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 EFTrelated quantities such as the expansion parameter. Furthermore, we demonstrate that modelchecking diagnostics—applied to the case of multiple curves—are powerful tools for EFT validation. As an example, we assess a set of nucleonnucleon scattering observables in chiral EFT. In an effort to be selfcontained, 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:

 The Ohio State Univ., Columbus, OH (United States)
 Ohio Univ., Athens, OH (United States); Technical Univ. of Darmstadt (Germany); GSIDarmstadt (Germany)
 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; PHY1614460; RC107839OSU; SC0014664; FG0293ER40756
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Physical Review C
 Additional Journal Information:
 Journal Volume: 100; Journal Issue: 4; Journal ID: ISSN 24699985
 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 EFTrelated quantities such as the expansion parameter. Furthermore, we demonstrate that modelchecking diagnostics—applied to the case of multiple curves—are powerful tools for EFT validation. As an example, we assess a set of nucleonnucleon scattering observables in chiral EFT. In an effort to be selfcontained, 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}
}
Web of Science
Figures / Tables:
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