Past exam of the advanced quantum field theory for particle physics course of the University of Oxford / 2021 / 1 / iii

TODO (source gap): Figure 1(c) and its four-momentum labels are unreadable. The assertion about this individual Feynman diagram therefore cannot be checked against its actual integrand. In particular, one must not identify the missing panel with a convenient vanishing seagull vertex graph by inference.

A useful criterion, once the drawing is recovered, is that dimensional regularization annihilates a vector integral of the formby the change of variables $l\mapsto -l$. This would prove vanishing for every $\xi$ if all remaining factors were functions of $l^2$; a denominator involving $l+k$ must first be checked rather than discarded. Whether this criterion applies to panel (c) is precisely the unavailable information.