Effective Field Theory Methods: From New-Physics Searches in Beta Decays to Strong Interactions

Abstract

The Standard Model (SM), while having been confirmed experimentally with remarkable accuracy, faces both theoretical and experimental challenges. Beta decay serves as a stringent probe for potential physics beyond the SM. To enhance its utility, advances are required in three key aspects of beta decays: enhancing the sensitivity of the experiments, improving the precision of the SM calculations, and developing theoretical frameworks capable of accommodating new physics. In this thesis, all three paths were investigated and discussed, with Effective Field Theory (EFT) providing the central framework. We employ the Standard Model EFT (SMEFT) to parametrize possible new interactions at energies above the electroweak scale and connect them to low-energy observables. Furthermore, we employed Chiral Effective Field Theory to systematically include higher-order corrections and suppress theoretical uncertainties, a key step toward enabling CKM unitarity tests with a precision at the $10^{-4}$ level. In addition to precision tests of the Standard Model through beta decay, the research advances the theoretical description of strongly interacting many-body systems using Chiral Effective Field Theory (ChEFT). ChEFT is an effective field theory that systematically describes the interactions of pions and nucleons, allowing the construction of nuclear forces. While two-body potentials provide the largest contributions to these interactions, three-nucleon (3N) forces can play an important role in systems like nuclei or neutron stars. The current derivation of the 3N force does not take into account the effects of interactions that involve four nucleons and two pions, with a coefficient proportional to the square of the pion mass, momentum, or energy. Although suppressed in conventional power counting, renormalization arguments promote these interactions to leading order. When the pions are integrated out, we find that these operators induce a sizable, previously unaccounted-for contribution to the 3N force.