Radiative corrections to semileptonic processes in the standard model

The Standard Model (SM) is currently our most complete, fundamental, and successful theory of nature. However, despite its ability to make some of the most precise predictions in all the physical sciences, there are scenarios where it has been shown to be inadequate or incomplete. This is why SM Precision tests are very important avenues to a solution because they can inform us where the SM is incorrect, and in a manner of speaking, by how much. In this dissertation, we look at two major precision tests: the weak mixing angle and the unitarity condition sum of the top row CKM matrix elements. In order to extract either of these quantities at the level of precision required to meaningfully test the SM, we must go beyond their leading order calculation, and compute all of their 1 loop radiative corrections. The physical process we consider acts like a host to perform both the calculation and the experiment and must be somewhat practical. Semileptonic reactions are a prime candidate as nucleons and nuclei provide practical targets in scattering experiments as well as ideal decay parents, as opposed to their leptonic alternatives. The cost of this experimental convenience are additional challenges when calculating the observables in the SM theory, as hadronic modeling becomes a necessity. This dissertation investigates some of the most troublesome radiative corrections in an attempt to reduce their hadronic uncertainties, using state-of-the-art dispersive techniques as well as update some previously calculated radiative corrections in the aforementioned test quantities. Using these methods, we have found that the CKM matrix is no longer consistent with unitarity and an updated relationship between the weak mixing angle and the weak charge of the proton is proposed.