiral two-pion exchange including $\Delta$'s
• Nuclear forces with Delta-excitations up to next-to-next-to-leading order I: peripheral nucleon-nucleon waves
• Delta-excitations and the three-nucleon force
• Rigorous constraints on three-nucleon forces in chiral effective field theory from fast and accurate calculations of few-body observables
• What is ab initio in nuclear theory?
• Nuclear matter properties from local chiral interactions with $\Delta$ isobar intermediate states
• Fast & accurate emulation of two-body scattering observables without wave functions
• Bayesian parameter estimation in $\chi$EFT using Hamiltonian Monte Carlo
• Emulating \emph{ab initio} computations of infinite nucleonic matter
• Nuclear-matter saturation and symmetry energy within $\Delta$--full chiral effective field theory

Cited by in corpus (5)

• Eigenvector Continuation and Projection-Based Emulators
• Multiscale physics of atomic nuclei from first principles
• Bayesian approach for many-body uncertainties in nuclear structure: Many-body perturbation theory for finite nuclei
• Active learning emulators for nuclear two-body scattering in momentum space
• Chiral interactions and superfluidity in the calcium isotopic chain