We studied the radiative muon decay mu(+) -> e(+) nu(nu) over bar gamma by using for the first time an almost fully polarized muon source. We identified a large sample (similar to 13,000) of these decays in a total sample of 1.8 x 10(14) positive muon decays collected in the MEG experiment in the years 2009-2010 and measured the branching ratio B(mu -> e nu(nu) over bar gamma) = (6.03 +/- 0.14(stat.) +/- 0.53(sys.)) x 10(-8) for E-e > 45 MeV and E-gamma > 40 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 mu(+) -> e(+)gamma process.
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