Electroweak Interactions and Fundamental Symmetries in Light Nuclei with Short-range Effective Field Theories

Effective field theories(EFTs) are powerful tools to study nuclear systems that display separation of scales. In this dissertation, we present halo EFT results for the $\beta$-delayed proton emission from $^{11}$Be, and pionless EFT results for three-nucleon systems. Halo nuclei are simply described by a tightly bound core and loosely bound valence nucleons. Using the halo EFT, we calculate the rate of the rare decay $^{11}$Be, which is a well-known halo nucleus, into $^{10}\text{Be} + p +e^- + \bar{\nu}_e$. We assume a shallow $1/2 ^+$ resonance in the $^{10}$Be$-p$ system with an energy consistent with a recent experiment by Ayyad {\it et al.} and obtain a branching ratio and a resonance width of this decay. Our calculation shows that the experimental branching ratio and resonance parameters of Ayyad {\it et al.} are consistent with each other. Thus, no exotic mechanism (such as beyond the standard model physics) is needed to explain the experimental decay rate. Electric dipole moments (EDMs) of nucleons receive negligible contributions from the CKM mechanism and are thus, extremely sensitive probes of CP-violation beyond the Standard Model. Using the pionless EFT, we calculate the EDMs of three-nucleon systems at leading order. Neglecting the Coulomb interaction, we consider the triton and ${}^3$He, and also investigate them in the Wigner-SU(4) symmetric limit. We also calculate the electric dipole form factor and find numerically that the momentum dependence of the electric dipole form factor in the Wigner limit is, up to an overall constant (and numerical accuracy), the same as the momentum dependence of the charge form factor. At last, under the same framework, charge form factors with Coulomb interactions are considered both perturbatively and non-perturbatively to NLO. The third Zemach moment of $^3$He is evaluated and compared to experimental results.