Two Point No Cutoff

Flow of the two-point function with the regulator insertion left out. The first diagram closes a loop with two dressed three-point vertices $\Gamma^{(3)}_k$ and the full propagators $G_k$; the second contracts a single four-point vertex $\Gamma^{(4)}_k$ into a tadpole. Without the cutoff derivative $\partial_k R_k$ nothing restricts the loop momenta, so these are the divergent integrals the regulator is introduced to tame.