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

TL;DR

This paper analyzes total cross section measurements of the $e^+e^- o \gamma\gamma$ process from multiple experiments to set limits on the electron's finite interaction length, testing for deviations from QED predictions.

Contribution

It provides the first experimental limit on the electron's interaction length in the context of direct contact terms using data from 1989 to 2003.

Findings

Limits the electron's interaction length to approximately 1.25 x 10^{-17} cm.

No significant deviation from QED observed within experimental uncertainties.

Sets constraints on models proposing finite-sized electrons.

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.