  We present the QCD analysis of the cumulative out-of-event-plane momentum
distribution in the process proton-antiproton into Z0 and a hard jet (event
plane defined by the proton, antiproton and Z0 momenta). Particular attention
is placed on the near-to-planar events for which we derive the all-order
resummed result to next-to-leading accuracy. We consider also the leading power
correction originating from the fact that, even in hard processes, the resummed
QCD coupling runs into the infrared region. We aim at the same level of
accuracy which, in e+e- annihilation, seems to be sufficient for making
predictions. Contributions from a ``soft underlying event'' due to beam remnant
interactions are discussed. Experimental data (not yet available) are needed to
cast light on the predictive level of standard QCD analysis in hard
hadron-hadron collisions. We plot examples of the predicted distribution at
Tevatron energies. The techniques here developed can be extended to other hard
hadron-hadron and hadron-lepton processes.
