Five-Dimensional Qed, Muon Pair Production and Correction to the Coulomb Potential

Abstract

We consider QED in five dimensions in a configuration where matter is localized on a 3-brane while foton propagates in the bulk. The idea is to investigate the effects of the Kaluza-Klein modes of the photon in the relativistic regime, but in low energy, and in the nonrelativistic regime. In the relativistic regime, we calculate the cross section for the reaction e + +e − → µ + +µ − . We compare our theoretical result with a precise measurement of this cross section at √ s = 57.77 GeV. As result, we extract a lower bound on the size of the extra dimension. In the nonrelativistic regime, we derive the contribution for the Coulomb potential due to the whole tower of the Kaluza-Klein excited modes of the photon. We use the modified potential to calculate the Rutherford scattering differential cross section.