Abstract
We present a detailed study of a $\ensuremath{\mu}e$ signal for detecting heavy neutral leptons in electron-positron colliding-beam experiments with the new ${e}^{+}{e}^{\ensuremath{-}}$ storage rings, which are now under construction. Potential backgrounds are also discussed. We conclude that with a judicial choice of the acceptance criteria there should be a viable $\ensuremath{\mu}e$ signal for heavy neutral leptons with masses up to 10 GeV, at the projected maximum beam energy of 20 + 20 GeV of these new storage-ring accelerators.
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