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

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Abstract

We have determined the momentum ${p}_{{\ensuremath{\mu}}^{+}}$ of muons from the decay ${\ensuremath{\pi}}^{+}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\nu}}_{\ensuremath{\mu}}$ at rest, by analyzing a surface muon beam in a magnetic spectrometer equipped with a silicon microstrip detector. The result ${p}_{{\ensuremath{\mu}}^{+}}=(29.79200\ifmmode\pm\else\textpm\fi{}0.00011)$ MeV/c leads to a squared muon-neutrino mass of ${m}_{{\ensuremath{\nu}}_{\ensuremath{\mu}}}^{2}=(\ensuremath{-}0.016\ifmmode\pm\else\textpm\fi{}0.023)$ 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 ${p}_{{\ensuremath{\mu}}^{+}}$ yield the pion mass ${m}_{{\ensuremath{\pi}}^{+}}=(139.57022\ifmmode\pm\else\textpm\fi{}0.00014)$ MeV. Alternatively, if one does not use the cosmological upper limit of ${m}_{{\ensuremath{\nu}}_{\ensuremath{\mu}}}$, then a combined fit including the new ${p}_{{\ensuremath{\mu}}^{+}}$ value, and the ${m}_{{\ensuremath{\mu}}^{+}}$ and ${m}_{{\ensuremath{\pi}}^{\ensuremath{-}}}$ values from other experiments and the $\mathrm{CPT}$ theorem (${m}_{{\ensuremath{\pi}}^{+}}={m}_{{\ensuremath{\pi}}^{\ensuremath{-}}}$) leads to ${m}_{{\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}}=(139.57037\ifmmode\pm\else\textpm\fi{}0.00021)$ 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 $\stackrel{-}{{T}_{{\ensuremath{\pi}}^{+}}}=(0.425\ifmmode\pm\else\textpm\fi{}0.016)$ eV. This is consistent with the hypothesis that the pions are trapped in the potential well of a spherical harmonic oscillator, $V(r)={V}_{0}+\frac{1}{2}{k}_{s}{r}^{2}$, with ${k}_{s}=(1.144\ifmmode\pm\else\textpm\fi{}0.088)\ifmmode\times\else\texttimes\fi{}{10}^{17}$ eV/${\mathrm{cm}}^{2}$.

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