Quantifying truncation errors in effective field theory

By Richard J. Furnstahl, N. Klco, D. Phillips, S. Wesolowski. 2015

172 citations recorded by the source corpus.

Bayesian procedures designed to quantify truncation errors in perturbative calculations of quantum chromodynamics observables are adapted to expansions in effective field theory (EFT). In the Bayesian approach, such truncation errors are derived from degree-of-belief (DOB) intervals for EFT predictions. Computation of these intervals requires specification of prior probability distributions ("priors") for the expansion coefficients. By encoding expectations about the naturalness of these coefficients, this framework provides a statistical interpretation of the standard EFT procedure where truncation errors are estimated using the order-by-order convergence of the expansion. It also permits exploration of the ways in which such error bars are, and are not, sensitive to assumptions about EFT-coefficient naturalness. We first demonstrate the calculation of Bayesian probability distributions for the EFT truncation error in some representative examples, and then focus on the application of chiral EFT to neutron-proton scattering. Epelbaum, Krebs, and Mei{\ss}ner recently articulated explicit rules for estimating truncation errors in such EFT calculations of few-nucleon-system properties. We find that their basic procedure emerges generically from one class of naturalness priors considered, and that all such priors result in consistent quantitative predictions for 68% DOB intervals. We then explore several methods by which the convergence properties of the EFT for a set of observables may be used to check the statistical consistency of the EFT expansion parameter.

Subfields: Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/9c10302e3d700835d106237f63ff681a242a9c1c

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Citations in the corpus

Nuclear effective field theory: Status and perspectives (2019, methodology): “A comprehensive theory of EFT error analysis based on Bayesian methods is currently being developed (Furnstahl et al., 2015b,a; Wesolowski et al., 2016) with the promise of becoming the standard in the field.”
A Guided Tour of ab initio Nuclear Many-Body Theory (2020, methodology): “The application of Bayesian methods has led to enormous progress in the quantification of the EFT uncertainties [282, 283, 284, 34, 36, 35, 285], and it would be highly desirable to apply the same approach to the many-body uncertainties as well.”
High-Precision Nuclear Forces From Chiral EFT: State-of-the-Art, Challenges, and Outlook (2019, background): “[131], the EKMuncertainties for the np total cross section were found to be consistent with 68% degree-of-belief (DoB) intervals.”