Theory inputs for Vud and Vus extraction

Several significant anomalies have been observed in the beta decay of mesons, nucleon and nuclei, in particular the apparent violation of the Cabibbo-Kobayashi-Maskawa (CKM) matrix unitarity involving the matrix elements Vud and Vus, which make them promising avenues for the search of the physics beyond the Standard Model (BSM). However, the current significant level of the observed anomalies is not yet sufficient to declare a discovery, and the major limiting factor is the precision level of the Standard Model (SM) theory inputs instead of experiments. In this talk, I will describe the major theory improvements needed to increase the significance level of the existing beta decay anomalies to 5 standard deviations, assuming that BSM physics is the underlying reason. They include high-precision studies of radiative corrections, isospin-breaking corrections and nuclear structure corrections to various beta decay processes.