Comparisons of Exact Results for the Virtual Photon Contribution to Single Hard Bremsstrahlung in Radiative Return for e+e− Annihilation.†

We compare fully differential exact results for the virtual photon correction to single hard photon bremsstrahlung obtained using independent calculations, both for ee annihilation at high-energy colliders and for radiative return applications. The results are compared using Monte Carlo evaluations of the matrix elements as well as by direct analytical evaluation of certain critical limits. Special attention is given to the issues of numerical stability and the treatment of finite-mass corrections. It is found that agreement on the order of 10 or better is obtained over most of the range of hard photon energies, at CMS energies relevant to both high energy collisions and radiative return experiments. Submitted to Phys. Rev. D PACS Number: 12.20.Ds † Work partly supported by Department of Energy grant DE-FG02-05ER41399 and NATO grant PST.CLG.980342.