Precision measurement of the muon momentum in pion decay at rest

At the Schweizerisches Institut f\"ur Nuklearforschung (SIN) we have measured the muon momentum in the pion decay π⁺→μ⁺+ν_μ at rest using a magnetic spectrometer. Our result is p_μ⁺=29.7877±0.0014 MeV/c. From our p_μ⁺ value and the rest masses of the muon, m_μ⁺=105.65946±0.00024 MeV/c², and the pion, m_π^-=139.5679±0.0015 MeV/c², we derive a new value for the squared muon-neutrino rest mass, m_ν_μ²=0.13±0.14 (MeV/c²)². From this we obtain m_νμ≤0.57 MeV/c² (90% C.L.), which is at present the lowest experimental upper limit for the muon-neutrino rest mass. Here the validity of the CPT theorem (m_π⁺=m_π^-) and energy and momentum conservation in pion decay were assumed. Our result can be interpreted in a second way: From cosmological arguments using the big-bang hypothesis an upper limit of about 40 eV/c² has been derived for the neutrino rest mass. With this limit and the above value of the muon mass we can calculate the pion-muon mass difference or the rest mass of the π⁺ with strongly improved precision from our measurement. The results are δm=m_π⁺-m_μ⁺=33.9063±0.0018 MeV/c² or m_π⁺=139.5658±0.018 MeV/c². This positive-pion mass is consistent with the present world average for the negative-pion mass, in agreement with the CPT theorem.