Renormalization-Group Invariant Formulation of Chiral Effective Field Theory Applied to the Nucleon-Nucleon System

Licentiate thesis, 2023

Chiral effective field theory (χEFT) promises a systematically improvable description of the strong interaction between nucleons consistent with the symmetries of quantum chromodynamics (QCD). A sound power counting (PC) scheme is vital to organize the order-by-order contributions of interaction diagrams to nuclear observables in compliance with renormalization-group (RG) invariance. Numerical values of the low-energy constants (LECs), governing the strengths of pion-nucleon and nucleon-contact diagrams, must be inferred from data and vary with the high-momentum cutoff to remove any dependence on the arbitrary regularization procedure. To date, most χEFT predictions of nuclear systems rely on a PC introduced in the 1990s that does not comply with RG-invariance. One can argue that the lacking RG-invariance makes the connection with QCD muddled and that predictive power is lost. I have developed Bayesian methods for inferring the probability distributions for the numerical values of the LECs at leading order in a recent and RG-invariant PC by Long and Yang. I find that conditioning the inference on neutron-proton (np) scattering observables, rather than scattering phase shifts as is typically done, significantly impacts the results. Furthermore, I use distorted-wave perturbation theory to compute predictions for low-energy np scattering observables up to the fourth chiral order in this PC using point estimates for the LECs. I find a clear order-by-order improvement in the theoretical description of experimental scattering data. This work is an important step towards enabling a Bayesian analysis of low-energy nuclear observables with the aim of assessing whether χEFT, formulated using an RG-invariant PC, accurately predicts the physics of atomic nuclei.