  We present our preliminary results on the calculation of hadronic
light-by-light forward scattering amplitudes using vector four-point
correlation functions computed on the lattice. Using a dispersive approach,
forward scattering amplitudes can be described by $\gamma^* \gamma^* \to$
hadrons fusion cross sections and then compared with phenomenology. We show
that only a few states are needed to reproduce our data. In particular, the sum
rules considered in this study imply relations between meson$-\gamma\gamma$
couplings and provide valuable information about individual form factors which
are often used to estimate the meson-pole contributions to the hadronic
light-by-light contribution to the $(g-2)$ of the muon.
