An experimentally verified mathematical model that precisely describes the attraction and motion between an electron and positron does not yet exist. Although there have been no direct experimental measurements of the particle velocity when the distance between the two particles approaches zero, the basic inverse square model used for point charges is thought to be inadequate because it would predict speeds in excess of c, the speed of light. Modifications to this basic model have been made by theorizing a variable velocity dependent relativistic mass or a velocity dependent force. Using these models, that assume the electron and positron both attain a velocity of approximately c during their annihilation collision, results in a very compelling model of a photon as an electron and positron in a two body orbital union traveling through space. However, photon models based on this assumption show that the photon translational velocity must have some dependence on the photon wavelength. Further exploration of the basic inverse square model of electron - positron attraction shows it predicts the first order two body photon model without this wavelength dependent dispersion. Furthermore, study of the electron-positron interaction with a hydrogen like entity shows that the popular notion of a photon having an angular momentum on the order of ħ and an energy of ħw can be derived from first principles.
Randy T. Dorn, Randy T. Dorn,
"Electron-positron annihilation and absorption models", Proc. SPIE 9570, The Nature of Light: What are Photons? VI, 95700H (10 September 2015); doi: 10.1117/12.2185588; https://doi.org/10.1117/12.2185588