Chiral Effective Field Theory with Partly Perturbative Pions Applied to the Few-Nucleon Sector

Doctoral thesis, 2026

Chiral effective field theory (χEFT) provides a framework for deriving systematically improvable models of the strong nuclear interaction that are consistent with quantum chromodynamics (QCD). This enables first-principles predictions of nuclear properties relevant for studying the stability of visible matter and for precision tests of physics within and beyond the Standard Model. A power counting scheme facilitates the organization of interaction diagrams contributing to the nuclear force according to their importance. Most existing χEFT calculations of nuclear systems rely on Weinberg power counting; however, it has been shown that this approach yields observables that depend on the regulator cutoff. In this thesis, I investigate an alternative power counting scheme that is designed to produce cutoff-independent, i.e., renormalization-group invariant, observables. A key difference compared to Weinberg power counting is that all subleading parts of the interaction are treated perturbatively. I analyze the two-nucleon system by studying scattering observables as well as spin entanglement in connection with accidental symmetries. Low-energy theorems are also investigated as a consistency check for the partly perturbative treatment of pion exchanges. These studies are performed for a wide range of cutoffs, demonstrating cutoff independence in the two-nucleon system. Furthermore, I implement and validate numerical algorithms for perturbatively computing ground-state energies in light nuclei within the no-core shell model. A total of 33 low-energy constants are calibrated, and the constructed interactions are employed to predict ground-state properties of ^2,3H, ⁴He, and ⁶Li up to fourth order in the power counting.
Accurate predictions are obtained for these light nuclei at low cutoffs (around 500 MeV), where numerical convergence can reliably be achieved. The studied power counting can be used to construct nuclear interaction models that possess predictive power for few-nucleon systems.
The inclusion of three-nucleon forces, the extension of the perturbative framework to other many-body methods, and further study of so-called exceptional cutoffs are important directions for future work.