Background suppression for $\mu \to e\gamma$ with polarized muons

A search for the lepton-flavor-violating ${\mu }^{+}\to e^{+}\gamma$ decay using polarized muons is reexamined in terms of suppression of the serious background arising from an accidental coincidence between an $e^{+}$ in the normal muon decay and a high energy photon in the radiative muon decay, ${\mu }^{+}\to e^{+}\nu \overline{\nu }\gamma$. It is found that a high energy photon in ${\mu }^{+}\to e^{+}\nu \overline{\nu }\gamma$ 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 ${\mu }^{+}\to e^{+}\gamma$ with right-handed and left-handed $e^{+}$’s, respectively.