Renormalization of Chiral Effective Field Theory in the Nucleon-Nucleon Sector

Abstract

The calculation of nuclear properties from QCD, the underlying theory of the strong nuclear force, is still an open problem in physics. Effective field theories provide a possible solution by describing nuclei in terms of effective degrees of freedom; neutrons, protons, and pions. The effective description comes at a cost, namely undetermined parameters known as low-energy constants (LECs), that need to be fixed by experimental data. Furthermore, while renormalization-group (RG) invariance of predictions is a field-theoretic requirement, it is known that interaction potentials constructed with Weinberg power counting (WPC) are not RG invariant at leading order. The purpose of this thesis is to study a leading order modified Weinberg power counting potential, with additional counter terms and their associated LECs promoted to leading order. We show that the modified potential gives RG invariant predictions of nucleon-nucleon scattering phase shifts in partial waves that are otherwise problematic in WPC. Moreover, Bayesian inference is used to determine LECs from measured total scattering cross sections, which allows to account for both experimental and model uncertainties. RG-invariant predictions of scattering cross sections are demonstrated using the obtained posterior distributions of LECs. In conclusion, we find that the modified potential performs better, producing RG-invariant results for phase shifts and cross sections. We also show that total scattering cross sections do not impose very hard constraints on all LECs which calls for the inclusion of more experimental data in the inference.