Effective theoretical approach of Gauge-Higgs unification model and its phenomenological applications

We derive the low energy effective theory of Gauge-Higgs unification (GHU) models in the usual four dimensional framework. We find that the theories are described by only the zero-modes with a particular renormalization condition in which essential informations about GHU models are included. We call this condition ``Gauge-Higgs condition'' in this letter. In other wards, we can describe the low energy theory as the SM with this condition if GHU is a model as the UV completion of the Standard Model. This approach will be a powerful tool to construct realistic models for GHU and to investigate their low energy phenomena.Comment: 18 pages, 2 figures; Two paragraphs discussing the applicable scope of this approach are adde

Dynamical symmetry breaking in Gauge-Higgs unification of 5D N=1{\mathcal N}=1 SUSY theory

We study the dynamical symmetry breaking in the gauge-Higgs unification of the 5D ${\mathcal N}=1$ SUSY theory, compactified on an orbifold, $S^1/Z_2$. This theory identifies Wilson line degrees of freedoms as ``Higgs doublets''. We consider $SU(3)_c \times SU(3)_W$ and SU(6) models, in which the gauge symmetries are reduced to $SU(3)_c \times SU(2)_L \times U(1)_Y$ and $SU(3)_c \times SU(2)_L \times U(1)_Y \times U(1)$, respectively, through the orbifolding boundary conditions. Quarks and leptons are bulk fields, so that Yukawa interactions can be derived from the 5D gauge interactions. We estimate the one loop effective potential of ``Higgs doublets'', and analyze the vacuum structures in these two models. We find that the effects of bulk quarks and leptons destabilize the suitable electro-weak vacuum. We show that the introduction of suitable numbers of extra bulk fields possessing the suitable representations can realize the appropriate electro-weak symmetry breaking.Comment: 15 pages, 4 figures;disscutions on Higgs quartic couplings adde

A general formula of the effective potential in 5D SU(N) gauge theory on orbifold

We show a general formula of the one loop effective potential of the 5D SU(N) gauge theory compactified on an orbifold, $S^1/Z_2$. The formula shows the case when there are fundamental, (anti-)symmetric tensor and adjoint representational bulk fields. Our calculation method is also applicable when there are bulk fields belonging to higher dimensional representations. The supersymmetric version of the effective potential with Scherk-Schwarz breaking can be obtained straightforwardly. We also show some examples of effective potentials in SU(3), SU(5) and SU(6) models with various boundary conditions, which are reproduced by our general formula.Comment: 22 pages;minor corrections;references added;typos correcte

Baryon Tri-local Interpolating Fields

We systematically investigate tri-local (non-local) three-quark baryon fields with U_L(2)*U_R(2) chiral symmetry, according to their Lorentz and isospin (flavor) group representations. We note that they can also be called as "nucleon wave functions" due to this full non-locality. We study their chiral transformation properties and find all the possible chiral multiplets consisting J=1/2 and J=3/2 baryon fields. We find that the axial coupling constant |g_A| = 5/3 is only for nucleon fields belonging to the chiral representation (1/2,1)+(1,1/2) which contains both nucleon fields and Delta fields. Moreover, all the nucleon fields belonging to this representation have |g_A| = 5/3.Comment: 8 pages, 3 tables, accepted by EPJ

Weak boson scattering in Gauge-Higgs Unification

The scattering amplitude for the longitudinal weak bosons is investigated in the SU(3) gauge-Higgs unification as a function of the scattering energy, the Wilson line phase \theta_H and the warp factor. The \theta_H-dependence of the amplitude is quite different in the flat and the warped spacetimes. Generically the amplitude is enhanced for \theta_H=O(1) in the warped case while it is almost independent of \theta_H in the flat case. This indicates the tree-level unitarity is violated in the warped case at a lower scale than that in the flat case.Comment: 22 pages, 8 figures, published version in JHE

RS1, Custodial Isospin and Precision Tests

We study precision electroweak constraints within a RS1 model with gauge fields and fermions in the bulk. The electroweak gauge symmetry is enhanced to SU(2)_L \times SU(2)_R \times U(1)_{B-L}, thereby providing a custodial isospin symmetry sufficient to suppress excessive contributions to the T parameter. We then construct complete models, complying with all electroweak constraints, for solving the hierarchy problem, without supersymmetry or large hierarchies in the fundamental couplings. Using the AdS/CFT correspondence our models can be interpreted as dual to a strongly coupled conformal Higgs sector with global custodial symmetry, gauge and fermionic matter being fundamental fields external to the CFT. This scenario has interesting collider signals, distinct from other RS models in the literature.Comment: 32 pages, 6 figures, latex2e, minor changes, references adde

Minimal gauge-Higgs unification with a flavour symmetry

We show that a flavour symmetry a la Froggatt-Nielsen can be naturally incorporated in models with gauge-Higgs unification, by exploiting the heavy fermions that are anyhow needed to realize realistic Yukawa couplings. The case of the minimal five-dimensional model, in which the SU(2)_L x U(1)_Y electroweak group is enlarged to an SU(3)_W group, and then broken to U(1)_em by the combination of an orbifold projection and a Scherk-Schwarz twist, is studied in detail. We show that the minimal way of incorporating a U(1)_F flavour symmetry is to enlarge it to an SU(2)_F group, which is then completely broken by the same orbifold projection and Scherk-Schwarz twist. The general features of this construction, where ordinary fermions live on the branes defined by the orbifold fixed-points and messenger fermions live in the bulk, are compared to those of ordinary four-dimensional flavour models, and some explicit examples are constructed.Comment: LaTex, 37 pages, 2 figures; some clarifying comments and a few references adde

Gauge-Higgs Unification in Orbifold Models

Six-dimensional orbifold models where the Higgs field is identified with some internal component of a gauge field are considered. We classify all possible T^2/Z_N orbifold constructions based on a SU(3) electroweak gauge symmetry. Depending on the orbifold twist, models with two, one or zero Higgs doublets can be obtained. Models with one Higgs doublet are particularly interesting because they lead to a prediction for the Higgs mass, which is twice the W boson mass at leading order: m_H=2 m_W. The electroweak scale is quadratically sensitive to the cut-off, but only through very specific localized operators. We study in detail the structure of these operators at one loop, and identify a class of models where they do not destabilize the electroweak scale at the leading order. This provides a very promising framework to construct realistic and predictive models of electroweak symmetry breaking.Comment: 27 pages, uses axodraw.sty; v2: version to appear in JHE

Coupled-channel effective field theory and proton-7^7Li scattering

We apply the renormalisation group (RG) to analyse scattering by short-range forces in systems with coupled channels. For two S-wave channels, we find three fixed points, corresponding to systems with zero, one or two bound or virtual states at threshold. We use the RG to determine the power countings for the resulting effective field theories. In the case of a single low-energy state, the resulting theory takes the form of an effective-range expansion in the strongly interacting channel. We also extend the analysis to include the effects of the Coulomb interaction between charged particles. The approach is then applied to the coupled $p+{^7}$Li and $n+{^7}$Be channels which couple to a $J^P=2^-$ state of $^8$Be very close to the $n+{^7}$Be threshold. At next-to-leading order, we are able to get a good description of the $p+{^7}$Li phase shift and the ${^7}$Be(n,p)${^7}$Li cross section using four parameters. Fits at one order higher are similarly good but the available data are not sufficient to determine all five parameters uniquely.Comment: 22 pages, 2 figures, RevTeX4, typos corrected, accepted for publication in European Physical Journal

Analysis of the Y(4140) and related molecular states with QCD sum rules

In this article, we assume that there exist scalar ${D}^\ast {\bar {D}}^\ast$, ${D}_s^\ast {\bar {D}}_s^\ast$, ${B}^\ast {\bar {B}}^\ast$ and ${B}_s^\ast {\bar {B}}_s^\ast$ molecular states, and study their masses using the QCD sum rules. The numerical results indicate that the masses are about $(250-500) \rm{MeV}$ above the corresponding ${D}^\ast -{\bar {D}}^\ast$, ${D}_s^\ast -{\bar {D}}_s^\ast$, ${B}^\ast -{\bar {B}}^\ast$ and ${B}_s^\ast -{\bar {B}}_s^\ast$ thresholds, the Y(4140) is unlikely a scalar ${D}_s^\ast {\bar {D}}_s^\ast$ molecular state. The scalar $D^\ast {\bar D}^\ast$, $D_s^\ast {\bar D}_s^\ast$, $B^\ast {\bar B}^\ast$ and $B_s^\ast {\bar B}_s^\ast$ molecular states maybe not exist, while the scalar ${D'}^\ast {\bar {D'}}^\ast$, ${D'}_s^\ast {\bar {D'}}_s^\ast$, ${B'}^\ast {\bar {B'}}^\ast$ and ${B'}_s^\ast {\bar {B'}}_s^\ast$ molecular states maybe exist.Comment: 19 pages, 36 figures, slight revisio