Speaker
Description
Recent analysis of Fermi decays by C.Y. Seng and M. Gorshteyn and the corresponding $V_{ud}$ determination have revealed a degree of tension with Cabibbo-Kobayashi-Maskawa (CKM) matrix unitarity, confirmation of which would indicate several potential deficiencies within the Standard Model (SM) weak sector. Extraction of $V_{ud}$ requires electroweak radiative corrections (EWRC) from theory to be applied to experimentally obtained $ft$-values. Novel calculations of corrections sensitive to hadronic structure, i.e., the $\gamma W$-box, are at the heart of the recent tension. Moreover, to further improve on the extraction of $V_{ud}$, a modern and consistent treatment of the two nuclear structure dependent corrections is critical. These corrections are (i) $\delta_C$, the isospin symmetry breaking correction (ii) and $\delta_{NS}$, the EWRC representing evaluation of the $\gamma W$-box on a nucleus. Preliminary estimations of $\delta_{\mathrm{NS}}$ have been made in the aforementioned analysis, however, a true nuclear many-body theory calculation of the quantity is required for desired precision goals. Via collaboration with C.Y. Seng and M. Gorshteyn and use of the Lanczos strength method, these corrections can be computed in ab initio nuclear theory for the first time. We apply the no-core shell model (NCSM), a nonrelativistic quantum many-body theory for describing low-lying bound states of $s$- and $p$-shell nuclei starting solely from nuclear interactions. We will present preliminary results for $\delta_{\mathrm{NS}}$ and $\delta_{\mathrm{C}}$ as determined in the NCSM for the $^{10}\text{C} \rightarrow {}^{10}\text{B}$ beta transition, with the eventual goal of extending the calculations to $^{14}\text{O} \rightarrow {}^{14}\text{N}$ and $^{18}\text{Ne} \rightarrow {}^{18}\text{F}$.
