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Chiral effective field theory (chiEFT) provides a systematic approach todescribe low-energy nuclear forces. Moreover, chiEFT is able to providewell-founded estimates of statistical and systematic uncertainties -- althoughthis unique advantage has not yet been fully exploited. We fill this gap byperforming an optimization and statistical analysis of all the low-energyconstants (LECs) up to next-to-next-to-leading order. Our optimization protocolcorresponds to a simultaneous fit to scattering and bound-state observables inthe pion-nucleon, nucleon-nucleon, and few-nucleon sectors, thereby utilizingthe full model capabilities of chiEFT. We study the effect on other observablesby demonstrating error-propagation methods that can easily be adopted by futureworks. We employ mathematical optimization and implement automaticdifferentiation to attain efficient and machine-precise first- and second-orderderivatives of the objective function with respect to the LECs. We usepower-counting arguments to estimate the systematic uncertainty that isinherent to chiEFT and we construct chiral interactions at different orderswith quantified uncertainties. Statistical error propagation is compared withMonte Carlo sampling showing that statistical errors are in general smallcompared to systematic ones. In conclusion, we find that a simultaneous fit todifferent sets of data is critical to (i) identify the optimal set of LECs,(ii) capture all relevant correlations, (iii) reduce the statisticaluncertainty, and (iv) attain order-by-order convergence in chiEFT. Furthermore,certain systematic uncertainties in the few-nucleon sector are shown to getsubstantially magnified in the many-body sector; in particlar when varying thecutoff in the chiral potentials. The methodology and results presented in thisPaper open a new frontier for uncertainty quantification in ab initio nucleartheory.

Uncertainty analysis and order-by-order optimization of chiral nuclear interactions