Estimate of the Energy of Upgoing Muons with Multiple Coulomb Scattering

Abstract

Upward throughgoing muons in underground detectors are induced by atmospheric $\nu_\mu$ with energies in the $1-10^4 GeV$ range. The oscillations of atmospheric muon neutrinos should affect mainly those with energy smaller than $E_\nu \sim 50 GeV$, or $E_\mu \le 10 GeV$ . We analyzed the MACRO upward throughgoing muons data set, using the Multiple Coulomb Scattering to estimate the energy $E_\mu$ of muons crossing the detector. We analyzed the event distribution for six event subsamples with different values of $<\ell_\nu / E_\nu>$. The event distribution is in agreement with the hypothesis of neutrino oscillations with $\Delta m^2$ few times $10^{-3} eV^2$ and maximum mixing.