There are Standard Model processes in which hadrons do not dissociate in the interaction. Without hadron dissociation there is no underlying event in the interaction - only a very clean, "exclusive", central system is observed in the detector.
Exclusive production of two photons via QCD (gluon exchange) is being searched for at CDF - with some very promising hints. The number of events produced and kinematic distributions agree with theoretical predictions (ExHuME MC and Durham group calculation). The results are detailed in the public note linked below.
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