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

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

Dark Matter and Neutrino Mass from the Smallest Non-Abelian Chiral Dark Sector

All pieces of concrete evidence for phenomena outside the standard model (SM) - neutrino masses and dark matter - are consistent with the existence of new degrees of freedom that interact very weakly, if at all, with those in the SM. We propose that these new degrees of freedom organize themselves into a simple dark sector, a chiral SU(3) x SU(2) gauge theory with the smallest nontrivial fermion content. Similar to the SM, the dark SU(2) is spontaneously broken while the dark SU(3) confines at low energies. At the renormalizable level, the dark sector contains massless fermions - dark leptons - and stable massive particles - dark protons. We find that dark protons with masses between 10-100 TeV satisfy all current cosmological and astrophysical observations concerning dark matter even if dark protons are a symmetric thermal relic. The dark leptons play the role of right-handed neutrinos and allow simple realizations of the seesaw mechanism or the possibility that neutrinos are Dirac fermions. In the latter case, neutrino masses are also parametrically different from charged-fermion masses and the lightest neutrino is predicted to be massless. Since the new "neutrino" and "dark matter" degrees of freedom interact with one another, these two new-physics phenomena are intertwined. Dark leptons play a nontrivial role in early universe cosmology while indirect searches for dark matter involve, decisively, dark matter annihilations into dark leptons. These, in turn, may lead to observable signatures at high-energy neutrino and gamma-ray observatories, especially once one accounts for the potential Sommerfeld enhancement of the annihilation cross-section, derived from the low-energy dark-sector effective theory, a possibility we explore quantitatively in some detail.Comment: 35 pages, 7 figures. Matches published versio

Non-Unitary Neutrino Propagation From Neutrino Decay

Neutrino propagation in space-time is not constrained to be unitary if very light states - lighter than the active neutrinos - exist into which neutrinos may decay. If this is the case, neutrino flavor-change is governed by a handful of extra mixing and "oscillation" parameters, including new sources of CP-invariance violation. We compute the transition probabilities in the two- and three-flavor scenarios and discuss the different phenomenological consequences of the new physics. These are qualitatively different from other sources of unitarity violation discussed in the literature.Comment: 8 pages, no figure

Low Temperature Static and Dynamic Behavior of the Two-Dimensional Easy-Axis Heisenberg Model

We apply the self-consistent harmonic approximation (SCHA) to study static and dynamic properties of the two-dimensional classical Heisenberg model with easy-axis anisotropy. The static properties obtained are magnetization and spin wave energy as functions of temperature, and the critical temperature as a function of the easy-axis anisotropy. We also calculate the dynamic correlation functions using the SCHA renormalized spin wave energy. Our analytical results, for both static properties and dynamic correlation functions, are compared to numerical simulation data combining cluster-Monte Carlo algorithms and Spin Dynamics. The comparison allows us to conclude that far below the transition temperature, where the SCHA is valid, spin waves are responsible for all relevant features observed in the numerical simulation data; topological excitations do not seem to contribute appreciably. For temperatures closer to the transition temperature, there are differences between the dynamic correlation functions from SCHA theory and Spin Dynamics; these may be due to the presence of domain walls and solitons.Comment: 12 pages, 14 figure

See-Saw Energy Scale and the LSND Anomaly

The most general, renormalizable Lagrangian that includes massive neutrinos contains ``right-handed neutrino'' Majorana masses of order M. While there are prejudices in favor of M much larger than the weak scale, virtually nothing is known about the magnitude of M. I argue that the LSND anomaly provides, currently, the only experimental hint: M around 1 eV. If this is the case, the LSND mixing angles are functions of the active neutrino masses and mixing and, remarkably, adequate fits to all data can be naturally obtained. I also discuss consequences of this ``eV-seesaw'' for supernova neutrino oscillations, tritium beta-decay, neutrinoless double-beta decay, and cosmology.Comment: revtex, 4 pages, no figure

On the relation between p-adic and ordinary strings

The amplitudes for the tree-level scattering of the open string tachyons, generalised to the field of p-adic numbers, define the p-adic string theory. There is empirical evidence of its relation to the ordinary string theory in the p_to_1 limit. We revisit this limit from a worldsheet perspective and argue that it is naturally thought of as a continuum limit in the sense of the renormalisation group.Comment: 13 pages harvmac (b), 2 eps figures; v2: revtex, shortened, published versio

Anarchy and Hierarchy

We advocate a new approach to study models of fermion masses and mixings, namely anarchy proposed in hep-ph/9911341. In this approach, we scan the O(1) coefficients randomly. We argue that this is the correct approach when the fundamental theory is sufficiently complicated. Assuming there is no physical distinction among three generations of neutrinos, the probability distributions in MNS mixing angles can be predicted independent of the choice of the measure. This is because the mixing angles are distributed according to the Haar measure of the Lie groups whose elements diagonalize the mass matrices. The near-maximal mixings, as observed in the atmospheric neutrino data and as required in the LMA solution to the solar neutrino problem, are highly probable. A small hierarchy between the Delta m^2 for the atmospheric and the solar neutrinos is obtained very easily; the complex seesaw case gives a hierarchy of a factor of 20 as the most probable one, even though this conclusion is more measure-dependent. U_{e3} has to be just below the current limit from the CHOOZ experiment. The CP-violating parameter sin delta is preferred to be maximal. We present a simple SU(5)-like extension of anarchy to the charged-lepton and quark sectors which works well phenomenologically.Comment: 26 page