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

A steepest descent calculation of RNA pseudoknots

We enumerate possible topologies of pseudoknots in single-stranded RNA molecules. We use a steepest-descent approximation in the large N matrix field theory, and a Feynman diagram formalism to describe the resulting pseudoknot structure

Charge breaking bounds in the Zee model

We study the possibility that charge breaking minima occur in the Zee model. We reach very different conclusions from those attained in simpler, two Higgs doublet models, and the reason for this is traced back to the existence of cubic terms in the potential. A scan of the Zee model's parameter space shows that CB is restricted to a narrow region of values of the parameters

Enumeration of RNA structures by Matrix Models

We enumerate the number of RNA contact structures according to their genus, i.e. the topological character of their pseudoknots. By using a recently proposed matrix model formulation for the RNA folding problem, we obtain exact results for the simple case of an RNA molecule with an infinitely flexible backbone, in which any arbitrary pair of bases is allowed. We analyze the distribution of the genus of pseudoknots as a function of the total number of nucleotides along the phosphate-sugar backbone.Comment: RevTeX, 4 pages, 2 figure

Propagation of Vortex Electron Wave Functions in a Magnetic Field

The physics of coherent beams of photons carrying axial orbital angular momentum (OAM) is well understood and such beams, sometimes known as vortex beams, have found applications in optics and microscopy. Recently electron beams carrying very large values of axial OAM have been generated. In the absence of coupling to an external electromagnetic field the propagation of such vortex electron beams is virtually identical mathematically to that of vortex photon beams propagating in a medium with a homogeneous index of refraction. But when coupled to an external electromagnetic field the propagation of vortex electron beams is distinctly different from photons. Here we use the exact path integral solution to Schrodingers equation to examine the time evolution of an electron wave function carrying axial OAM. Interestingly we find that the nonzero OAM wave function can be obtained from the zero OAM wave function, in the case considered here, simply by multipling it by an appropriate time and position dependent prefactor. Hence adding OAM and propagating can in this case be replaced by first propagating then adding OAM. Also, the results shown provide an explicit illustration of the fact that the gyromagnetic ratio for OAM is unity. We also propose a novel version of the Bohm-Aharonov effect using vortex electron beams.Comment: 14 pages, 2 figures, submitted to Phys Rev

Anomalies at finite density and chiral fermions

Using perturbation theory in the Euclidean (imaginary time) formalism as well as the non-perturbative Fujikawa method, we verify that the chiral anomaly equation remains unaffected in the presence of nonzero chemical potential, $\mu$. We extend our considerations to fermions with exact chiral symmetry on the lattice and discuss the consequences for the recent Bloch-Wettig proposal for the Dirac operator at finite chemical potential. We propose a new simpler method of incorporating $\mu$ and compare it with the Bloch-Wettig idea.Comment: 12 pages, 3 figures,some typos corrected, a better proof for the \mu independence of anomaly is given in section IIB, v4: the published versio

Predictions from the Fritzsch-Type Lepton Mass Matrices

We revisit the Fritzsch-type lepton mass matrix models confronted with new experiments for neutrino mixings. It is shown that the model is viable and leads to a rather narrow range of free parameters. Using empirical mixing information between $\nu_e$ and $\nu_\mu$, and between $\nu_\mu$ and $\nu_\tau$, it is predicted that the mixing angle between $nu_e$ and $\nu_\tau$ is in the range $0.04<|U_{13}|<0.20$, consistent with the CHOOZ experiment and the lightest neutrino mass is $0.0004<m_1<0.0030$ eV. The range of the effective mass measured in double beta decay is $0.002<0.007$ eV.Comment: Latex file with 13 pages, 6 eps file

Towards Resolution of Hierarchy Problems in a Cosmological Context

A cosmological scenario is proposed, which simultaneously solves the mass hierarchy and the small dark energy problem. In the present scenario an effective gravity mass scale (inverse of the Newton's constant) increases during the inflationary period. The small cosmological constant or the dark energy density in the present universe is dynamically realized by introducing two, approximately O(2) symmetric dilatons, taking the fundamental mass scale at TeV.Comment: 12 pages, no figur