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Title: Quantifying correlated truncation errors in effective field theory

Abstract

Effective field theories (EFTs) organize the description of complex systems into an infinite sequence of decreasing importance. Predictions are made with a finite number of terms, which induces a truncation error that is often left unquantified. Here, we formalize the notion of EFT convergence and propose a Bayesian truncation error model for predictions that are correlated across the independent variables, e.g., energy or scattering angle. Central to our approach are Gaussian processes that encode both the naturalness and correlation structure of EFT coefficients. Our use of Gaussian processes permits efficient and accurate assessment of credible intervals, allows EFT fits to easily include correlated theory errors, and provides analytic posteriors for physical EFT-related quantities such as the expansion parameter. Furthermore, we demonstrate that model-checking diagnostics—applied to the case of multiple curves—are powerful tools for EFT validation. As an example, we assess a set of nucleon-nucleon scattering observables in chiral EFT. In an effort to be self-contained, appendices include thorough derivations of our statistical results. Our methods are packaged in Python code, called gsum, that is available for download on GitHub.

Authors:
ORCiD logo [1];  [1];  [2];  [1];  [3]
  1. The Ohio State Univ., Columbus, OH (United States)
  2. Ohio Univ., Athens, OH (United States); Technical Univ. of Darmstadt (Germany); GSI-Darmstadt (Germany)
  3. Salisbury Univ., MD (United States)
Publication Date:
Research Org.:
The Ohio State Univ., Columbus, OH (United States); Michigan State Univ., East Lansing, MI; Oak Ridge Associated Univ., Oak Ridge, TN (United States) (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Workforce Development for Teachers and Scientists (WDTS); USDOE Office of Science (SC), Nuclear Physics (NP); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR). Scientific Discovery through Advanced Computing (SciDAC)
OSTI Identifier:
1630533
Grant/Contract Number:  
SC0018083; PHY-1614460; RC107839-OSU; SC0014664; FG02-93ER-40756
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review C
Additional Journal Information:
Journal Volume: 100; Journal Issue: 4; Journal ID: ISSN 2469-9985
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
73 NUCLEAR PHYSICS AND RADIATION PHYSICS

Citation Formats

Melendez, J. A., Furnstahl, R. J., Phillips, D. R., Pratola, M. T., and Wesolowski, S. Quantifying correlated truncation errors in effective field theory. United States: N. p., 2019. Web. https://doi.org/10.1103/PhysRevC.100.044001.
Melendez, J. A., Furnstahl, R. J., Phillips, D. R., Pratola, M. T., & Wesolowski, S. Quantifying correlated truncation errors in effective field theory. United States. https://doi.org/10.1103/PhysRevC.100.044001
Melendez, J. A., Furnstahl, R. J., Phillips, D. R., Pratola, M. T., and Wesolowski, S. Thu . "Quantifying correlated truncation errors in effective field theory". United States. https://doi.org/10.1103/PhysRevC.100.044001. https://www.osti.gov/servlets/purl/1630533.
@article{osti_1630533,
title = {Quantifying correlated truncation errors in effective field theory},
author = {Melendez, J. A. and Furnstahl, R. J. and Phillips, D. R. and Pratola, M. T. and Wesolowski, S.},
abstractNote = {Effective field theories (EFTs) organize the description of complex systems into an infinite sequence of decreasing importance. Predictions are made with a finite number of terms, which induces a truncation error that is often left unquantified. Here, we formalize the notion of EFT convergence and propose a Bayesian truncation error model for predictions that are correlated across the independent variables, e.g., energy or scattering angle. Central to our approach are Gaussian processes that encode both the naturalness and correlation structure of EFT coefficients. Our use of Gaussian processes permits efficient and accurate assessment of credible intervals, allows EFT fits to easily include correlated theory errors, and provides analytic posteriors for physical EFT-related quantities such as the expansion parameter. Furthermore, we demonstrate that model-checking diagnostics—applied to the case of multiple curves—are powerful tools for EFT validation. As an example, we assess a set of nucleon-nucleon scattering observables in chiral EFT. In an effort to be self-contained, appendices include thorough derivations of our statistical results. Our methods are packaged in Python code, called gsum, that is available for download on GitHub.},
doi = {10.1103/PhysRevC.100.044001},
journal = {Physical Review C},
number = 4,
volume = 100,
place = {United States},
year = {2019},
month = {10}
}

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Figures / Tables:

Figure 1 Figure 1: The roadmap from EFT predictions to prediction coefficients: (a) the predictions themselves as a function of a generic variable x, (b) the leading-order prediction y0 and the increasingly suppressed order-by-order corrections ∆yn, and (c) the dimensionless coefficients cn (using yref = 10 and $\mathcal{Q}$ = 0.5). One mightmore » object that |∆y3| is often larger than |∆y2|, or that the coefficients in (c) do not appear sufficiently random. This is a consequence of a small sample size and seeing patterns in randomness: the coefficients cn shown above are actual random draws from an underlying GP and were used to build parts (a) and (b). By chance c2 is relatively small, and thus the correction |∆y2| is actually smaller than |∆y3| for this choice of $\mathcal{Q}$. It pays to remember this example when considering real EFT predictions.« less

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