Two-Loop Corrections to Bhabha Scattering

TL;DR

The two-loop radiative photonic corrections to Bhabha scattering are computed in the leading order of the small electron mass expansion up to the nonlogarithmic term and the infrared-finite result for the differential cross section is obtained.

Abstract

The two-loop radiative photonic corrections to the Bhabha scattering are computed in the leading order of the small electron mass expansion up to nonlogarithmic term. After including the soft photon bremsstrahlung we obtain the infrared finite result for the differential cross section, which can be directly applied to precise luminosity determination of the present and future $e^+e^-$ colliders.

Figures (2)

• Figure 1: Logarithmically enhanced (dashed line) and nonlogarithmic (solid line) second order corrections to the differential cross section of the small angle Bhabha scattering as functions of the scattering angle for $\sqrt{s}=100$ GeV and $\ln(\varepsilon_{cut}/\varepsilon)=0$, in units of $10^{-3}$.
• Figure 2: The same as Fig. (\ref{['fig1']}) but for the large angle Bhabha scattering and $\sqrt{s}=1$ GeV.