Effective Field Theory Studies of Few-nucleon Systems: Fundamental Symmetry Violation, Electromagnetic Interactions, and Direct Detection of Dark Matter

Effective field theory (EFT) has evolved as a powerful model-independent theoretical framework for illuminating complicated interactions across a wide range of physics areas and subfields. It takes advantage of the scale separation exsiting in physical systems to invoke a systematic expansion to capture the physics at a certain energy scale. The symmetries of the high-energy/short-distance theory constrain these interactions, limiting the number of unknown low-energy coefficients (LECs) that must be extracted from the experiment or calculated directly from the underlying theory.

The utilization of EFTs in nuclear physics has facilitated our understanding of atomic nuclei and bridged the gap between quantum chromodynamics (QCD), the theory of strong interactions, and nuclear structure and interactions. In particular, EFTs have been proven successful in describing the structure and dynamics of few-body nuclei. In this dissertation, we present several studies on applying the EFT technique to research problems in nuclear physics. We first apply pionless EFT (\eftnopi) to study parity violation in two-nucleon systems and the dark matter scattering off light nuclei. The operators contributing to these elusive processes are accompanied by unknown LECs. We show that the large-\Nc expansion can systematically separate these LECs into those that occur at leading order in $N_c$ and those that occur at next-to-leading order in \Nc. The large-\Nc ordering could provide a powerful reduction in the number of experiments needed to understand these processes at every order in this combined expansion, as well as help prioritize future experiments and lattice QCD calculations.

In the second part, we consider the low-energy proton–deuteron and deuteron-Helium-4 systems at low energies in cluster EFT. Below the deuteron breakup threshold, the deuteron and Helium-4 can be treated as structureless degrees of freedom. In particular, we focus on the deuteron + Helium-4 cluster configuration of the Lithium-6 nucleus. We illustrate how to directly extract the asymptotic normalization coefficient, $\mathcal{C}_0$, and the asymptotic $D/S$ ratio, $\eta_{sd}$, from the three electromagnetic form factors of Lithium-6. The fitting to these form factor data yields $C_0\approx 2.20$ fm$^{-1/2}$ and $\eta_{sd}\approx -0.0224$.