Comparisons of Virtual Corrections to Bremsstrahlung in Radiative Return at High Energy $e^+ e^-$ Colliders

Radiating a photon from the initial state provides a useful tool for studying a range of low energy physics using a high-energy $e^+ e^-$ accelerator. Accurate results require careful calculation of the first order virtual photon corrections. We compare two exact results for initial state radiative corrections, finding agreement to within $10^{-5}$ or better as a fraction of the Born cross section.