Geometric Mean Neutrino Mass Relation

Present experimental data from neutrino oscillations have provided much information about the neutrino mixing angles. Since neutrino oscillations only determine the mass squared differences $\Delta m^2_{ij} = m^2_i - m^2_j$, the absolute values for neutrino masses $m_i$ can not be determined using data just from oscillations. In this work we study implications on neutrino masses from a geometric mean mass relation $m_2=\sqrt{m_1 m_3}$ which enables one to determined the absolute masses of the neutrinos. We find that the central values of the three neutrino masses and their $2\sigma$ errors to be $m_1 = (1.58\pm 0.18){meV}$, $m_2 = (9.04\pm 0.42){meV}$, and $m_3 = (51.8\pm 3.5){meV}$. Implications for cosmological observation, beta decay and neutrinoless double beta decays are discussed.Comment: 7 pages. Talk given at COSPA06. A reference adde

The Tensor Current Divergence Equation in U(1) Gauge Theories is Free of Anomalies

The possible anomaly of the tensor current divergence equation in U(1) gauge theories is calculated by means of perturbative method. It is found that the tensor current divergence equation is free of anomalies.Comment: Revtex4, 7 pages, 2 figure

Bosonic Reduction of Susy Generalized Harry Dym Equation

In this paper we construct the two component supersymmetric generalized Harry Dym equation which is integrable and study various properties of this model in the bosonic limit. In particular, in the bosonic limit we obtain a new integrable system which, under a hodograph transformation, reduces to a coupled three component system. We show how the Hamiltonian structure transforms under a hodograph transformation and study the properties of the model under a further reduction to a two component system. We find a third Hamiltonian structure for this system (which has been shown earlier to be a bi-Hamiltonian system) making this a genuinely tri-Hamiltonian system. The connection of this system to the modified dispersive water wave equation is clarified. We also study various properties in the dispersionless limit of our model.Comment: 21 page

CP Violation in Fermion Pair Decays of Neutral Boson Particles

We study CP violation in fermion pair decays of neutral boson particles with spin 0 or 1. We study a new asymmetry to measure CP violation in $\eta, K_L \rightarrow \mu^+\mu^-$ decays and discuss the possibility of measuring it experimentally. For the spin-1 particles case, we study CP violation in the decays of $J/\psi$ to $SU(3)$ octet baryon pairs. We show that these decays can be used to put stringent constraints on the electric dipole moments of $\Lambda$, $\Sigma$ and $\Xi$.Comment: 14p, OZ-93/22, UM-93/89, OITS 51

ARPES and NMTO Wannier Orbital Theory of LiMo6_{6}O17_{17} - Implications for Unusually Robust Quasi-One Dimensional Behavior

We present the results of a combined study by band theory and angle resolved photoemission spectroscopy (ARPES) of the purple bronze, Li$_{1-x}$Mo$_{6}$O$_{17}$. Structural and electronic origins of its unusually robust quasi-one dimensional (quasi-1D) behavior are investigated in detail. The band structure, in a large energy window around the Fermi energy, is basically 2D and formed by three Mo $t_{2g}$-like extended Wannier orbitals, each one giving rise to a 1D band running at a 120$^\circ$ angle to the two others. A structural "dimerization" from $\mathbf{c}/2$ to $\mathbf{c}$ gaps the $xz$ and $yz$ bands while leaving the $xy$ bands metallic in the gap, but resonantly coupled to the gap edges and, hence, to the other directions. The resulting complex shape of the quasi-1D Fermi surface (FS), verified by our ARPES, thus depends strongly on the Fermi energy position in the gap, implying a great sensitivity to Li stoichiometry of properties dependent on the FS, such as FS nesting or superconductivity. The strong resonances prevent either a two-band tight-binding model or a related real-space ladder picture from giving a valid description of the low-energy electronic structure. We use our extended knowledge of the electronic structure to newly advocate for framing LiMo$_{6}$O$_{17}$ as a weak-coupling material and in that framework can rationalize both the robustness of its quasi-1D behavior and the rather large value of its Luttinger liquid (LL) exponent $\alpha$. Down to a temperature of 6$\,$K we find no evidence for a theoretically expected downward renormalization of perpendicular single particle hopping due to LL fluctuations in the quasi-1D chains.Comment: 53 pages, 17 Figures, 6 year