  We extend the discussion of the recently discovered 'anomaly poles' in QCD
Compton scattering. We perform the complete one-loop calculation of the Compton
amplitude using momentum transfer $t$ as the regulator of collinear
divergences. In the gluon channel, we confirm the presence of poles $1/t$ in
both the real and imaginary parts of the amplitude. In the quark channel, we
find unexpected infrared single $1/\epsilon$ and double $1/\epsilon^2$ poles.
We then perform the one-loop calculation of the leading-twist quark generalized
parton distributions (GPDs) for quark and gluon external states with the same
regulators and find that all these singular terms can be systematically
absorbed into the GPDs, showing that QCD factorization is restored to this
order. Having established this, we discuss the fate of the $1/t$ poles. We
argue that they become the nonperturbative building blocks of GPDs that encode
the chiral and trace anomalies of QCD, in a way consistent with the known
constraints these anomalies impose on the nucleon axial and gravitational form
factors. The scope of research on GPDs can therefore be expanded to address the
manifestation and implications of quantum anomalies in high-energy exclusive
processes.
