Gennari, Michael2025-08-152025-08-152025https://hdl.handle.net/1828/22619A systematically improvable, ab initio model is developed to compute nuclear-structure-dependent elec troweak radiative corrections in superallowed Fermi β decays. With inter-nucleon interactions derived from the low-energy symmetries of quantum chromo-dynamics via a prescription of effective field theory, the nuclear many-body configurations are obtained in the quasi-exact, no-core shell model. This approach rigorously treats all nucleons as active degrees of freedom in solution of the non-relativistic, many-body Schrödinger equation with Hamiltonian constructed from chiral effective field theory. One of the two key nuclear-structure corrections to superallowed β decays, known as δNS, arises from modifications to the one-nucleon γW box diagram when immersed in the nuclear medium. It is computed for the two lightest superallowed transitions: the 10C → 10B and 14O → 14N transitions. The nuclear γW box amplitude is itself explicitly evaluated as the time-ordered product of the electromagnetic and charge-changing weak current operators, providing a transparent multipole decomposition of the currents. The resulting complicated amplitude structure involves many-body resolvent operators which are treated with the Lanczos strengths method, the key tool of this dissertation. As much as is permitted by the Lanczos algorithm, this method incorporates quasi-exact information about the complete intermediate nuclear spectrum. For 10C → 10B, we find the nuclear-structure-dependent radiative correction δNS to be δNS [10C → 10B] = −0.422 (14) PME (4)Ω(9)χ(24)sh(12)n,el % , which represents a 1.6x reduction in the quoted uncertainty compared to prior literature estimates despite the accounting for additional uncertainties. Preliminary results for the 14O → 14N transition indicate a markedly different distribution of the amplitude strengths, reflecting a strong Gamow-Teller suppression and highlighting the need for higher-multipole analysis before a final value is quoted. These precision gains directly impact the determination of Vud and thus the top-row, Cabibbo Kobayashi-Maskawa matrix unitarity test, motivating renewed experimental efforts– particularly a more precise measurement of the 10C branching ratio– and opening the way to analogous, precision ab initio studies for other electroweak processes in light nuclei.enAvailable to the World Wide Webnuclear theorymany-body theoryelectroweak physicsThesisGennari, M., Drissi, M., Gorchtein, M., Navrátil, P., & Seng, C. Y. (2025). Ab Initio Strategy for Taming the Nuclear-Structure Dependence of V ud Extractions: The C 10→ B 10 Superallowed Transition. Physical Review Letters, 134(1), 012501. DOI: https://doi.org/10.1103/PhysRevLett.134.012501