Factorization beyond Coherence

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). We calculate the anomalous dimensions required for the resummation of coherence-violating logarithms and establish a general framework for the systematic treatment of coherence violation. Our findings imply that most existing factorization formulas for global LHC observables must be revised.