  At very high energy and wide angles, Compton scattering on the proton (gamma
p -> gamma p) is described by perturbative QCD. The perturbative QCD
calculation has been performed several times previously, at leading twist and
at leading order in alpha_s, with mutually inconsistent results, even when the
same light-cone distribution amplitudes have been employed. We have
recalculated the helicity amplitudes for this process, using contour
deformations to evaluate the singular integrals over the light-cone momentum
fractions. We do not obtain complete agreement with any previous result. Our
results are closest to those of the most recent previous computation, differing
significantly for just one of the three independent helicity amplitudes, and
only for backward scattering angles. We present results for the unpolarized
cross section, and for three different polarization asymmetries. We compare the
perturbative QCD predictions for these observables with those of the handbag
and diquark models. In order to reduce uncertainties associated with alpha_s
and the three-quark wave function normalization, we have normalized the Compton
cross section using the proton elastic form factor. The theoretical predictions
for this ratio are about an order of magnitude below existing experimental
data.
