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, these 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 intricate relations between mesons 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.

Hadron Structure