Order-by-order uncertainties of nucleon-nucleon Wolfenstein amplitudes in chiral effective field theory

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 semi-local coordinate space potential implementation of chiral effective field theory (χEFT) for neutron-proton and proton-proton scattering for laboratory kinetic energies between 25 and 200 MeV. Our analysis uses the Gaussian-Process methods developed by the BUQEYE collaboration to describe the contributions of each χEFT 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 χEFT breakdown scale for each amplitude, finding, on average, Λ_b between 750 and 800 MeV. With this choice of Λ_b, the EFT truncation uncertainties cover both higher-order results and empirical Wolfenstein amplitudes well for all orders other than the leading order.