  Relating the forward light-by-light scattering to energy weighted integrals
of the \gamma* \gamma -fusion cross sections, with one real photon (\gamma) and
one virtual photon (\gamma*), we find two new exact super-convergence
relations. They complement the known super-convergence relation based on the
extension of the GDH sum rule to the light-light system. We also find a set of
sum rules for the low-energy photon-photon interaction. All of the new
relations are verified here exactly at leading order in scalar and spinor QED.
The super-convergence relations, applied to the \gamma* \gamma -production of
mesons, lead to intricate relations between the \gamma \gamma -decay widths or
the \gamma* \gamma -transition form factors for (pseudo-) scalar, axial-vector
and tensor mesons. We discuss the phenomenological implications of these
results for mesons in both the light-quark sector and the charm-quark sector.
