Muons Produced by Atmospheric Neutrinos: Analysis

Abstract

The experimental rate of muons produced deep underground by neutrinos is used together with neutrino cross sections from experiments at CERN and the atmospheric-neutrino spectrum as determined from cosmic-ray-muon data, to deduce the high-energy (> 10 GeV) bahavior of neutrino cross sections. We use a cutoff parameter ${M}_{W}$ to limit the linear increase of the inverse-$\ensuremath{\beta}$-reaction cross section with energy which would otherwise result from scale invariance. A comparison (neglecting uncertainties) of the calculated and the experimentally determined muon rates shows a deviation from linearity that would be observable at a neutrino lab energy of \ensuremath{\sim}50 GeV. If the hypothetical $W$ boson of weak interactions provides the mechanism for this saturation, then a (weak) upper limit can be set on its mass. At 1 standard deviation, this limit is ${M}_{W}\ensuremath{\le}45 \frac{\mathrm{GeV}}{{c}^{2}}$. Should the $W$ boson exist, it can also be produced copiously if it has sufficiently small mass. Thus a lower limit on its mass can also be set. At 1 standard deviation, this limit is ${M}_{W}\ensuremath{\gtrsim}2.9 \frac{\mathrm{Gev}}{{c}^{2}}$, where this limit is independent of $W$ decay modes. More accurate accelerator-neutrino (antineutrino) experiments at energies up to 10 GeV and an improvement in our knowledge of the underground muon rate could reduce significantly the spread between the upper and lower limits on ${M}_{W}$. The underground results are also used to set limits on neutrino fluxes from extraterrestrial sources, e.g., for a saturation energy of \ensuremath{\sim}60 GeV, the 1-standard-deviation upper limit on an extraterrestrial-neutrino flux is \ensuremath{\sim}\textonehalf{} of the atmospheric-neutrino flux.