Uncertainty Analysis and Order-by-Order Optimization of Chiral Nuclear Interactions

Abstract

Chiral effective field theory (χEFT) provides a systematic approach to describe low-energy nuclear forces. Moreover, χEFT 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 χEFT. Finally, we study the effect on other observables by demonstrating forwarderror-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. This is also vital for the regression analysis. We use power-counting arguments to estimate the systematic uncertainty that is inherent to χEFT, 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 χEFT. Furthermore, certain systematic uncertainties in the few-nucleon sector are shown to get substantially magnified in the many-body sector, in particular 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.

High-precision QEC -value measurement of the superallowed β+ emitter Mg22 and an ab

“…This includes the excitation energy of the T = 1, J π = 0 + IAS in 22 Na which is at an 8 keV level of agreement with experiment. Of course, the full theoretical uncertainties are likely larger than this (and a subject of current study [21]), however along with the strong agreement across the nuclear chart using the 1.8/2.0(EM) approach, this indicates that these methods are nonetheless approaching the level of accuracy achievable with currently adopted phenomenological methods.…”

“…So far, these new methods have provided useful insight into where some of the older phenomenological approaches may be incomplete [13], but have not yet reached the level of refinement needed for testing the Standard Model. These new approaches are nonetheless intriguing, as they may offer some insight into quantifying any elusive model-dependent uncertainties, particularly using ab-initio many-body approaches based on nuclear forces from chiral effective field theory (χ-EFT) [19][20][21]. These efforts are critical due to the dramatic implications of a deviation from unity in the top-row sum of the CKM matrix resulting from a shift in the δ C calculations [5].…”

Asymmetric nuclear matter based on chiral two- and three-nucleon interactions

“…There are currently ongoing efforts to develop novel chiral EFT interactions (see, e.g., Ref. [31][32][33]) that enable order-byorder studies of matter and nuclei in the chiral expansion and allow to test the validity of the chiral power counting at nuclear densities in a systematic way.…”

The Falsification of Nuclear Forces

“…Normality of residuals provides a criterion of "falsibility" to distinguish those NN interactions that can come in conflict with observation and those that cannot. Interactions that fail the criterion [5,29] come in conflict with observation, even if they apparently give a good description of the data, because the chi-squared distribution cannot be used to test goodness of fit, and require more complex statistical techniques to analyze the data. Even though the description here is for statistical uncertainties, a certain glance into the systematic uncertainty can already be perceived by looking into the differences in phase-shifts and scattering amplitude predictions given by the different realistic potentials with χ 2 min /d.o.f.…”

“…Error propagation and uncertainty quantification have recently become a central topic in nuclear physics [1][2][3][4][5][6]. In the particular field of phenomenological Nucleon-Nucleon (NN) interactions uncertainties can be classified as statistical or systematic 1 .…”