Theoretical Aspects of Neutrino Oscillation

I review some aspects concerning the physics of neutrino mixing and oscillations. I discuss in some detail the physical neutrino oscillations parameter space in the case of two and three family mixing, and briefly describe the current knowledge of neutrino mixing parameters according to the present solar, atmospheric, and reactor neutrino data. I also briefly comment on the possibility of solving the LNSD anomaly together with the solar and atmospheric ones. I conclude by emphasising that that even though in five to ten years time a lot will be learnt from the next round of neutrino experiments, a great deal about neutrino masses and neutrino mixing will remain unknown.Comment: Invited Plenary Talk at the NUFACT'01 Conference, 14 pages, 2 figure

The Dark Side of the Solar Neutrino Parameter Space

Results of neutrino oscillation experiments have always been presented on the (sin^2 2theta, Delta m^2) parameter space for the case of two-flavor oscillations. We point out, however, that this parameterization misses the half of the parameter space pi/4 < theta <= pi/2 (``the dark side''), which is physically inequivalent to the region 0 <= theta <= pi/4 (``the light side'') in the presence of matter effects. The MSW solutions to the solar neutrino problem can extend to the dark side, especially if we take the conservative attitude to allow higher confidence levels, ignore some of the experimental results in the fits, or relax theoretical predictions. Furthermore even the so-called ``vacuum oscillation'' solution distinguishes the dark and the light sides. We urge experimental collaborations to present their results on the entire parameter space.Comment: 4 pages, 3 figures, uses psfig. Fixed typos in Eq. (3). An imprecise comment in the footnote remove

A Three-Flavor, Lorentz-Violating Solution to the LSND Anomaly

We investigate whether postulating the existence of Lorentz-violating, CPT-conserving interactions allows three-neutrino solutions to the LSND anomaly that are also consistent with all other neutrino data. We show that Lorentz-violating interactions that couple only to one of the active neutrinos have the right properties to explain all the data. The details of the data make this solution unattractive. We find, for example, that a highly non-trivial energy dependence of the Lorentz-violating interactions is required.Comment: 15 pages, two eps figures. V2 - Minor modification

Neutrinos Have Mass - So What?

In this brief review, I discuss the new physics unveiled by neutrino oscillation experiments over the past several years, and discuss several attempts at understanding the mechanism behind neutrino masses and lepton mixing. It is fair to say that, while significant theoretical progress has been made, we are yet to construct a coherent picture that naturally explains non-zero, yet tiny, neutrino masses and the newly revealed, puzzling patterns of lepton mixing. I discuss what the challenges are, and point to the fact that more experimental input (from both neutrino and non-neutrino experiments) is dearly required - and that new data is expected to reveal, in the next several years, new information. Finally, I draw attention to the fact that neutrinos may have only just begun to reshape fundamental physics, given the fact that we are still to explain the LSND anomaly and because the neutrino oscillation phenomenon is ultimately sensitive to very small new-physics effects.Comment: invited brief review, 15 pages, 1 eps figure, typo corrected, reference adde

Addressing the Majorana vs. Dirac Question with Neutrino Decays

The Majorana versus Dirac nature of neutrinos remains an open question. This is due, in part, to the fact that virtually all the experimentally accessible neutrinos are ultra-relativistic. Noting that Majorana neutrinos can behave quite differently from Dirac ones when they are non-relativistic, we show that, at leading order, the angular distribution of the daughters in the decay of a heavy neutrino into a lighter one and a self-conjugate boson is isotropic in the parent's rest frame if the neutrinos are Majorana, independent of the parent's polarization. If the neutrinos are Dirac fermions, this is, in general, not the case. This result follows from CPT invariance and is independent of the details of the physics responsible for the decay. We explore the feasibility of using these angular distributions -- or, equivalently, the energy distributions of the daughters in the laboratory frame -- in order to address the Majorana versus Dirac nature of neutrinos if a fourth, heavier neutrino mass eigenstate reveals itself in the current or next-generation of high-energy colliders, intense meson facilities, or neutrino beam experiments.Comment: 11 pages, 3 figure

The Physical Range of Majorana Neutrino Mixing Parameters

If neutrinos are Majorana fermions, the lepton mixing parameter space consists of six mixing parameters: three mixing angles and three CP-odd phases. A related issue concerns the physical range of the mixing parameters. What values should these take so that all physically distinguishable mixing scenarios are realized? We present a detailed discussion of the lepton mixing parameter space in the case of two and three active neutrinos, and in the case of three active and N sterile neutrinos. We emphasize that this question, which has been a source of confusion even among "neutrino" physicists, is connected to an unambiguous definition of the neutrino mass eigenstates. We find that all Majorana phases can always be constrained to lie between 0 and pi, and that all mixing angles can be chosen positive and at most less than or equal to pi/2 provided the Dirac phases are allowed to vary between -pi and pi. We illustrate our results with several examples. Finally, we point out that, in the case of new flavor-changing neutrino interactions, the lepton mixing parameter space may need to be enlarged. We properly qualify this statement, and offer concrete examples.Comment: 16 pages, 2 .eps figures, references added, minor typos correcte