  Astonishing cancellations take place in the calculation of high-energy
scattering cross sections in quantum quadratic gravity, a quantum field theory
for gravity. Tree-level differential cross sections that are minimally
inclusive behave as $1/E^2$, as desired for a well-behaved UV completion. Such
cross sections are calculated for the various spin states of the massless and
massive graviparticles. These describe the hard scattering processes that occur
in a picture involving the gravitational analog of parton showers. The
structure of some of the simpler amplitudes is also explored. Unitarity without
positivity is the key property of the perturbative theory.
