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

TL;DR

This paper investigates the convergence and uncertainties of nucleon-nucleon Wolfenstein amplitudes in chiral effective field theory across various energies, providing insights into the EFT breakdown scale and improving uncertainty quantification.

Contribution

It introduces a systematic order-by-order analysis of Wolfenstein amplitudes using Gaussian-Process methods to quantify truncation uncertainties in chiral EFT.

Findings

EFT breakdown scale between 750 and 800 MeV

Uncertainties cover higher-order results and empirical data

Good convergence observed beyond leading order

Abstract

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 ($\chi$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 $\chi$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 $\chi$EFT breakdown scale for each amplitude, finding, on average, $\Lambda_b$ between 750 and 800 MeV. With this choice of $\Lambda_b$, the EFT truncation uncertainties cover both higher-order results and empirical Wolfenstein amplitudes well for all orders other than the leading order.