Neutrino-oscillation search with cosmic-ray neutrinos

A sensitive search for neutrino oscillations involving ${\nu }_e$, ${\nu }_{\mu }$, and ${\nu }_{\tau }$ may be provided by measurements of the ratio of the total interaction rates of upward- and downward-going cosmic-ray neutrinos within a massive (∼10 kton) detector. Assuming mixing between all pairs of ${\nu }_e$, ${\nu }_{\mu }$, and ${\nu }_{\tau }$, the experiment is capable of observing time-averaged probabilities ${〈P_{e\tau }〉}_t$ and ${〈P_{\mu \tau }〉}_t$ of magnitude set by mixing strengths corresponding to, e.g., the $d$- to $s$-quark mixing strength, and of reaching the limit $\Delta m_{\mathrm{ij}}^2\equiv |{m_i}^2-{m_j}^2|\approx {10}^{-4\mathrm{}}$ ${\mathrm{eV}}^2$, where $m_i$, and $m_j$ are neutrino mass eigenstates, and $P_{e\tau }$ and $P_{\mu \tau }$ are the probabilities for ${\nu }_e$ and ${\nu }_{\mu }$, respectively, to oscillate into ${\nu }_{\tau }$ after traversing a distance $L\approx$ diameter of the Earth. Possible ambiguities may be resolved through comparison of the ratios $\frac{N_e}{N_{\mu }}$ for the upward- and downward-going neutrinos.