  We show that the resummation of large perturbative corrections in QCD leads
to ambiguities in high energy cross sections that are suppressed by powers of
large momentum scales. These ambiguities are caused by infrared renormalons,
which are a general feature of resummed hard-scattering functions in
perturbative QCD, even though these functions are infrared safe order-by-order
in perturbation theory. As in the case of the operator product expansion, the
contributions of infrared renormalons to coefficient functions may be absorbed
into the definition of higher-dimensional operators, which induce
nonperturbative corrections that are power-suppressed at high energies. The
strength of the suppression is determined by the location of the dominant
infrared renormalon, which may be identified explicitly in the resummed series.
In contrast to the operator product expansion, however, the relevant operators
in factorized hadron-hadron scattering and jet cross sections are generally
nonlocal in QCD, although they may be expressed as local operators in an
effective theory for eikonalized quarks. In this context, we verify and
interpret the presence of $1/Q$ corrections to the inclusive Drell-Yan cross
section with $Q$ the pair mass. In a similar manner, we find $\exp(-b^2\ln Q)$
corrections in the impact parameter space of the transverse momentum
distributions of the Drell-Yan process and $e^+e^-$ annihilation. We also show
that the dominant nonperturbative corrections to cone-based jet cross sections
behave as $1/(Q\delta)$, with $\delta$ the opening angle of the jet and $Q$ the
center of mass energy.
