Speaker
Description
Recent 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 a deficiency within the SM weak sector. Necessary for extracting $V_{ud}$ from experiment is calculation of several theoretical corrections to the Fermi transition values. In fact, the development of the novel dispersion relation framework (DRF) for evaluating the nucleon $\gamma W$-box contribution to the electro-weak radiative corrections (EWRC) is at the centre of the recent tension with unitarity. Thus, what remains is to calculate the two nuclear structure dependent corrections: (i) $\delta_C$, the isospin symmetry breaking correction (ii) $\delta_{NS}$, the EWRC representing evaluation of the $\gamma W$--box on a nucleus. These corrections are calculable within the ab initio no-core shell model (NCSM), which describes nuclei as systems of nucleons experiencing inter-nucleonic forces derived from the underlying symmetries of Quantum Chromo-Dynamics (QCD). As we have explored calculations of $\delta_C$ in the past, it is a natural next step to calculate $\delta_{NS}$ in the same approach, providing a consistent evaluation of both nuclear structure dependent corrections to Fermi transitions. Preliminary evaluations of $\delta_{NS}$ have already been made using the DRF, however, while one can capture various contributions to $\delta_{NS}$ in the DRF, the approach cannot include effects from low-lying nuclear states. These contributions require a true many-body treatment and can be directly computed in the NCSM using the Lanczos continued fractions method. Hence, by studying Fermi transitions in light-nuclei, e.g. the $^{10}\text{C} \rightarrow {}^{10}\text{B}$ and $^{14}\text{O} \rightarrow {}^{14}\text{N}$ beta transitions, we may perform a hybrid calculation of $\delta_{NS}$ utilizing the ab initio NCSM and the novel DRF. We aim to present a preliminary calculation of $\delta_{NS}$ for the $^{10}\text{C} \rightarrow {}^{10}\text{B}$ transition.
