We consider deeply virtual Compton scattering (DVCS) on a photon target,
gamma^*(Q) gamma -> gamma gamma, in two different kinematical regimes in
which the QCD factorization of the scattering amplitude takes place, and
in which we calculate the scattering amplitude at the Born order and in
the leading logarithmic approximation.

In the generalized Bjorken limit we obtain the result as a factorized
amplitude of a hard process described by handbag diagrams and anomalous
generalized parton distributions (GPDs) in the photon [1]. This anomalous
part of GPDs, with its characteristic ln Q^2 dependence violating Bjorken
scaling, is present both in the DGLAP and in the ERBL regions. As a
consequence, the generalized parton distributions of the photon obey
DGLAP-ERBL evolution equations with an inhomogeneous term.

At the low energy and high photon virtuality region the scattering
amplitude takes form of a convolution of handbag coefficient function and
anomalous part of diphoton generalized distribution amplitudes (GDAs) [2].
As in the case of the anomalous photon structure functions, the gamma
gamma GDA exhibits a characteristic ln Q^2 behaviour and obeys
inhomogeneous ERBL evolution equations.

[1] S. Friot et al, Phys.Lett. B645 (2007) 153-160
[2] M. El Beiyad et al, Phys.Rev.D78 (2008) 034009