Irreducible Bhabha background in the detection of muonium-antimuonium conversion

Abstract: Experiments such as MACS and the proposed MACE study muonium-antimuonium conversion by the energies of the final-state $e^\pm$. The $e^+$ and $e^-$ from an antimuonium decay tend to be non-relativistic and relativistic, respectively, and vice versa for muonium. However, these $e^\pm$ can exchange their energies by hard Bhabha scattering, causing muonium to fake an antimuonium decay signal. We compute the rate for this background and find that, while negligible for MACE, it will become larger than the signal for conversion probabilities less than $10^{-18}$. Measuring the helicity of the $e^-$ will reduce this to $10^{-22}$.