Background Suppression for $\mu\to e\gamma$ with Polarized Muons

A search for the lepton-flavor violating $\mu^{+}\rightarrow e^{+}\gamma$ 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, $\mu^{+} \rightarrow e^{+} \nu \overline{\nu} \gamma$. It is found that a high energy photon in $\mu^{+} \rightarrow e^{+} \nu \overline{\nu} \gamma$ 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 $\mu^{+} \rightarrow e^{+} \gamma$ with right-handed and left-handed $e^{+}$s respectively.