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Title: Quantifying correlated truncation errors in effective field theory

Journal Article · · Physical Review C
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)
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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.

Research Organization:
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 Organization:
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)
Grant/Contract Number:
SC0018083; PHY-1614460; RC107839-OSU; SC0014664; FG02-93ER-40756
OSTI ID:
1630533
Journal Information:
Physical Review C, Vol. 100, Issue 4; ISSN 2469-9985
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 79 works
Citation information provided by
Web of Science

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Figures / Tables (15)

Figure 1(p. 3)figure Figure 1
FIG. 2(p. 4)figure FIG. 2
FIG. 3(p. 5)figure FIG. 3
FIG. 4(p. 6)figure FIG. 4
FIG. 5(p. 7)figure FIG. 5
FIG. 6(p. 9)figure FIG. 6
TABLE I(p. 12)table TABLE I
FIG. 7(p. 13)figure FIG. 7
FIG. 8(p. 13)figure FIG. 8
FIG. 9(p. 14)figure FIG. 9
FIG. 10(p. 15)figure FIG. 10
FIG. 11(p. 17)figure FIG. 11
FIG. 12(p. 17)figure FIG. 12
FIG. 13(p. 18)figure FIG. 13
TABLE II(p. 19)table TABLE II

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