Speaker
Description
Recent global analysis of Fermi decays within a dispersion relation framework and the corresponding $V_{ud}$ determination have revealed tension with the Standard Model (SM) expectation of Cabibbo-Kobayashi-Maskawa (CKM) matrix unitarity, theoretical confirmation of which would indicate a deficiency within the SM weak sector. Extracting $V_{ud}$ requires electroweak radiative corrections (EWRC) from theory to be applied to the experimentally obtained $ft$-values. Novel calculations of the pieces 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) $\delta_{NS}$, the EWRC representing evaluation of the $\gamma W$-box on a nucleus. Preliminary estimations of $\delta_{NS}$ have been made in the dispersion relation framework, however the approach cannot include effects from low-lying nuclear states which require a true many-body treatment. Via collaboration with C.Y. Seng and M. Gorshteyn and use of the Lanczos continued fraction method, these corrections are now calculable within the ab initio no-core shell model (NCSM). The NCSM is 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 $\delta_{NS}$ and $\delta_{C}$ 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 $^{18}\text{Ne} \rightarrow {}^{18}\text{F}$.
