This letter of intent proposes an experiment to search for an electric dipole moment of the muon based on the frozen-spin technique. We intend to exploit the high electric field, $E=1{rm GV/m}$, experienced in the rest frame of the muon with a momentum of $p=125 {rm MeV/}c$ when passing through a large magnetic field of $|vec{B}|=3{rm T}$. Current muon fluxes at the $mu$E1 beam line permit an improved search with a sensitivity of $sigma(d_mu)leq 6times10^{-23}e{rm cm}$, about three orders of magnitude more sensitivity than for the current upper limit of $|d_mu|leq1.8times10^{-19}e{rm cm}$,(C.L. 95%). With the advent of the new high intensity muon beam, HIMB, and the cold muon source, muCool, at PSI the sensitivity of the search could be further improved by tailoring a re-acceleration scheme to match the experiments injection phase space. While a null result would set a significantly improved upper limit on an otherwise un-constrained Wilson coefficient, the discovery of a muon EDM would corroborate the existence of physics beyond the Standard Model.
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