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Background Suppression for $μ\to eγ$ with Polarized Muons

A search for the lepton-flavor violating $μ^{+}\rightarrow e^{+}γ$ decay using polarized muons is revisited in terms of suppression of the serious background arising from an accidental coincidence between a $e^{+}$ in the normal muon decay and a high energy photon in the radiative muon decay, $μ^{+} \rightarrow e^{+} ν\overlineν γ$. It is found that a high energy photon in $μ^{+} \rightarrow e^{+} ν\overlineν γ$ decay is preferentially emitted parallel to the muon spin direction, similarly to $e^{+}$ in the normal muon decay. The selective measurements of either $e^{+}$s or photons moving antiparallel to the muon spin direction would suppress the accidental background for $μ^{+} \rightarrow e^{+} γ$ with right-handed and left-handed $e^{+}$s respectively.