Comments on Neutrino Tests of Special Relativity

We point out that the assumption of Lorentz noninvariance examined recently by Coleman and Glashow leads to neutrino flavor oscillations which are phenomenologically equivalent to those obtained by assuming the neutrinos violate the principle of equivalence. We then comment on the limits on Lorentz noninvariance which can be derived from solar, atmospheric, and accelerator neutrino experiments.Comment: 5 pages, Revte

Coherent Neutrino Interactions in a Dense Medium

Motivated by the effect of matter on neutrino oscillations (the MSW effect) we study in more detail the propagation of neutrinos in a dense medium. The dispersion relation for massive neutrinos in a medium is known to have a minimum at nonzero momentum p \sim (G_F\rho)/\sqrt{2}. We study in detail the origin and consequences of this dispersion relation for both Dirac and Majorana neutrinos both in a toy model with only neutral currents and a single neutrino flavour and in a realistic "Standard Model" with two neutrino flavours. We find that for a range of neutrino momenta near the minimum of the dispersion relation, Dirac neutrinos are trapped by their coherent interactions with the medium. This effect does not lead to the trapping of Majorana neutrinos.Comment: 28 pages, 6 figures, Latex; minor changes, one reference added; version to appear in Phys. Rev.

Do many-particle neutrino interactions cause a novel coherent effect?

We investigate whether coherent flavor conversion of neutrinos in a neutrino background is substantially modified by many-body effects, with respect to the conventional one-particle effective description. We study the evolution of a system of interacting neutrino plane waves in a box. Using its equivalence to a system of spins, we determine the character of its behavior completely analytically. We find that, if the neutrinos are initially in flavor eigenstates, no coherent flavor conversion is realized, in agreement with the effective one-particle description. This result does not depend on the size of the neutrino wavepackets and therefore has a general character. The validity of the several important applications of the one-particle formalism is thus confirmed.Comment: 25 pages, 1 figur

Probing the matter term at long baseline experiments

We consider (\nu_\mu --> \nu_e) oscillations in long baseline experiments within a three flavor framework. A non-zero measurement of this oscillation probability implies that the (13) mixing angle `phi' is non-zero. We consider the effect of neutrino propagation through the matter of earth's crust and show that, given the constraints from solar neutrino and CHOOZ data, matter effects enhance the mixing for neutrinos rather than for anti-neutrinos. We need data from two different experiments with different baseline lengths (such as K2K and MINOS) to distinguish matter effects unambiguously.Comment: 9 pages including three figure

Constraints on Exotic Mixing of Three Neutrinos

Exotic explanations are considered for atmospheric neutrino observations. Our analysis includes matter effects and the mixing of all three neutrinos under the simplifying assumption of only one relevant mixing scale. Constraints from accelerator, reactor and solar neutrinos are included. We find that the proposed mixing mechanisms based on violations of Lorentz invariance or on violations of the equivalence principle cannot explain the recent observations of atmospheric neutrino mixing. However the data still allow a wide range of energy dependences for the vacuum mixing scale, and also allow large electron-neutrino mixing of atmospheric neutrinos. Next generation long baseline experiments will constrain these possibilities.Comment: 27 pages, 4 figure

Determining the sign of Δ31\Delta_{31} at long baseline neutrino experiments

Recently it is advocated that high intensity and low energy $(E_\nu \sim 2 GeV)$ neutrino beams should be built to probe the $(13)$ mixing angle $\phi$ to a level of a few parts in $10^4$. Experiments using such beams will have better signal to background ratio in searches for $\nu_\mu \to \nu_e$ oscillations. We propose that such experiments can also determine the sign of $\Delta_{31}$ even if the beam consists of {\it neutrinos} only. By measuring the $\nu_\mu \to \nu_e$ transitions in two different energy ranges, the effects due to propagation of neutrinos through earth's crust can be isolated and the sign of $\Delta_{31}$ can be determined. If the sensitivity of an experiment to $\phi$ is $\epsilon$, then the same experiment is automatically sensitive to matter effects and the sign of $\Delta_{31}$ for values of $\phi \geq 2 \epsilon$.Comment: Title changed and paper rewritten. 4 pages, 1 figure, revte