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

Tri-bimaximal Mixing and Cabibbo Angle in S4 Flavor Model with SUSY

We present a flavor model of quarks and leptons with the non-Abelian discrete symmetry $S_4$ in the framework of the SU(5) SUSY GUT. Three generations of $\bar 5$-plets in SU(5) are assigned to ${\bf 3}$ of $S_4$ while the first and second generations of 10-plets in SU(5) are assigned to ${\bf 2}$ of $S_4$, and the third generation of 10-plet is assigned to ${\bf 1}$ of $S_4$. Right-handed neutrinos are also assigned to ${\bf 2}$ for the first and second generations and ${\bf 1}'$ for the third generation. We predict the Cabibbo angle as well as the tri-bimaximal mixing of neutrino flavors. We also predict the non-vanishing $U_{e3}$ of the neutrino flavor mixing due to higher dimensional mass operators. Our predicted CKM mixing angles and the CP violation are consistent with experimental values. We also study SUSY breaking terms in the slepton sector. Our model leads to smaller values of flavor changing neutral currents than the present experimental bounds.Comment: 32 pages, 4 figures, some references are added, with minor modificatio

Irregular conformal blocks, with an application to the fifth and fourth Painlev\'e equations

We develop the theory of irregular conformal blocks of the Virasoro algebra. In previous studies, expansions of irregular conformal blocks at regular singular points were obtained as degeneration limits of regular conformal blocks; however, such expansions at irregular singular points were not clearly understood. This is because precise definitions of irregular vertex operators had not been provided previously. In this paper, we present precise definitions of irregular vertex operators of two types and we prove that one of our vertex operators exists uniquely. Then, we define irregular conformal blocks with at most two irregular singular points as expectation values of given irregular vertex operators. Our definitions provide an understanding of expansions of irregular conformal blocks and enable us to obtain expansions at irregular singular points. As an application, we propose conjectural formulas of series expansions of the tau functions of the fifth and fourth Painlev\'e equations, using expansions of irregular conformal blocks at an irregular singular point.Comment: 26 page

Asperity characteristics of the Olami-Feder-Christensen model of earthquakes

Properties of the Olami-Feder-Christensen (OFC) model of earthquakes are studied by numerical simulations. The previous study indicated that the model exhibits ``asperity''-like phenomena, {\it i.e.}, the same region ruptures many times near periodically [T.Kotani {\it et al}, Phys. Rev. E {\bf 77}, 010102 (2008)]. Such periodic or characteristic features apparently coexist with power-law-like critical features, {\it e.g.}, the Gutenberg-Richter law observed in the size distribution. In order to clarify the origin and the nature of the asperity-like phenomena, we investigate here the properties of the OFC model with emphasis on its stress distribution. It is found that the asperity formation is accompanied by self-organization of the highly concentrated stress state. Such stress organization naturally provides the mechanism underlying our observation that a series of asperity events repeat with a common epicenter site and with a common period solely determined by the transmission parameter of the model. Asperity events tend to cluster both in time and in space

Universal Seesaw Mechanism with Universal Strength for Yukawa Couplings

Hypotheses of the universal seesaw mechanism and the {\it universal strength for Yukawa couplings} are applied to explain one possible origin of quasi-democratic mass matrices of a special type in a left-right symmetric model with the gauge group $SU(3)_c\times SU(2)_L\times SU(2)_R\times U(1)$. Two kinds of Higgs doublets are postulated to mediate scalar interactions between the $i$-th generation of light fermion doublets and the $j$-th generation of heavy fermion singlets with relative Yukawa coupling constants of the exponential form $e^{i\phi_{ij}}$, where $\phi_{ij}$ are real phase constants. The lowest seesaw approximation results effectively in self-adjoint mass matrices which are quasi-democratic and have the same diagonal elements. A set of values for the parameters $\phi_{ij}$ is found which reproduces the present experimental data for the absolute values of the CKM matrix elements, the Jarlskog parameter and the Wolfenstein parameters.Comment: Latex, 16 pages, no figure

Resonant growth of stellar oscillations by incident gravitational waves

Stellar oscillation under the combined influences of incident gravitational wave and radiation loss is studied in a simple toy model. The star is approximated as a uniform density ellipsoid in the Newtonian gravity including radiation damping through quadrupole formula. The time evolution of the oscillation is significantly controlled by the incident wave amplitude $h$, frequency $\nu$ and damping time $\tau$. If a combination $h \nu \tau$ exceeds a threshold value, which depends on the resonance mode, the resonant growth is realized.Comment: 11 pages, 6 figures, Accepted for the publication in Classical and Quantum Gravit

Systematic Errors in the Hubble Constant Measurement from the Sunyaev-Zel'dovich effect

The Hubble constant estimated from the combined analysis of the Sunyaev-Zel'dovich effect and X-ray observations of galaxy clusters is systematically lower than those from other methods by 10-15 percent. We examine the origin of the systematic underestimate using an analytic model of the intracluster medium (ICM), and compare the prediction with idealistic triaxial models and with clusters extracted from cosmological hydrodynamical simulations. We identify three important sources for the systematic errors; density and temperature inhomogeneities in the ICM, departures from isothermality, and asphericity. In particular, the combination of the first two leads to the systematic underestimate of the ICM spectroscopic temperature relative to its emission-weighed one. We find that these three systematics well reproduce both the observed bias and the intrinsic dispersions of the Hubble constant estimated from the Sunyaev-Zel'dovich effect.Comment: 26 pages, 7 figures, accepted for publication in ApJ, Minor change

Bending strength of multi‐layered alumina with controlled residual stress

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