Finite Size of Electron in $e^+e^- \to \gamma\gamma $ Annihilation in differential cross section of centre-of-mass energies 55-207 GeV

The experimental data of the $ e^{+}e^{-}\to\gamma\gamma $ reaction from the VENUS, TOPAS, OPAL, DELPHI, ALEPH and L3 collaborations, collected from 1989 to 2003, are used to test the QED in performing a comprehensive $ \chi^{2} $ test to search for an excited electron mass $ m_{e^{*}} $ and a finite annihilation length in a direct contact term approach. The experimental data of the differential cross section compared to the QED cross section in a $ \chi^{2} $ test allows to set an approximately 5 $ \times \sigma $ significance on the mass of an excited electron to $ m_{e^{*}} = 308 \pm 14 $ GeV . A similar 5 $ \times \sigma $ significance effect was found for a charge distribution radius of the electron $ r_{e}=(1.57\pm 0.07) \times 10 ^{-17} $ cm.