Assessing Correlated Truncation Errors in Modern NucleonNucleon Potentials
Abstract
We test the BUQEYE model of correlated effective field theory (EFT) truncation errors on Reinert, Krebs, and Epelbaum's semilocal momentumspace implementation of the chiral EFT ($\chi$EFT) expansion of the nucleonnucleon (NN) potential. This Bayesian model hypothesizes that dimensionless coefficient functions extracted from the orderbyorder corrections to NN observables can be treated as draws from a Gaussian process (GP). We combine a variety of graphical and statistical diagnostics to assess when predicted observables have a $\chi$EFT convergence pattern consistent with the hypothesized GP statistical model. Our conclusions are: First, the BUQEYE model is generally applicable to the potential investigated here, which enables statistically principled estimates of the impact of higher EFT orders on observables. Second, parameters defining the extracted coefficients such as the expansion parameter $Q$ must be well chosen for the coefficients to exhibit a regular convergence pattern  a property we exploit to obtain posterior distributions for such quantities. Third, the assumption of GP stationarity across lab energy and scattering angle is not generally met; this necessitates adjustments in future work. We provide a workflow and interpretive guide for our analysis framework, and show what can be inferred about probability distributions for $Q$, the EFT breakdown scale $\Lambda_b$, the scale associated with soft physics in the $\chi$EFT potential $m_{\rm eff}$, and the GP hyperparameters. All our results can be reproduced using a publicly available Jupyter notebook, which can be straightforwardly modified to analyze other $\chi$EFT NN potentials.
 Publication:

arXiv eprints
 Pub Date:
 February 2024
 DOI:
 10.48550/arXiv.2402.13165
 arXiv:
 arXiv:2402.13165
 Bibcode:
 2024arXiv240213165M
 Keywords:

 Nuclear Theory;
 High Energy Physics  Phenomenology;
 Physics  Data Analysis;
 Statistics and Probability
 EPrint:
 29 pages, 33 figures