Search forμ+→e+γ

Abstract

This paper describes a kinematically complete search for the muon decay ${\ensuremath{\mu}}^{+}\ensuremath{\rightarrow}{e}^{+}\ensuremath{\gamma}$. 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 $\ensuremath{\gamma}$-ray energy and impact point. The positrons were mostly from normal muon decay while the $\ensuremath{\gamma}$ rays were mostly from internal and external bremsstrahlung. Approximately 3\ifmmode\times\else\texttimes\fi{}${10}^{2}$ muons were stopped in a 50-mg/${\mathrm{cm}}^{2}$ polyethylene target. The relative timing between the positron and the $\ensuremath{\gamma}$ 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 $\ensuremath{\gamma}$ ray. The positron energy resolution averaged over all data was 8.8% FWHM, and the $\ensuremath{\gamma}$-ray energy resolution was 8% FWHM, both at 52.8 MeV. When the $\ensuremath{\gamma}$ 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 $\ensuremath{\gamma}$-ray momentum vectors was 37 mrad. The acceptance of the apparatus for ${\ensuremath{\mu}}^{+}\ensuremath{\rightarrow}{e}^{+}\ensuremath{\gamma}$ events was (1.75\ifmmode\pm\else\textpm\fi{}0.04)%. A maximum-likelihood analysis established a 90%-confidence upper limit for the branching ratio $\frac{\ensuremath{\Gamma}({\ensuremath{\mu}}^{+}\ensuremath{\rightarrow}{e}^{+}\ensuremath{\gamma})}{\ensuremath{\Gamma}({\ensuremath{\mu}}^{+}\ensuremath{\rightarrow}{e}^{+}\ensuremath{\nu}\overline{\ensuremath{\nu}})}$ of 1.7\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}10}$.