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

We have determined the momentum $p_{{\mu }^{+}}$ of muons from the decay ${\pi }^{+}\to {\mu }^{+}{\nu }_{\mu }$ at rest, by analyzing a surface muon beam in a magnetic spectrometer equipped with a silicon microstrip detector. The result $p_{{\mu }^{+}}=(29.792\mathrm{}00\pm 0.00011)$ MeV/c leads to a squared muon-neutrino mass of $m_{{\nu }_{\mu }}^2=(-0.016\mathrm{}\pm 0.023)$ Me${\mathrm{V}}^2$, 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 $p_{{\mu }^{+}}$ yield the pion mass $m_{{\pi }^{+}}=(139.570\mathrm{}22\pm 0.00014)$ MeV. Alternatively, if one does not use the cosmological upper limit of $m_{{\nu }_{\mu }}$, then a combined fit including the new $p_{{\mu }^{+}}$ value, and the $m_{{\mu }^{+}}$ and $m_{{\pi }^{-}}$ values from other experiments and the $\mathrm{CPT}$ theorem ($m_{{\pi }^{+}}=m_{{\pi }^{-}}$) leads to $m_{{\pi }^{\pm }}=(139.570\mathrm{}37\pm 0.00021)$ 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 $\overline{T_{{\pi }^{+}}}=(0.425\mathrm{}\pm 0.016)$ eV. This is consistent with the hypothesis that the pions are trapped in the potential well of a spherical harmonic oscillator, $V\left(r\right)=V_0+\frac{1}{2}{k}_s{r}^2$, with $k_s=(1.144\mathrm{}\pm 0.088)\times {10}^{17}$ eV/${\mathrm{cm}}^2$.