Dipole moments of elementary particles served since the dawn of particle physics as an important test bench for theoretical models. Nowadays, they provide a powerful probe for new physics beyond the Standard Model, and their importance have been strongly boosted by the long-standing and recently confirmed deviation of the anomalous magnetic moment of the muon (g-2) form theoretical predictions. While there are intensive experimental plans to improve the muon g-2 measurement, and investigations of the dipole moments of the electron are continuously improved, searches for an electric dipole moment (EDM) of the muon have been recently performed only as a by-product of g-2 experiments. We propose here a dedicated experiment to search for a muon EDM with a frozen-spin technique in a storage magnet, where the (g-2)-dependent spin precession on the orbital plane is canceled by an electric field, while vertical precession due to a non-null EDM is searched for, with a goal sensitivity of 6 x 10^-23 e*cm, three orders of magnitude below the current bound. A muon EDM observation would reveal sources of CP violation beyond the Standard Model, that could give a clue about the origin of the matter-antimatter asymmetry in the Universe.

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