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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 γ^* γ^* → 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-γγdoi:10.1051/epjconf/201817506030 fatcat:5jxcs7njgfaozf5jmijo46vy6y