Multi-phases in gauge theories on non-simply connected spaces

It is pointed out that phase structures of gauge theories compactified on non-simply connected spaces are not trivial. As a demonstration, an SU(2) gauge model on $M^3\otimes S^1$ is studied and is shown to possess three phases: Hosotani, Higgs and coexisting phases. The critical radius and the order of the phase transitions are explicitly determined. A general discussion about phase structures for small and large scales of compactified spaces is given. The appearance of phase transitions suggests a GUT scenario in which the gauge hierarchy problem is replaced by a dynamical problem of how to stabilize a radius of a compactified space in close vicinity to a critical radius.Comment: 12 pages, 1 figur

Branching Ratios, Forward-backward Asymmetry and Angular Distributions of B→K1l+l−B\to K_1l^+l^- Decays

Using the $B\to K_1$ form factors evaluated in the perturbative QCD approach, we study semileptonic $B\to K_1(1270)l^+l^-$ and $B\to K_1(1400)l^+l^-$ decays, where $K_1(1270)$ and $K_1(1400)$ are mixtures of $K_{1A}$ and $K_{1B}$ which are $^3P_1$ and $^1P_1$ states, respectively. Using the technique of helicity amplitudes, we express the decay amplitudes in terms of several independent and Lorentz invariant pieces. We study the dilepton invariant mass distributions, branching ratios, polarizations and forward-backward asymmetries of $B\to K_1l^+l^-$ decays. The ambiguity in the sign of the mixing angle will induce much large differences to branching ratios of semileptonic B decays: branching ratios without resonant contributions either have the order of $10^{-6}$ or $10^{-8}$. But the polarizations and the forward-backward asymmetries are not sensitive to the mixing angles. We find that the resonant contributions will dramatically change the dilepton invariant mass distributions in the resonant region. We also provide the angular distributions of $B\to K_1l^+l^-\to (K\pi\pi)l^+l^-$ decays.Comment: 14 pages, 6 figures, version appears in PR

Tensor mesons produced in tau lepton decays

Light tensor mesons (T = a_2, f_2 and K_2^*) can be produced in decays of tau leptons. In this paper we compute the branching ratios of tau --> T pi nu decays by assuming the dominance of intermediate virtual states to model the form factors involved in the relevant hadronic matrix element. The exclusive f_2(1270) pi^- decay mode turns out to have the largest branching ratio, of O(10^-4) . Our results indicate that the contributions of tensor meson intermediate states to the three-pseudoscalar channels of tau decays are rather small.Comment: 10 pages, 1 figure. Version accepted for publication in PRD, some typos are corrected and comments are added in section 4. Conclusions remain unchange

Finite Higgs mass without Supersymmetry

We identify a class of chiral models where the one-loop effective potential for Higgs scalar fields is finite without any requirement of supersymmetry. It corresponds to the case where the Higgs fields are identified with the components of a gauge field along compactified extra dimensions. We present a six dimensional model with gauge group U(3)xU(3) and quarks and leptons accomodated in fundamental and bi-fundamental representations. The model can be embedded in a D-brane configuration of type I string theory and, upon compactification on a T^2/Z_2 orbifold, it gives rise to the standard model with two Higgs doublets.Comment: 28 pages, 4 figures, uses axodraw. Some typos corrected and references rearrange

The Gauge Hierarchy Problem and Higher Dimensional Gauge Theories

We report on an attempt to solve the gauge hierarchy problem in the framework of higher dimensional gauge theories. Both classical Higgs mass and quadratically divergent quantum correction to the mass are argued to vanish. Hence the hierarchy problem in its original sense is solved. The remaining finite mass correction is shown to depend crucially on the choice of boundary condition for matter fields, and a way to fix it dynamically is presented. We also point out that on the simply-connected space $S^2$ even the finite mass correction vanishes.Comment: LaTeX2e. 12 pages, 3 Postscript figures; Added references, some comment

Radiative and Semileptonic B Decays Involving Higher K-Resonances in the Final States

We study the radiative and semileptonic B decays involving a spin-$J$ resonant $K_J^{(*)}$ with parity $(-1)^J$ for $K_J^*$ and $(-1)^{J+1}$ for $K_J$ in the final state. Using the large energy effective theory (LEET) techniques, we formulate $B \to K_J^{(*)}$ transition form factors in the large recoil region in terms of two independent LEET functions $\zeta_\perp^{K_J^{(*)}}$ and $\zeta_\parallel^{K_J^{(*)}}$, the values of which at zero momentum transfer are estimated in the BSW model. According to the QCD counting rules, $\zeta_{\perp,\parallel}^{K_J^{(*)}}$ exhibit a dipole dependence in $q^2$. We predict the decay rates for $B \to K_J^{(*)} \gamma$, $B \to K_J^{(*)} \ell^+ \ell^-$ and $B \to K_J^{(*)}\nu \bar{\nu}$. The branching fractions for these decays with higher $K$-resonances in the final state are suppressed due to the smaller phase spaces and the smaller values of $\zeta^{K_J^{(*)}}_{\perp,\parallel}$. Furthermore, if the spin of $K_J^{(*)}$ becomes larger, the branching fractions will be further suppressed due to the smaller Clebsch-Gordan coefficients defined by the polarization tensors of the $K_J^{(*)}$. We also calculate the forward backward asymmetry of the $B \to K_J^{(*)} \ell^+ \ell^-$ decay, for which the zero is highly insensitive to the $K$-resonances in the LEET parametrization.Comment: 27 pages, 4 figures, 7 tables;contents and figures corrected, title and references revise

Asymmetry Parameter of the K1(1270,1400)K_{1} (1270, 1400) by Analyzing the B→K1ννˉB\to K_{1}\nu \bar{\nu} Transition Form Factors within QCD

Separating the mixture of the $K_{1}(1270)$ and $K_{1}(1400)$ states, the $B\to K_{1}(1270, 1400)\nu\bar{\nu}$ transition form factors are calculated in the three-point QCD sum rules approach. The longitudinal, transverse and total decay widths as well as the asymmetry parameter, characterizing the polarization of the axial $K_{1}(1270, 1400)$ and the branching ratio for these decays are evaluated.Comment: 25 pages, 3 figures, 3 table