Precision measurement of the muon momentum in pion decay at rest

Abstract

At the Schweizerisches Institut f\"ur Nuklearforschung (SIN) we have measured the muon momentum in the pion decay ${\ensuremath{\pi}}^{+}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}+{\ensuremath{\nu}}_{\ensuremath{\mu}}$ at rest using a magnetic spectrometer. Our result is ${p}_{{\ensuremath{\mu}}^{+}}=29.7877\ifmmode\pm\else\textpm\fi{}0.0014$ MeV/c. From our ${p}_{{\ensuremath{\mu}}^{+}}$ value and the rest masses of the muon, ${m}_{{\ensuremath{\mu}}^{+}}=105.65946\ifmmode\pm\else\textpm\fi{}0.00024$ ${\mathrm{M}\mathrm{e}\mathrm{V}/\mathit{c}}^{2}$, and the pion, ${m}_{{\ensuremath{\pi}}^{\ensuremath{-}}}=139.5679\ifmmode\pm\else\textpm\fi{}0.0015$ ${\mathrm{M}\mathrm{e}\mathrm{V}/\mathit{c}}^{2}$, we derive a new value for the squared muon-neutrino rest mass, ${{m}_{{\ensuremath{\nu}}_{\ensuremath{\mu}}}}^{2}=0.13\ifmmode\pm\else\textpm\fi{}0.14$ (${\mathrm{M}\mathrm{e}\mathrm{V}/{\mathit{c}}^{2})}^{2}$. From this we obtain ${m}_{\ensuremath{\nu}\ensuremath{\mu}}\ensuremath{\le}0.57$ ${\mathrm{M}\mathrm{e}\mathrm{V}/\mathit{c}}^{2}$ (90% C.L.), which is at present the lowest experimental upper limit for the muon-neutrino rest mass. Here the validity of the $\mathrm{CPT}$ theorem (${m}_{{\ensuremath{\pi}}^{+}}={m}_{{\ensuremath{\pi}}^{\ensuremath{-}}}$) 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 ${\mathrm{e}\mathrm{V}/\mathit{c}}^{2}$ 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 ${\ensuremath{\pi}}^{+}$ with strongly improved precision from our measurement. The results are $\ensuremath{\delta}m={m}_{{\ensuremath{\pi}}^{+}}\ensuremath{-}{m}_{{\ensuremath{\mu}}^{+}}=33.9063\ifmmode\pm\else\textpm\fi{}0.0018$ ${\mathrm{M}\mathrm{e}\mathrm{V}/\mathit{c}}^{2}$ or ${m}_{{\ensuremath{\pi}}^{+}}=139.5658\ifmmode\pm\else\textpm\fi{}0.018$ ${\mathrm{M}\mathrm{e}\mathrm{V}/\mathit{c}}^{2}$. This positive-pion mass is consistent with the present world average for the negative-pion mass, in agreement with the $\mathrm{CPT}$ theorem.