Novel proposal for a low emittace muon beam using positron beam on target

Muon beams are customarily obtained via $K\mathrm{/}\pi$ decays produced in proton interaction on target. In this paper we investigate the possibility to produce low emittance muon beams from electron-positron collisions at centre-of-mass energy just above the ${\mu }^{+}{\mu }^{-}$ production threshold with maximal beam energy asymmetry, corresponding to a positron beam of about 45 GeV interacting on electrons on target. We present the main features of this scheme with an outline of the possible applications.