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We propose a novel approach for studying $\nu_\mu \to \nu_\tau$ oscillationswith extragalactic neutrinos. Active Galactic Nuclei and Gamma Ray Bursts arebelieved to be sources of ultrahigh energy muon neutrinos. With distances of100 Mpc or more, they provide an unusually long baseline for possible detectionof $\nu_\mu \to \nu_\tau$ with mixing parameters $\Delta m^2$ down to$10^{-17}$eV$^2$, many orders of magnitude below the current acceleratorexperiments. By solving the coupled transport equations, we show thathigh-energy $\nu_\tau$'s, as they propagate through the earth, cascade down inenergy, producing the enhancement of the incoming $\nu_\tau$ flux in the lowenergy region, in contrast to the high-energy $\nu_\mu$'s, which get absorbed.For an AGN quasar model we find the $\nu_\tau$ flux to be a factor of 2 to 2.5larger than the incoming flux in the energy range between $10^2$ GeV and $10^4$GeV, while for a GRB fireball model, the enhancement is 10%-27% in the sameenergy range and for zero nadir angle. This enhancement decreases with largernadir angle, thus providing a novel way to search for $\nu_\tau$ appearance bymeasuring the angular dependence of the muons. To illustrate how the cascadeeffect and the $\nu_\tau$ final flux depend on the steepness of the incoming$\nu_\tau$, we show the energy and angular distributions for several genericcases of the incoming tau neutrino flux, $F_\nu^0 \sim E^{-n}$ for n=1,2 and3.6. We show that for the incoming flux that is not too steep, the signal forthe appearance of high-energy $\nu_\tau$ is the enhanced production of lowerenergy $\mu$ and their distinctive angular dependence, due to the contributionfrom the $\tau$ decay into $\mu$ just below the detector.Comment: 11 pages, including 4 color figure

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

Searching for<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>ν</mml:mi></mml:mrow><mml:mrow><mml:mi>μ</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>→</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>ν</mml:mi></mml:mrow><mml:mrow><mml:mi>τ</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>oscillations with extragalactic neutrinos

Searching forνμ→ντoscillations with extragalactic neutrinos