Abstract
Chiral effective field theory (chiEFT) provides a systematic approach to describe low-energy nuclear forces. Moreover, chiEFT is able to provide well-founded estimates of statistical and systematic uncertainties -- although this unique advantage has not yet been fully exploited. We fill this gap by performing an optimization and statistical analysis of all the low-energy constants (LECs) up to next-to-next-to-leading order. Our optimization protocol corresponds to a simultaneous fit to scattering and bound-state observables in the pion-nucleon, nucleon-nucleon, and few-nucleon sectors, thereby utilizing the full model capabilities of chiEFT. We study the effect on other observables by demonstrating error-propagation methods that can easily be adopted by future works. We employ mathematical optimization and implement automatic differentiation to attain efficient and machine-precise first- and second-order derivatives of the objective function with respect to the LECs. We use power-counting arguments to estimate the systematic uncertainty that is inherent to chiEFT and we construct chiral interactions at different orders with quantified uncertainties. Statistical error propagation is compared with Monte Carlo sampling showing that statistical errors are in general small compared to systematic ones. In conclusion, we find that a simultaneous fit to different sets of data is critical to (i) identify the optimal set of LECs, (ii) capture all relevant correlations, (iii) reduce the statistical uncertainty, and (iv) attain order-by-order convergence in chiEFT. Furthermore, certain systematic uncertainties in the few-nucleon sector are shown to get substantially magnified in the many-body sector; in particlar when varying the cutoff in the chiral potentials. The methodology and results presented in this Paper open a new frontier for uncertainty quantification in ab initio nuclear theory.
Highlights
Uncertainty quantification is essential for generating new knowledge in scientific studies
Theoretical error bars have been estimated in various fields such as neurodynamics [1], global climate models [2], molecular dynamics [3], density functional theory [4], and high-energy physics [5]
We provide a common statistical regression analysis of two key frameworks in theoretical nuclear physics: ab initio many-body methods and chiral effective field theory
Summary
Uncertainty quantification is essential for generating new knowledge in scientific studies. The currently viable approach to accurately describe atomic nuclei in χEFT requires that the LECs are constrained from experimental low-energy data The bulk of this fit data traditionally consists of cross sections measured in nucleon-nucleon (NN) scattering experiments. The so-called power-counting scheme of the χEFT approach offers a systematically improvable description of NN, three-nucleon (NNN), and pion-nucleon (πN) interactions It provides a consistent framework in which LECs from the effective πN Lagrangian govern the strength of pion exchanges in the NN potential and of longand intermediate-range NNN forces. This implies that πN scattering data can be used to constrain some LECs that enter the chiral nuclear Hamiltonian.
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