On the Bayesian approach to neutrino mass ordering

We study the framework of Bayesian statistics for analyzing the capabilities and results of future experiments looking to solve the issue of the neutrino mass ordering. Starting from the general scenario, we then give examples of the procedure for experiments with Gaussian and non-Gaussian distributions for the indicator. We describe in detail what can and cannot be said about the neutrino mass ordering and a future experiment's capabilities to determine it. Finally, we briefly comment on the application to other binary measurements, such as the determination of the octant of $\theta_{23}$.Comment: 23 pages, 5 figures, REVTeX

Exact series solution to the two flavor neutrino oscillation problem in matter

In this paper, we present a real non-linear differential equation for the two flavor neutrino oscillation problem in matter with an arbitrary density profile. We also present an exact series solution to this non-linear differential equation. In addition, we investigate numerically the convergence of this solution for different matter density profiles such as constant and linear profiles as well as the Preliminary Reference Earth Model describing the Earth's matter density profile. Finally, we discuss other methods used for solving the neutrino flavor evolution problem.Comment: 18 pages, 5 figures, RevTeX4. Final version to be published in Journal of Mathematical Physic

Effective Neutrino Mixing and Oscillations in Dense Matter

We investigate the effective case of two-flavor neutrino oscillations in infinitely dense matter by using a perturbative approach. We begin by briefly summarizing the conditions for the three-flavor neutrino oscillation probabilities to take on the same form as the corresponding two-flavor probabilities. Then, we proceed with the infinitely dense matter calculations. Finally, we study the validity of the approximation of infinitely dense matter when the effective matter potential is large, but not infinite, this is done by using both analytic and numeric methods.Comment: 12 pages, 4 figures, Elsevier LaTeX, Final version to be published in Phys. Lett.

Prospects for cosmic neutrino detection in tritium experiments in the case of hierarchical neutrino masses

We discuss the effects of neutrino mixing and the neutrino mass hierarchy when considering the capture of the cosmic neutrino background (CNB) on radioactive nuclei. The implications of mixing and hierarchy at future generations of tritium decay experiments are considered. We find that the CNB should be detectable at these experiments provided that the resolution for the kinetic energy of the outgoing electron can be pushed to a few 0.01 eV for the scenario with inverted neutrino mass hierarchy, about an order of magnitude better than that of the upcoming KATRIN experiment. Another order of magnitude improvement is needed in the case of normal neutrino mass hierarchy. We also note that mixing effects generally make the prospects for CNB detection worse due to an increased maximum energy of the normal beta decay background.Comment: 12 pages, 4 figures, REVTeX4, minor updates, final version, to be published in Phys. Rev.

Determination of the neutrino mass ordering by combining PINGU and Daya Bay II

The relatively large measured value of theta_13 has opened various possiblities to determine the neutrino mass ordering, among them using PINGU, the low-energy extention of the IceCube neutrino telescope, to observe matter effects in atmospheric neutrinos, or a high statistics measurment of the neutrino energy spectrum at a reactor neutrino experiment with a baseline of around 60 km, such as the Daya Bay II project. In this work we point out a synergy between these two approaches based on the fact that when data are analysed with the wrong neutrino mass ordering the best fit occurs at different values of |Delta m^2_31| for PINGU and Daya Bay II. Hence, the wrong mass ordering can be excluded by a mismatch of the values inferred for |Delta m^2_31|, thanks to the excellent accuracy for Delta m^2_31 of both experiments. We perform numerical studies of PINGU and Daya Bay II sensitivities and show that the synergy effect may lead to a high significance determination of the mass ordering even in situations where the individual experiments obtain only poor sensitivity.Comment: 23 pages, 7 figures (15 eps files), typos and minor mistakes corrected, final version to appear in JHE

Approximative two-flavor framework for neutrino oscillations with nonstandard interactions

In this paper, we develop approximative two-flavor neutrino oscillation formulas including subleading nonstandard interaction effects. Especially, the limit when the small mass-squared difference approaches zero is investigated. The approximate formulas are also tested against numerical simulations in order to determine their accuracy and they will probably be most useful in the GeV energy region, which is the energy region where most upcoming neutrino oscillation experiments will be operating. Naturally, it is important to have analytical formulas in order to interpret the physics behind the degeneracies between standard and nonstandard parameters.Comment: 21 pages, 7 figures, REVTeX4. Final version published in Phys. Rev.

Neutrino Propagation in Matter

We describe the effects of neutrino propagation in the matter of the Earth relevant for experiments with atmospheric and accelerator neutrinos and aimed at the determination of the neutrino mass hierarchy and CP-violation. These include (i) the resonance enhancement of neutrino oscillations in matter with constant or nearly constant density, (ii) adiabatic conversion in matter with slowly changing density, (iii) parametric enhancement of oscillations in a multi-layer medium, (iv) oscillations in thin layers of matter. We present the results of semi-analytic descriptions of flavor transitions for the cases of small density perturbations, in the limit of large densities and for small density widths. Neutrino oscillograms of the Earth and their structure after determination of the 1-3 mixing are described. A possibility to identify the neutrino mass hierarchy with the atmospheric neutrinos and multi-megaton scale detectors having low energy thresholds is explored. The potential of future accelerator experiments to establish the hierarchy is outlined.Comment: 40 pages, 14 figures, REVTeX4, Review article published in Advances in High Energy Physics (see journal reference