Correlated Effective Field Theory Truncation Errors: From Neutron-Proton Scattering Amplitudes to Observables

Abstract

The strong force governing Nucleon-Nucleon (NN) scattering can be modelled with an Effective Field Theory (EFT) of low-energy quantum chromodynamics. The Feyn man diagrams contributing to this force are considered order-by-order in an expan sion with decreasing importance. NN scattering observables can then be predicted by considering all contributions up to some finite order, while neglected orders result in predictable truncation errors. Contrary to previous studies, the EFT truncation errors of different NN observable types should not be considered independent since all of them depend on only five complex so-called scattering amplitudes. Instead, truncation errors must be correlated not only across energies and scattering angles but also across different observable types. In this thesis, we modelled and investi gated such correlations between the uncertainties of different neutron-proton scat tering observables resulting from a truncation of the chiral EFT guided by Weinberg power counting. We applied a Bayesian uncertainty-quantification model, consisting of a fixed kernel Gaussian process, on the leading order chiral EFT truncation errors of the neutron-proton scattering amplitudes. The resulting errors were then propagated to errors of various observables. We considered both Saclay and helicity conventions for the NN scattering amplitudes with their specific angular boundary constraints. Firstly, we found that the symmetry constraints of amplitudes propagate to observ ables, resulting in angle- and energy-dependent uncertainties. Secondly, we observed strong angle-dependent correlations and rigid inequalities between different observ able types, cutting the joint posteriors into characteristic shapes traced back to their amplitude dependencies. Finally, we examined the extent to which our error model violates the unitarity constraint of the scattering operator by comparing the optical-theorem and integrated total cross section. There was little to no correlation between the uncertainties of these theoretically identical expressions. While we suc cessfully incorporated unitarity on average, future studies are necessary to explicitly implement unitarity constraints into the error model. This work is an important step in a larger effort to understand correlated EFT truncation errors, considering rigorously the correlation between different NN scattering observable types. The resulting error model could enhance the physical robustness of EFT parameter inference and the reliability of theoretical predictions for nuclear observables.