Upper limit of the muon-neutrino mass and charged-pion mass from momentum analysis of a surface muon beam

We have determined the momentum p_μ⁺ of muons from the decay π⁺→μ⁺ν_μ at rest, by analyzing a surface muon beam in a magnetic spectrometer equipped with a silicon microstrip detector. The result p_μ⁺=(29.79200±0.00011) MeV/c leads to a squared muon-neutrino mass of m_ν_μ²=(-0.016±0.023) MeV², which corresponds to a "laboratory" upper limit of 0.17 MeV (C.L.=0.9) for the muon-neutrino mass. The cosmological upper limit of the neutrino mass (65 eV), the muon mass, and the new value of p_μ⁺ yield the pion mass m_π⁺=(139.57022±0.00014) MeV. Alternatively, if one does not use the cosmological upper limit of m_ν_μ, then a combined fit including the new p_μ⁺ value, and the m_μ⁺ and m_π^- values from other experiments and the CPT theorem (m_π⁺=m_π^-) leads to m_π^±=(139.57037±0.00021) MeV. As a side result, the mean kinetic energy of the pions stopped in the production target, made of isotropic graphite, immediately before their decay is found to be -T_π⁺=(0.425±0.016) eV. This is consistent with the hypothesis that the pions are trapped in the potential well of a spherical harmonic oscillator, V(r)=V₀+1/2kₛr², with kₛ=(1.144±0.088)×10¹⁷ eV/cm².