Quantum mechanical invariance principles dictate the most general operator structure that can be present in the nucleon-nucleon (NN) interaction. Five independent operators appear in the on-shell NN amplitude together with five corresponding coefficient functions. The usual choice for these coefficient functions is known as the NN Wolfenstein amplitudes. We analyze the order-by-order convergence of each of the five NN Wolfenstein amplitudes predicted by a semilocal coordinate space potential implementation of chiral effective field theory ($\chi \mathrm{EFT}$). We do this at laboratory kinetic energies between 25 and 200 MeV for both neutron-proton and proton-proton scattering. Our analysis uses the Gaussian-process methods developed by the BUQEYE Collaboration to describe the contributions of each $\chi \mathrm{EFT}$ order, and so yields truncation uncertainties for each Wolfenstein amplitude that are correlated across scattering angles. We combine information on the size of different orders in the EFT to infer the $\chi \mathrm{EFT}$ breakdown scale for each amplitude, finding, on average, ${\mathrm{\Lambda }}_b$ between 750 and 800 MeV. With this choice of ${\mathrm{\Lambda }}_b$, the EFT truncation uncertainties cover both higher-order results and empirical Wolfenstein amplitudes well for all orders other than the leading order.

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• Effective field theory
• Nucleon-nucleon interactions
• Bayesian methods
• Few-body systems