Photon - photon scattering in QED at low energies can be accurately described by the Euler-Heisenberg effective Lagrangian. This only involves the photons (naturally) because the electron has been integrated out, $\omega \ll m$ where $\omega$ is the photon energy and $m$ is the electron mass.
What type of effective photon - photon interaction does this correspond to? I mean is the effective interaction between photons attractive or repulsive? Since the photon is massless I'm not even sure the interaction between two photons can be interpreted as attractive/repulsive to be honest.
At the same time one usually derives the attractive or repulsive nature of an interaction via the 2-2 scattering and its matrix element (and its sign) so this procedure seems well-defined for photon-photon as well. So it seems a definite sign can be obtained which would tell us if the effective interaction is attractive or repulsive.