Comparisons of fully differential exact results for O(α) virtual corrections to single hard bremsstrahlung in e+e− annihilation at high energies

We present comparisons of the fully differential exact virtual correction to the important single hard bremsstrahlung process in e+e− annihilation at high energies, which is essential for precision studies of the Standard Model from 1 GeV to 1 TeV, as calculated by two completely independent methods and groups. We show that the two sets of results are in excellent agreement. Phenomenological implications are discussed.