Questions Pertaining to Charge Dependence of Radiative Corrections to Superallowed Fermi Transitions

We consider the problem posed by the near equality of the $\mathrm{ft}$ values for the nine $0^P\to 0^P$ ($P=+ or -$) superallowed Fermi transitions. So long as one is oblivious to radiative effects, this near equality of $\mathrm{ft}$ values may be (as, indeed, it has been) regarded as a triumph of the CVC (conserved-vector-current) hypothesis. However, if one takes note of the fact that CVC, which guarantees the equality of the "bare" $\mathrm{ft}$ values, is broken by electromagnetism and that the charge of the decaying nuclei varies from $Z=1\mathrm{}$ (for ${\pi }^{\pm }$) to $Z=27\mathrm{}$ (for ${\mathrm{Co}}^{54}$), the relationship between CVC and the physical $\mathrm{ft}$ values becomes obscure; CVC can be upheld only if one can establish that the renormalization effects are small. In a previous contribution we used a combination of general theorems and model-dependent arguments to show that, in the limit of vanishing lepton momenta, $Z$-dependent renormalization effects arise only in order $Z^2{\alpha }^2$ (3.9% for ${\mathrm{Co}}^{54}$). The present paper contains a fuller explanation of the aforementioned theorems as well as amplified and improved proofs. Also, topics not treated in our earlier work (corrections for finite lepton momenta, effects of real photon emission, etc.) are discussed and the model-dependent part of the argument is reviewed.