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