Explicit renormalization of late-time logarithmic divergences in cutoff regularization

Demonstrate explicitly the existence and form of counterterm operators that absorb the late-time logarithmic divergence displayed in Equation (Eqn:naive_secular_div) for the cutoff-regularized 1-loop bispectrum (Diagram 21), and show that these divergences cancel upon renormalization so that no true secular growth remains.

Background

In the cutoff-regularized computation of Diagram 21, the authors find power-law divergences in the cutoff Λ accompanied by late-time logarithmic divergences. They argue these terms should not represent true secular growth because the same feature does not arise in dimensional regularization, suggesting that renormalization should remove them.

They therefore highlight the need to explicitly construct and verify counterterms that cancel the specific divergence term (Eqn:naive_secular_div), which they did not perform in the present work.