Hint for a Minimal Interaction Length in e+e−⟶γγ Annihilation in Total Cross Section of Center-of-Mass Energies 55-207 GeV

Abstract

The measurements of the total cross section of the $e^{+}{e}^{-}⟶\gamma \gamma \left(\gamma \right)$ reaction from the VENUS, TOPAS, OPAL, DELPHI, ALEPH, and L3 collaborations, collected between 1989 and 2003, are used to perform a ${\chi }^2$ test to validate the current quantum electrodynamics (QED) theory and search for possible deviations with the direct contact term annihilation. By observing a deviation from the QED predictions on the total cross section of the $e^{+}{e}^{-}⟶\gamma \gamma \left(\gamma \right)$ reaction above $\sqrt{s}=180.0$ GeV, a non-QED direct contact term is introduced following the dimension 6 effective theory to explain the deviation. In the non-QED direct contact term, a threshold energy scale $\Lambda$ is included and explained to the finite interaction length in direct contact term and in consequence the size of the electron involved in the annihilation area. The experimental data of the total cross section is compared to the QED cross section by a ${\chi }^2$ test, which gives a best fit of the $\Lambda$ to be $1576\pm 202$ GeV, corresponding to a finite interaction length of $r_e=\left(1.25\pm 0.16\right)\times 10^{-17}$ (cm). In the direct contact term annihilation, this interaction length is a measure of the size of an electron $r_e$. By combining all the data results from the mentioned collaborations, we have at least 2 to 3 times more statistics than every single experiment at high $\sqrt{s}$ region. This induces the best precision on $r_e$ compared to the previous measurements.