Two-loop correction to Bhabha scattering

We present the two-loop virtual QED corrections to $e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-}$ and Bhabha scattering in dimensional regularization. The results are expressed in terms of polylogarithms. The form of the infrared divergences agrees with previous expectations. These results are a crucial ingredient in the complete next-to-next-to-leading order QED corrections to these processes. A future application will be to reduce theoretical uncertainties associated with luminosity measurements at $e^{+}{e}^{-}$ colliders. The calculation also tests methods that may be applied to analogous QCD processes.