Factorization is the foundation of precision particle physics. It says that the cross section for a hadron collision can be separated into pieces: parton distributions (what's inside the protons), hard scattering (the high-energy collision), and soft radiation (the low-energy gluon cloud). Each piece is computed independently. The separation works because of color coherence — soft gluons emitted at wide angles see the colliding partons as a single color charge and factor out of the hard process.
The factorization formulas used at the LHC are built on this assumption. They are the basis for every precision measurement — Higgs boson properties, W boson mass, top quark mass, strong coupling constant. If the formulas are wrong, the measurements are wrong.
Becher, Hager, Neubert, and Schwienbacher (arXiv:2603.12383, March 2026) show that Glauber gluons — a class of soft gluon exchanges that don't factor out because they transfer momentum transversely between the colliding beams — violate the coherence assumption. The violation generates new logarithmic terms at four-loop and five-loop order that existing factorization formulas miss entirely.
The effect is not a correction within the existing framework. It is a new term that the framework doesn't predict. The authors state it directly: “most existing factorization formulas for global LHC observables must be revised.”
The structural lesson is about the gap between working and correct. Factorization formulas have worked spectacularly well for decades because the missing terms are suppressed at low loop order. At four and five loops — the precision frontier that the LHC is now reaching — the suppression lifts and the missing terms become relevant. The formula was always incomplete; the incompleteness was below the precision that anyone could measure. Now it isn't. The foundation held because it was never tested at the level where it breaks.