 Solution

TODO (source gap): Figure 1(a), including its internal connections and four-momentum labels, is absent from the recoverable source. The local PDF renderer reports missing image objects, and the matching official PDF's figure could not be retrieved for visual inspection. Therefore the individual Feynman diagram called (a) cannot be assigned an integrand and its separate independence of $\xi$ cannot be verified from the available diagram. A guessed replacement drawing would not resolve this gap.

An independent determination of the complete ultraviolet pole, given in part (iv), remains possible from the scalar QED Ward identity. Together with the textually supplied integral in part (iv), it fixes the sum of the contributions outside that integral to $3i{e}^3{C}_{ϵ}{k}^{\mu }$ in the stated scalar electrodynamics three-point vertex convention. That sum alone does not identify the contents of panel (a).