This paper describes a kinematically complete search for the muon decay ${\mu }^{+}\to e^{+}\gamma$. The experiment used a magnetic spectrometer outfitted with proportional chambers to measure the positron momentum vector and a large segmented NaI(T1) array to determine the $\gamma$-ray energy and impact point. The positrons were mostly from normal muon decay while the $\gamma$ rays were mostly from internal and external bremsstrahlung. Approximately 3×${10}^2$ muons were stopped in a 50-mg/${\mathrm{cm}}^2$ polyethylene target. The relative timing between the positron and the $\gamma$ ray was measured with a resolution of 1.9 ns full width at half maximum (FWHM) by the use of a plastic-scintillator hodoscope for the positron and by NaI(T1) constant-fraction timing for the $\gamma$ ray. The positron energy resolution averaged over all data was 8.8% FWHM, and the $\gamma$-ray energy resolution was 8% FWHM, both at 52.8 MeV. When the $\gamma$ ray is assumed to originate at the same place in the target as the positron, the rms error in the measurement of the angle between the positron and $\gamma$-ray momentum vectors was 37 mrad. The acceptance of the apparatus for ${\mu }^{+}\to e^{+}\gamma$ events was (1.75±0.04)%. A maximum-likelihood analysis established a 90%-confidence upper limit for the branching ratio $\frac{\Gamma ({\mu }^{+}\to e^{+}\gamma )}{\Gamma ({\mu }^{+}\to e^{+}\nu \overline{\nu })}$ of 1.7×${10}^{-10\mathrm{}}$.

• Received 8 June 1981

DOI:https://doi.org/10.1103/PhysRevD.25.2846