High-time-resolution counters based on plastic scintillator with silicon photomultiplier (SiPM) readout have been developed for applications to high energy physics experiments for which relatively large-sized counters are required. We have studied co
unter sizes up to $120times40times5$ mm^3 with series connection of multiple SiPMs to increase the sensitive area and thus achieve better time resolution. A readout scheme with analog shaping and digital waveform analysis is optimized to achieve the highest time resolution. The timing performance is measured using electrons from a Sr-90 radioactive source, comparing different scintillators, counter dimensions, and types of near-ultraviolet sensitive SiPMs. As a result, a resolution of $sigma =42 pm 2$ ps at 1 MeV energy deposition is obtained for counter size $60times 30 times 5$ mm^3 with three SiPMs ($3times3$ mm^2 each) at each end of the scintillator. The time resolution improves with the number of photons detected by the SiPMs. The SiPMs from Hamamatsu Photonics give the best time resolution because of their high photon detection efficiency in the near-ultraviolet region. Further improvement is possible by increasing the number of SiPMs attached to the scintillator.
We studied the radiative muon decay $mu^+ to e^+ ubar{ u}gamma$ by using for the first time an almost fully polarized muon source. We identified a large sample (~13000) of these decays in a total sample of 1.8x10^14 positive muon decays collected in
the MEG experiment in the years 2009--2010 and measured the branching ratio B($mu^+ to e^+ ubar{ u}gamma$) = (6.03+-0.14(stat.)+-0.53(sys.))x10^-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 $mu^+ to e^+gamma$ process.
