Experimental study of the reactions $e^{+}$$e^{\mathrm{-}}$→$e^{+}$$e^{\mathrm{-}}$ and $e^{+}$$e^{\mathrm{-}}$→γγ at 29 GeV

This paper reports measurements of the differential cross sections for the reactions $e^{+}$ $e^{\mathrm{-}}$→$e^{+}$ $e^{\mathrm{-}}$ (Bhabha scattering) and $e^{+}$ $e^{\mathrm{-}}$→γγ (γ-pair production). The reactions are studied at a center-of-mass energy of 29 GeV and in the polar-angular region ‖costheta‖<0.55. A direct cross-section comparison between these two reactions provides a sensitive test of the predictions of quantum electrodynamics (QED) to order ${\alpha }^3$. When the ratio of γ-pair to Bhabha experimental cross sections, integrated over ‖costheta‖<0.55, is divided by the same ratio predicted from ${\alpha }^3$ QED theory, the result is 1.007±0.009±0.008. The 95%-confidence limits on the QED-cutoff parameters are ${\Lambda }_{+}$>154 GeV and ${\Lambda }_{\mathrm{-}}$>220 GeV for Bhabha scattering, and ${\Lambda }_{+}$>59 GeV and ${\Lambda }_{\mathrm{-}}$>59 GeV for γ-pair production.