Unregularized Propagator Diagrams

The two one-loop diagrams renormalizing the two-point function before any regulator is introduced: a loop closed by two dressed three-point vertices $\Gamma_k^{(3)}$, minus a tadpole carrying one four-point vertex $\Gamma_k^{(4)}$. Without a regulator insertion these momentum integrals diverge, which is exactly what the cutoff in the regularized version cures.