Quantifying truncation errors in effective field theory

R. J. Furnstahl, N. Klco, D. R. Phillips, and S. Wesolowski
Phys. Rev. C 92, 024005 – Published 18 August 2015

Abstract

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 Meißner 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.

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  • Received 12 June 2015

DOI:https://doi.org/10.1103/PhysRevC.92.024005

©2015 American Physical Society

Authors & Affiliations

R. J. Furnstahl1,*, N. Klco2,†, D. R. Phillips2,‡, and S. Wesolowski1,§

  • 1Department of Physics, The Ohio State University, Columbus, Ohio 43210, USA
  • 2Institute of Nuclear and Particle Physics and Department of Physics and Astronomy, Ohio University, Athens, Ohio 45701, USA

  • *furnstahl.1@osu.edu
  • klcon@uw.edu
  • phillips@phy.ohiou.edu
  • §wesolowski.14@osu.edu

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Issue

Vol. 92, Iss. 2 — August 2015

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