Flavor Mixing and the Permutation Symmetry among Generations

In the standard model, the permutation symmetry among the three generations of fundamental fermions is usually regarded to be broken by the Higgs couplings. It is found that the symmetry is restored if we include the mass matrix parameters as physical variables which transform appropriately under the symmetry operation. Known relations between these variables, such as the renormalization group equations, as well as formulas for neutrino oscillations (in vacuum and in matter), are shown to be covariant tensor equations under the permutation symmetry group.Comment: 12 page

Renormalization of the Neutrino Mass Matrix

In terms of a rephasing invariant parametrization, the set of renormalization group equations (RGE) for Dirac neutrino parameters can be cast in a compact and simple form. These equations exhibit manifest symmetry under flavor permutations. We obtain both exact and approximate RGE invariants, in addition to some approximate solutions and examples of numerical solutions.Comment: 15 pages, 1figur

Rephasing invariance and neutrino mixing

A rephasing invariant parametrization is introduced for three flavor neutrino mixing. For neutrino propagation in matter, these parameters are shown to obey evolution equations as functions of the induced neutrino mass. These equations are found to preserve (approximately) some characteristic features of the mixing matrix, resulting in solutions which exhibit striking patterns as the induced mass varies. The approximate solutions are compared to numerical integrations and found to be quite accurate.Comment: 18 pages, 6 figure

Properties of the Neutrino Mixing Matrix

For neutrino mixing we propose to use the parameter set $X_{i}$ $(=|V_{ei}|^{2})$ and $\Omega_{i}$ $(=\epsilon_{ijk}|V_{\mu j}|^{2}|V_{\tau k}|^{2})$, with two constraints. These parameters are directly measurable since the neutrino oscillation probabilities are quadratic functions of them. Physically, the set $\Omega_{i}$ signifies a quantitative measure of $\mu-\tau$ asymmetry. Available neutrino data indicate that all the $\Omega_{i}$'s are small $(\lesssim O(10^{-1}))$, but with large uncertainties. The behavior of $\Omega_{i}$ as functions of the induced neutrino mass in matter are found to be simple, which should facilitate the analyses of long baseline experiments.Comment: 14 pages, 5 figure

Rephasing invariance and the neutrino mu-tau symmetry

The vacuum neutrino mixing is known to exhibit an approximate $\mu-\tau$ symmetry, which was shown to be preserved for neutrino propagating in matter. This symmetry reduces the neutrino transition probabilities to very simple forms when expressed in a rephasing invariant parametrization introduced earlier. Applications to long baseline experiments are discussed.Comment: 12 pages, 4 figure

A morphological study of waves in the thermosphere using DE-2 observations

Theoretical model and data analysis of DE-2 observations for determining the correlation between the neutral wave activity and plasma irregularities have been presented. The relationships between the observed structure of the sources, precipitation and joule heating, and the fluctuations in neutral and plasma parameters are obtained by analyzing two measurements of neutral atmospheric wave activity and plasma irregularities by DE-2 during perigee passes at an altitude on the order of 300 to 350 km over the polar cap. A theoretical model based on thermal nonlinearity (joule heating) to give mode-mode coupling is developed to explore the role of neutral disturbance (winds and gravity waves) on the generation of plasma irregularities

DEMAND FOR FOOD QUANTITY AND QUALITY IN CHINA

As their incomes rise, Chinese consumers are changing their diets and demanding greater quality, convenience, and safety in food. Food expenditures grow faster than quantities purchased as income rises, suggesting that consumers with higher incomes purchase more expensive foods. The top-earning Chinese households appear to have reached a point where the income elasticity of demand for quantity of most foods is near zero. China’s food market is becoming segmented. The demand for quality by high-income households has fueled recent growth in modern food retail and sales of premium-priced food and beverage products. Food expenditures and incomes have grown much more slowly for rural and low-income urban households.China, food, consumption, demand, income, elasticities, Engel curve, households, rural, urban, Food Consumption/Nutrition/Food Safety,

Quark Mass Matrices with Four and Five Texture Zeroes, and the CKM Matrix, in terms of Mass Eigenvalues

Using the triangular matrix techniques of Kuo et al and Chiu et al for the four and five texture zero cases, with vanishing (11) elements for U and D matrices, it is shown, from the general eigenvalue equations and hierarchy conditions, that the quark mass matrices, and the CKM matrix can be expressed (except for the phases) entirely in terms of quark masses. The matrix structures are then quite simple and transparent. We confirm their results for the five texture zero case but find, upon closer examination of all the CKM elements which our results provide, that six of their nine patterns for the four texture zero case are not compatible with experiments. In total, only one five-texture zero and three four-texture zero patterns are allowed.Comment: 15 pages, 3 table