AMANDA-II 2000-2006

John Kelley, UW-Madison, May 2008

Neutrino oscillations provide a quantum interferometer sensitive to very small shifts in energy, and can thus act as a sensitive probe of deviations from the Standard Model. These effects are detectable by the same method as standard neutrino oscillations — muon neutrinos generated in the atmosphere change flavor as they propagate to the detector. Because of the different path lengths at different zenith angles, this results in a measurable distortion from the expected zenith angle / energy spectrum. Unlike standard atmospheric oscillations, which decrease with energy and are essentially negligible above 100 GeV, these effects often increase with energy.

Specific models that can be tested with this technique include:

- Violations of Lorentz invariance (VLI) resulting from different limiting neutrino velocities (hep-ph/0502223);
- Quantum decoherence of neutrinos through interactions with a foamy quantum-gravitational space-time (astro-ph/0412618, hep-ph/0208166).

From a practical perspective, we can simulate the new physics (NP) effects simply by weighting atmospheric neutrino events with a muon neutrino survival probability, calculated for the NP model and parameters that we are interested in. For VLI, the observable parameters are:

Parameter |
Range |
Description |

log10(delta_c/c) |
-28 to -24 |
Splitting of VLI eigenstates. Controls what
energy new oscillations turn on. |

sin(2 xi) |
-1 to 1 |
Mixing angle. Controls depth of oscillation minima. |

cos(eta) |
0 or 1 |
Phase between conventional and VLI oscillations
(see below). |

The phase *eta* is only important when *delta_c/c* is so large that the VLI
and conventional oscillations overlap; however, since AMANDA-II is not
sensitive to conventional oscillations, we can safely neglect this
parameter and set *cos(eta)* to zero. This also has the nice side effect
that we only have to vary the mixing angle from 0 to pi/4.

For quantum decoherence, the observable parameters are:

Parameter |
Range |
Description |

log10(gamma_3*), log10(gamma_8*) |
-34 to -27 |
Decoherence threshold 1; lose 1/6 of nu_mu |

log10(gamma_6*), log10(gamma_7*) |
-34 to -27 |
Decoherence threshold 2; lose 1/2 of nu_mu |

Setting all the *gamma** parameters to the same value means there is
just one threshold at which 1:1:1 decoherence turns on (lose 2/3 of
nu_mu). Also, in the survival probability, the *gamma** are
multiplied by an energy factor which depends on the phenomenology; here
we choose an E^2 model.

Additional background and theoretical motivation of Lorentz violations is presented
in Coleman and Glashow (PRD
**59** (1999) 116008) as well as Glashow (hep-ph/0407087).
Additional background on quantum decoherence is available in Ellis *et al.*
(Nucl.
Phys. B**241** (1984) 381-405) and Anchordoqui *et al.*
(hep-ph/0506168).

In the absence of new physics, we can test how well the atmospheric neutrino
spectrum agrees with current models, such as Barr *et al.* ("Bartol",
astro-ph/0403630) or Honda
*et al.* ("Honda 2006", astro-ph/0611418).
These models have been extrapolated to high energies (above 700 GeV) by T. Montaruli,
C. Lewis, and JK in the NeutrinoFlux
class. By comparing the predicted zenith angle / energy spectra for these models
with data, we can constrain the various models in the AMANDA-II energy region.