Speaker
Description
Ab initio approaches such as the no-core shell model with continuum (NCSMC) describe nuclei as systems of nucleons experiencing inter-nucleonic forces derived from the underlying Quantum Chromo-Dynamical (QCD) structure. This, along with the NCSMC's unified description of nuclear structure and reaction theory, provide a rigorous framework that can be applied to tests of fundamental symmetries of the standard model (SM) that involve nuclei. New global analysis of Fermi decays, and the corresponding $V_{ud}$ determination, reveal a statistical discrepancy with the well-established SM expectation for Cabibbo-Kobayashi-Maskawa (CKM) matrix unitarity. Theoretical confirmation of the discrepancy would point to beyond SM physics. Necessary for extracting $V_{ud}$ from experiment is calculation of corrections to Fermi transition matrix elements; computing the isospin symmetry breaking correction $\delta_C$ is the main effort of this work. By studying Fermi transitions in light-nuclei, such as the $^{10}\text{C} \rightarrow {}^{10}\text{B}$ beta transition, we may perform a precision calculation of $\delta_C$ within an ab initio framework. Further, there exists significant motivation from the nuclear physics community for understanding the structure of the aforementioned systems. In particular, $^{10}\text{C}$ is of great interest as little is known experimentally about its structure. We present nuclear structure results for the following systems (i) $^{10}\text{C} \rightarrow p + {}^{9}\text{B}$ (ii) $^{10}\text{B} \rightarrow (n + {}^{9}\text{B}) + (p + {}^{9}\text{Be}$) (iii) $^{10}\text{Be} \rightarrow n + {}^{9}\text{Be}$. A high-quality description of the first two of these systems is necessary to guarantee the accuracy of $\delta_C$, and the third system provides an additional check on the NCSMC. We present results for $^{10}\text{C}$ which indicate a good description of the $0^+$ ground-state for calculation of $\delta_C$. Importantly, we also present novel structure results for the $^{10}\text{B}$ system considered as two mass partitions, including the charge-exchange reaction. Lastly, we aim to present a preliminary result for the determination of $\delta_C$ in the NCSMC.
