Use of RadiativeπDecay to Limit the Neutrino Mass

A limit on the $\mu$-neutrino mass may be obtained by observing radiative $\pi$ decay. If one measures the $\gamma$-ray energy, then a value within $\frac{3}{4}$ MeV of the maximum possible $\gamma$ energy is required to limit the neutrino mass to 1 MeV. If one also measures the coincident $\mu$ momentum, then the $\gamma$ energy must be within, say, 3 MeV of the maximum, and the $\mu$ momentum within 0.1 MeV/c of its maximum. "Useful" events for both processes occur once in about ${10}^8\pi$ decays.