Zeroes of the Neutrino Mass Matrix

We assume there to be precisely three left-handed neutrino states whose Majorana masses are generated by an unspecified mechanism. Were CP conserved, the symmetric neutrino mass matrix M would be real and all six of its distinct entries could be experimentally determined. But CP is not conserved so that M is likely to be complex. As a result, not all nine of its convention-independent real parameters can be determined without an appeal to theory. Thus we examine the possibility that a restricted class of neutrino mass matrices may suffice to describe current data, namely those complex symmetric matrices several of whose entries vanish. We find that there are seven acceptable textures with two independent zeroes, and we explore their contrasting phenomenological implications. Textures with more than two independent zeroes appear to be excluded by experiment.Comment: Version to appear in PL

Can the Zee ansatz for neutrino masses be correct?

Working in the framework of three chiral neutrinos with Majorana masses, we investigate a scenario first realized in an explicit model by Zee: that the neutrino mass matrix is strictly off-diagonal in the flavor basis, with all its diagonal entries precisely zero. This CP-conserving ansatz leads to two relations among the three mixing angles $(\theta_1, \theta_2, \theta_3)$ and two squared mass differences. We impose the constraint $|m_3^2 - m_2^2| \gg |m^2_2 - m_1^2|$ to conform with experiment, which requires the $\theta_i$ to lie nearby one of four 1-parameter domains in $\theta$-space. We exhibit the implications for solar and atmospheric neutrino oscillations in each of these cases. A unique version of the Zee {\it ansatz} survives confrontation with experimental data, one which necessarily involves maximal just-so vacuum oscillations of solar neutrinos.Comment: 7 pages, harvmac, typo corrected, ref. added, text modifie

Turnaround in Cyclic Cosmology

It is speculated how dark energy in a brane world can help reconcile an infinitely cyclic cosmology with the second law of thermodynamics. A cyclic cosmology is described, in which dark energy leads to a turnaround at a time, extremely shortly before the would-be Big Rip, at which both volume and entropy of our universe decrease by a gigantic factor, while very many independent similarly small contracting universes are spawned. The entropy of our universe decreases almost to zero at turnaround but increases for the remainder of the cycle by a vanishingly small amount during contraction, empty of matter and radiation, then by a very large factor during inflationary expansion

Production of doubly charged vector bilepton pairs at γγ\gamma \gamma colliders

The production of pairs of doubly charged vector bileptons is studied at future $\gamma \gamma$ colliders. The unpolarized cross--section for the $\gamma \gamma \to Y^{--}Y^{++}$ subprocess is analytically calculated and convoluted to predict the number of events in the complete $e^+e^-\to \gamma \gamma \to Y^{--}Y^{++}$ process. The gauge or non--gauge character of the vector bilepton $Y^{\pm \pm}$ is discussed. It is found that as a consequence of its spectacular signature, as it decays dominantly into two identical charged leptons, and also due to its charge contents, which significantly enhance the cross--section, the detection of this class of particles with mass in the sub--TeV region can be at the reach of these colliders. The model--independent nature of our results is stressed.Comment: 9 pages, 7 figures, submitted to physical review

Chiral Fermions and Quadratic Divergences

In an approach towards naturalness without supersymmetry, renormalization properties of nonsupersymmetric abelian quiver gauge theories are studied. In the construction based on cyclic groups Z_p the gauge group is U(N)^p, the fermions are all in bifundamentals and the construction allows scalars in adjoints and bifundamentals. Only models without adjoint scalars, however, exhibit both chiral fermions and the absence of one-loop quadratic divergences in the scalar propagator.Comment: 11 page

Relic Neutrinos and Z-Resonance Mechanism for Highest-Energy Cosmic Rays

The origin of the highest-energy cosmic rays remains elusive. The decay of a superheavy particle (X) into an ultra-energetic neutrino which scatters from a relic (anti-)neutrino at the Z-resonance has attractive features. Given the necessary X mass of $10^{14\sim15}$ GeV, the required lifetime, $10^{15\sim16}$ y, renders model-building a serious challenge but three logical possibilities are considered: (i) X is a Higgs scalar in SU(15) belonging to high-rank representation, leading to {\it power}-enhanced lifetime; (ii) a global X quantum number has {\it exponentially}-suppressed symmetry-breaking by instantons; and (iii) with additional space dimension(s) localisation of X within the real-world brane leads to {\it gaussian} decay suppression, the most efficient of the suppression mechanisms considered.Comment: 10 page LaTeX and one postscript figure. References adde

Cabibbo Mixing and the Search for CP Violation

We examine certain extensions of the standard model in which $CP$ violation is spontaneous and the strong $CP$ problem is resolved. In these models, the $3 \times 3$ quark mixing matrix is neither real nor unitary. However, to a precision of 0.1%, it is real and orthogonal. There are no readily observable $CP$-violating effects besides those in the neutral kaon system.Comment: 6 pages, latex, no figure