Renormalization Group Effects on the Mass Relation Predicted by the Standard Model with Generalized Covariant Derivatives

Renormalization group analysis is made on the relation $m_{\rm H} \simeq \sqrt{2}m_t$ for masses of the top quark and the Higgs boson, which is predicted by the standard model based on generalized covariant derivatives with gauge and Higgs fields. This relation is a low energy manifestation of a tree level constraint which holds among the quartic Higgs self-coupling constant and the Yukawa coupling constants at a certain high energy scale $\mu_0$. With the renormalization group equation at one-loop level, the evolution of the constraint is calculated from $\mu_0$ down to the low energy region around the observed top quark mass. The result of analysis shows that the Higgs boson mass is in $m_t \lesssim m_{\rm H} \lesssim \sqrt{2}m_t$ for a wide range of the energy scale $\mu_0 \gtrsim m_t$ and it approaches to 177 GeV ($\approx m_t$) for large values of $\mu_0$.Comment: 13 pages, LaTeX, no figure

Approximate Sum Rules of CKM Matrix Elements from Quasi-Democratic Mass Matrices

To extract sum rules of CKM matrix elements, eigenvalue problems for quasi-democratic mass matrices are solved in the first order perturbation approximation with respect to small deviations from the democratic limit. Mass spectra of up and down quark sectors and the CKM matrix are shown to have clear and distinctive hierarchical structures. Numerical analysis shows that the absolute values of calculated CKM matrix elements fit the experimental data quite well. The order of the magnitude of the Jarlskog parameter is estimated by the relation $|J| \approx \sqrt{2}(m_c/m_t + m_s/m_b)|V_{us}|^2|V_{cb}|/4$.Comment: Latex, 15 pages, no figure

Observation of Radiative B Meson Decays into Higher Kaonic Resonances

We have studied radiative B meson decays into higher kaonic resonances decaying into a two-body or three-body final state, using a data sample of 21.3 fb$^{-1}$ recorded at the $\Upsilon(4S)$ resonance with the Belle detector at KEKB. For the two-body final state, we extract the $B \to K_2^{*}(1430)^0 \gamma$ component from an analysis of the helicity angle distribution, and obtain ${\cal B}(B^0 \to K_2^{*}(1430)^0 \gamma) = (1.26\pm 0.66\pm 0.10)\times 10^{-5}$. For the three-body final state, we observe a $B \to K\pi\pi\gamma$ signal that is consistent with a mixture of $B \to K^* \pi \gamma$ and $B \to K \rho \gamma$. This is the first time that $B \to K^* \pi \gamma$ and $B \to K \rho \gamma$ have been observed separately. We find their branching fractions to be ${\cal B}(B \to K^* \pi \gamma; M_{K^*\pi}<2.0 GeV/c^2) = (5.6\pm 1.1\pm 0.9)\times 10^{-5}$ and ${\cal B}(B \to K \rho \gamma; M_{K\rho} < 2.0 GeV/c^2) = (6.5\pm 1.7^{+1.1}_{1.2})\times 10^{-5}$, respectively

Phases of a bilayer Fermi gas

We investigate a two-species Fermi gas in which one species is confined in two parallel layers and interacts with the other species in the three-dimensional space by a tunable short-range interaction. Based on the controlled weak coupling analysis and the exact three-body calculation, we show that the system has a rich phase diagram in the plane of the effective scattering length and the layer separation. Resulting phases include an interlayer s-wave pairing, an intralayer p-wave pairing, a dimer Bose-Einstein condensation, and a Fermi gas of stable Efimov-like trimers. Our system provides a widely applicable scheme to induce long-range interlayer correlations in ultracold atoms.Comment: 5 pages, 5 figures; (v2) stability of trimer is emphasized; (v3) published versio

Small scale noise and wind tunnel tests of upper surface blowing nozzle flap concepts. Volume 1. Aerodynamic test results

The results and analyses of aerodynamic and acoustic studies conducted on the small scale noise and wind tunnel tests of upper surface blowing nozzle flap concepts are presented. Various types of nozzle flap concepts were tested. These are an upper surface blowing concept with a multiple slot arrangement with seven slots (seven slotted nozzle), an upper surface blowing type with a large nozzle exit at approximately mid-chord location in conjunction with a powered trailing edge flap with multiple slots (split flow or partially slotted nozzle). In addition, aerodynamic tests were continued on a similar multi-slotted nozzle flap, but with 14 slots. All three types of nozzle flap concepts tested appear to be about equal in overall aerodynamic performance but with the split flow nozzle somewhat better than the other two nozzle flaps in the landing approach mode. All nozzle flaps can be deflected to a large angle to increase drag without significant loss in lift. The nozzle flap concepts appear to be viable aerodynamic drag modulation devices for landing

Marginally unstable Holmboe modes

Marginally unstable Holmboe modes for smooth density and velocity profiles are studied. For a large family of flows and stratification that exhibit Holmboe instability, we show that the modes with phase velocity equal to the maximum or the minimum velocity of the shear are marginally unstable. This allows us to determine the critical value of the control parameter R (expressing the ratio of the velocity variation length scale to the density variation length scale) that Holmboe instability appears R=2. We then examine systems for which the parameter R is very close to this critical value. For this case we derive an analytical expression for the dispersion relation of the complex phase speed c(k) in the unstable region. The growth rate and the width of the region of unstable wave numbers has a very strong (exponential) dependence on the deviation of R from the critical value. Two specific examples are examined and the implications of the results are discussed.Comment: Submitted to Physics of Fluid

Quantizing Majorana Fermions in a Superconductor

A Dirac-type matrix equation governs surface excitations in a topological insulator in contact with an s-wave superconductor. The order parameter can be homogenous or vortex valued. In the homogenous case a winding number can be defined whose non-vanishing value signals topological effects. A vortex leads to a static, isolated, zero energy solution. Its mode function is real, and has been called "Majorana." Here we demonstrate that the reality/Majorana feature is not confined to the zero energy mode, but characterizes the full quantum field. In a four-component description a change of basis for the relevant matrices renders the Hamiltonian imaginary and the full, space-time dependent field is real, as is the case for the relativistic Majorana equation in the Majorana matrix representation. More broadly, we show that the Majorana quantization procedure is generic to superconductors, with or without the Dirac structure, and follows from the constraints of fermionic statistics on the symmetries of Bogoliubov-de Gennes Hamiltonians. The Hamiltonian can always be brought to an imaginary form, leading to equations of motion that are real with quantized real field solutions. Also we examine the Fock space realization of the zero mode algebra for the Dirac-type systems. We show that a two-dimensional representation is natural, in which fermion parity is preserved.Comment: 26 pages, no figure

A Phenomenological Formula for KM Matrix

We propose a phenomenological formula relating the Kobayashi-Maskawa matrix $V_{KM}$ and quark masses in a form $(m_d,\ m_s,\ m_b)\propto (m_u,\ m_c,\ m_t)V_{KM}$. The formula agrees with experimental data well and has an interesting geometric picture. The origin of such a formula is discussed in the standard model.Comment: 9 pages, LaTeX, no figure

Influence of self-gravity on the runaway instability of black hole-torus systems

Results from the first fully general relativistic numerical simulations in axisymmetry of a system formed by a black hole surrounded by a self-gravitating torus in equilibrium are presented, aiming to assess the influence of the torus self-gravity on the onset of the runaway instability. We consider several models with varying torus-to-black hole mass ratio and angular momentum distribution orbiting in equilibrium around a non-rotating black hole. The tori are perturbed to induce the mass transfer towards the black hole. Our numerical simulations show that all models exhibit a persistent phase of axisymmetric oscillations around their equilibria for several dynamical timescales without the appearance of the runaway instability, indicating that the self-gravity of the torus does not play a critical role favoring the onset of the instability, at least during the first few dynamical timescales.Comment: To appear on Phys.Rev.Let