Assessing Convergence Patterns Across Modern Nucleon-Nucleon Potentials

TL;DR

This paper evaluates the convergence patterns of modern nucleon-nucleon potentials using the BUQEYE EFT truncation error model, identifying irregularities and improving the model's assumptions for better error estimation.

Contribution

The study tests and refines the BUQEYE model for EFT truncation errors on various chiral EFT NN potentials, revealing nonstationary Gaussian process behavior and the importance of the EFT breakdown scale.

Findings

Irregular convergence patterns in soft regulator potentials.

Nonstationary Gaussian process length scale inversely related to momentum.

Optimal EFT breakdown scale found to be 600-750 MeV for various potentials.

Abstract

The BUQEYE model for correlated effective field theory (EFT) truncation errors assumes a regular pattern of dimensionless coefficients extracted from order-by-order observable calculations. This enables results from lower orders to inform statistical predictions for error estimates of omitted higher orders. We test the model for multiple chiral EFT ($\chi$EFT) nucleon-nucleon (NN) potentials using a suite of six common NN scattering observables represented as functions of relative momentum and scattering angle. First, we flag irregularity in the convergence patterns of potentials with so-called "soft" regulator scales, namely that the sizes of the coefficients in the observables' expansions are mismatched between the even and odd orders. Second, we test the BUQEYE model's assumption of Gaussian process (GP) stationarity against the data and find that the GP's correlation structure as encoded in its length scale is nonstationary: The GP length scale in the angular dimension $\ell_{\theta}$ is approximately inversely proportional to the relative momentum of the scattering process. After we remediate this issue by allowing $\ell_{\theta}$ to vary with momentum, diagnostics show significant improvement, validating the application of the BUQEYE model after this modification. Third, we find that good performance of the BUQEYE model relies on properly choosing the $\chi$EFT breakdown scale $\Lambda_{b}$. With $m_{\text{eff}}$ held fixed at the physical pion mass we find $\Lambda_{b}=600$--$750$ MeV for various N$^{3}$LO interactions. Statistically consistent distributions for $\Lambda_{b}$ across orders are only found for the SMS potential at a regulator scale of 450 or 500 MeV. All our results can be reproduced using a publicly available Jupyter notebook, which can be straightforwardly modified to analyze other $\chi$EFT NN potentials.