  We examine the effects of QCD initial-state radiation on a class of
quantities, designed to probe the mass scale of new physics at hadron
colliders, which involve longitudinal as well as transverse final-state
momenta. In particular, we derive universal functions that relate the invariant
mass and energy distribution of the visible part of the final state to that of
the underlying hard subprocess. Knowledge of this relationship may assist in
checking hypotheses about new processes, by providing additional information
about their scales. We compare our results with those of Monte Carlo studies
and find good general agreement.
