A comprehensive theory framework for perturbative calculations of $δ_C$ in superallowed beta decays

The present high precision determination of $|V_{ud}|$ from superallowed beta decays of $J^P=0^+$, $T=1$ nuclei is largely built on top of the ``standard'' calculation of the isospin breaking correction $δ_C$ to the Fermi matrix element, which assumes the splitting $δ_C=δ_{C1}+δ_{C2}$, where $δ_{C1}