Classification and Application of Triangular Quark Mass Matrices

The hierarchical structure in the quark masses and mixings allows its ten physical parameters to be most conveniently encoded in mass matrices of the upper triangular form. We classify these matrices in the hierarchical, minimal parameter basis where the mismatch between the weak and mass eigenstates involves only small mixing angles. Ten such pairs are obtained for the up and down quarks. This analysis can be used to classify texture zeros of general mass matrices. For hermitian mass matrices with five texture zeros, this method yields immediately five pairs of textures with simple, analytic predictions for the quark mixings. Comparison with data indicates that, of the five pairs, three are disfavored, one is marginally acceptable, while the fifth fits well.Comment: 18 pages, ReVTe

Neutrino mixing in matter

Three-neutrino mixing in matter is studied through a set of evolution equations which are based on a rephasing invariant parametrization. Making use of the known properties of measured neutrino parameters, analytic, approximate, solutions are obtained. Their accuracy is confirmed by comparison with numerical integration of these equations. The results, when expressed in the elements squared of the mixing matrix, exhibit striking patterns as the matter density varies.Comment: Revised, 5 pages, 3 figures, references added

Solar Neutrinos with Three Flavor Mixings

The recent 71Ga solar neutrino observation is combined with the 37Cl and Kamiokande-II observations in an analysis for neutrino masses and mixings. The allowed parameter region is found for matter enhanced mixings among all three neutrino flavors. Distortions of the solar neutrino spectrum unique to three flavors are possible and may be observed in continuing and next generation experiments.Comment: August 1992 (Revised) PURD-TH-92-

Renormalization of the neutrino mass matrix

The renormalization group equations for the general 2 by 2, complex, neutrino mass matrix are shown to have exact, analytic solutions. Simple formulas are given for the physical mixing angle, complex phase and mass ratio in terms of their initial values and the energy scales. We also establish a (complex) renormalization invariant relating these parameters. The qualitative features of the physical parameters' renormalization are clearly illustrated in vector field plots. In both the SM and MSSM, maximal mixing is a saddle point.Comment: 16 pages, 5 figure

Constraints on Three-Neutrino Mixing from Atmospheric and Reactor Data

Observations of atmospheric neutrinos are usually analyzed using the simplifying approximation that either $\nu_\mu \leftrightarrow \nu_\tau$ or $\nu_e \leftrightarrow \nu_\mu$ two-flavor mixing is relevant. Here we instead consider the data using the simplifying approximation that only one neutrino mass scale is relevant. This approximation is the minimal three-flavor notation that includes the two relevant two-flavor approximations. The constraints in the parameter space orthogonal to the usual, two-flavor analyses are studied.Comment: 15 pages, preprint IUHET-26

Maximal Neutrino Mixing from an Attractive Infrared Fixed Point

In the Standard Model (and MSSM), renormalization effects on neutrino mixing are generally very small and the attractive fixed points are at vanishing neutrino mixing. However for multi-higgs extensions of the Standard Model, renormalization effects on neutrino mixing can be large and nontrivial fixed points are possible. Here we examine a simple two-higgs model. For two flavors, maximal mixing is an attractive infrared fixed point. For three flavors, the neutrino mass matrix evolves towards large off-diagonal elements at low energies. The experimentally suggested bimaximal neutrino mixing pattern is one possible attractive infrared fixed point.Comment: 16 page

The Oscillation Probability of GeV Solar Neutrinos of All Active Species

In this paper, I address the oscillation probability of O(GeV) neutrinos of all active flavours produced inside the Sun and detected at the Earth. Flavours other than electron-type neutrinos may be produced, for example, by the annihilation of WIMPs which may be trapped inside the Sun. In the GeV energy regime, matter effects are important both for the ``1-3'' system and the ``1-2'' system, and for different neutrino mass hierarchies. A numerical scan of the multidimensional three-flavour parameter space is performed, ``inspired'' by the current experimental situation. One important result is that, in the three-flavour oscillation case, P{alpha,beta} is different from P{beta,alpha} for a significant portion of the parameter space, even if there is no CP-violating phase in the MNS matrix. Furthermore, P{mu,mu} has a significantly different behaviour from P{tau,tau}, which may affect expectations for the number of events detected at large neutrino telescopes.Comment: 38 pages, 10 figure

Supernova neutrino oscillations: A simple analytical approach

Analyses of observable supernova neutrino oscillation effects require the calculation of the electron (anti)neutrino survival probability P_ee along a given supernova matter density profile. We propose a simple analytical prescription for P_ee, based on a double-exponential form for the crossing probability and on the concept of maximum violation of adiabaticity. In the case of two-flavor transitions, the prescription is shown to reproduce accurately, in the whole neutrino oscillation parameter space, the results of exact numerical calculations for generic (realistic or power-law) profiles. The analytical approach is then generalized to cover three-flavor transitions with (direct or inverse) mass spectrum hierarchy, and to incorporate Earth matter effects. Compact analytical expressions, explicitly showing the symmetry properties of P_ee, are provided for practical calculations.Comment: 22 pages (RevTeX) + 5 figures (PostScript

Testing quark mass matrices with right-handed mixings

In the standard model, several forms of quark mass matrices which correspond to the choice of weak bases lead to the same left-handed mixings $V_L=V_{CKM}$, while the right-handed mixings $V_R$ are not observable quantities. Instead, in a left-right extension of the standard model, such forms are ansatze and give different right-handed mixings which are now observable quantities. We partially select the reliable forms of quark mass matrices by means of constraints on right-handed mixings in some left-right models, in particular on $V^R_{cb}$. Hermitian matrices are easily excluded.Comment: 12 pages RevTex, no figures. Minor corrections. Comment on SO(10) changed and one reference adde

Non-adiabatic level crossing in (non-) resonant neutrino oscillations

We study neutrino oscillations and the level-crossing probability P_{LZ}=\exp(-\gamma_n\F_n\pi/2) in power-law like potential profiles $A(r)\propto r^n$. After showing that the resonance point coincides only for a linear profile with the point of maximal violation of adiabaticity, we point out that the ``adiabaticity'' parameter $\gamma_n$ can be calculated at an arbitrary point if the correction function \F_n is rescaled appropriately. We present a new representation for the level-crossing probability, P_{LZ}=\exp(-\kappa_n\G_n), which allows a simple numerical evaluation of $P_{LZ}$ in both the resonant and non-resonant cases and where \G_n contains the full dependence of $P_{LZ}$ on the mixing angle $\theta$. As an application we consider the case $n=-3$ important for oscillations of supernova neutrinos.Comment: 4 pages, revtex, 3 eps figure