Author(s): Thomas Becher, Patrick Hager, Matthias Neubert, and Dominik Schwienbacher We propose a novel factorization theorem for $N$-jettiness at hadron colliders, which incorporates coherence-violating effects induced by Glauber gluons and several new momentum modes. Their interplay generates coherence-violating logarithms starting at four-loop ($N≥1$) or five-loop order ($N=0$). … [Phys. Rev. Lett. 137, 121902] Published Wed Sep 16, 2026