Quantum field theoretic approach to neutrino oscillations in matter

We consider neutrino oscillations in non-uniform matter in a quantum field theoretic (QFT) approach, in which neutrino production, propagation and detection are considered as a single process. We find the conditions under which the oscillation probability can be sensibly defined and demonstrate how the properly normalized oscillation probability can be obtained in the QFT framework. We derive the evolution equation for the oscillation amplitude and discuss the conditions under which it reduces to the standard Schr\"odinger-like evolution equation. It is shown that, contrary to the common usage, the Schr\"odinger-like evolution equation is not applicable in certain cases, such as oscillations of neutrinos produced in decays of free pions provided that sterile neutrinos with $\Delta m^2\gtrsim 1$ eV$^2$ exist.Comment: LaTeX, 24 pages + 16 pages of appendices, 1 figure. V2: typos correcte

Searching for sterile neutrinos in ice

Oscillation interpretation of the results from the LSND, MiniBooNE and some other experiments requires existence of sterile neutrino with mass $\sim 1$ eV and mixing with the active neutrinos $|U_{\mu 0}|^2 \sim (0.02 - 0.04)$. It has been realized some time ago that existence of such a neutrino affects significantly the fluxes of atmospheric neutrinos in the TeV range which can be tested by the IceCube Neutrino Observatory. In view of the first IceCube data release we have revisited the oscillations of high energy atmospheric neutrinos in the presence of one sterile neutrino. Properties of the oscillation probabilities are studied in details for various mixing schemes both analytically and numerically. The energy spectra and angular distributions of the $\nu_\mu-$events have been computed for the simplest $\nu_s-$mass, and $\nu_s - \nu_\mu$ mixing schemes and confronted with the IceCube data. An illustrative statistical analysis of the present data shows that in the $\nu_s-$mass mixing case the sterile neutrinos with parameters required by LSND/MiniBooNE can be excluded at about $3\sigma$ level. The $\nu_s- \nu_\mu$ mixing scheme, however, can not be ruled out with currently available IceCube data.Comment: 41 pages, 16 figures. Accepted for publication in JHEP. Minor changes from the previous versio