Very low Emittance Muon Beam using positron beam on target

Muon beams are customarily obtained via K/π decays produced in proton interaction on target.
We are proposing a new scheme to produce very low emittance muon beams using a positron beam of about 45 GeV interacting on electrons on target.  This is a challenging and innovative scheme that needs a full design study. One of the innovative topics to be investigated is the behaviour of the positron beam stored in a low emittance  ring  with a thin target, that is directly inserted in the ring chamber to produce muons. Muons will be immediately collected at the exit of the target and transported to two mu+ and mu- accumulator rings.  We present the main features of this scheme with an outline of the possible applications for Higgs factory and Multi-TeV collider.