Measurement of the radiative decay of polarized muons in the MEG experiment

We studied the radiative muon decay \({\upmu }^{+} \rightarrow \mathrm {e}^{+} {\upnu }\bar{{\upnu }}{\upgamma }\) by using for the first time an almost fully polarized muon source. We identified a large sample (\(\sim \)13,000) of these decays in a total sample of \(1.8\times 10^{14}\) positive muon decays collected in the MEG experiment in the years 2009–2010 and measured the branching ratio \(\mathcal {B}({\upmu } \rightarrow \mathrm {e} {\upnu }\bar{{\upnu }}{\upgamma }) = (6.03\pm 0.14\mathrm {(stat.)}\pm 0.53\mathrm {(sys.)})\times 10^{-8}\) for \(E_\mathrm {e}>45~\mathrm {MeV}\) and \(E_{{\upgamma }}>40~\mathrm {MeV}\), consistent with the Standard Model prediction. The precise measurement of this decay mode provides a basic tool for the timing calibration, a normalization channel, and a strong quality check of the complete MEG experiment in the search for \({\upmu }^{+} \rightarrow \mathrm {e}^{+} {\upgamma }\) process.