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.
Two such processes have been observed at CDF: exclusive production of two photons via QCD (gluon exchange) and electron pair production via QED (through two-photon exchange). The cross sections and kinematic distributions agree with theoretical predictions (ExHuME MC and Durham group calculation for γγ, and LPAIR MC for ee). The results of each measurment are detailed in the public notes linked below.
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