Hint for a minimal interaction length in $e^{+}{e}^{-}\to \gamma \gamma$ annihilation in total cross section of centre-of-mass energies 55-207 GeV

Abstract

The measurements of the total cross section of the $e^{+}{e}^{-}\to \gamma \gamma$ reaction from the VENUS, TOPAS, OPAL, DELPHI, ALEPH and L3 collaborations, collected between 1989 to 2003, are used to perform a ${\chi }^2$ test to search for a finite interaction length in direct contact term. The experimental data of the total cross section compared to the QED cross section of a ${\chi }^2$ test allows, to set limit on a finite interaction length $r_e=(1.25\pm 0.16)\times 10^{-17}[cm]$. In the direct contact term annihilation is this interaction lengths a measure for the size of the electron.