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

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

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

Light-emitting current of electrically driven single-photon sources

The time-dependent tunnelling current arising from the electron-hole recombination of exciton state is theoretically studied using the nonequilibrium Green's function technique and the Anderson model with two energy levels. The charge conservation and gauge invariance are satisfied in the tunnelling current. Apart from the classical capacitive charging and discharging behavior, interesting oscillations superimpose on the tunnelling current for the applied rectangular pulse voltage.Comment: 14 pages, 5 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

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

Stem-root flow effect on soil–atmosphere interactions and uncertainty assessments

Abstract. Soil water can rapidly enter deeper layers via vertical redistribution of soil water through the stem–root flow mechanism. This study develops the stem–root flow parameterization scheme and coupled this scheme with the Simplified Simple Biosphere model (SSiB) to analyze its effects on land–atmospheric interactions. The SSiB model was tested in a single column mode using the Lien Hua Chih (LHC) measurements conducted in Taiwan and HAPEX-Mobilhy (HAPEX) measurements in France. The results show that stem–root flow generally caused a decrease in the moisture content at the top soil layer and moistened the deeper soil layers. Such soil moisture redistribution results in significant changes in heat flux exchange between land and atmosphere. In the humid environment at LHC, the stem–root flow effect on transpiration was minimal, and the main influence on energy flux was through reduced soil evaporation that led to higher soil temperature and greater sensible heat flux. In the Mediterranean environment of HAPEX, the stem–root flow significantly affected plant transpiration and soil evaporation, as well as associated changes in canopy and soil temperatures. However, the effect on transpiration could either be positive or negative depending on the relative changes in the moisture content of the top soil vs. deeper soil layers due to stem–root flow and soil moisture diffusion processes