gauge-Higgs Unification Model Research Articles

Attempt at constructing a model of grand gauge-Higgs unification with family unification

We discuss a possibility whether a model of grand gauge-Higgs unification incorporating family unification in higher dimensions can be constructed. We first extend a five-dimensional SU(6) grand gauge-Higgs unification model to a five-dimensional SU(7) grand gauge-Higgs unification model compactified on an orbifold S1/Z2 to obtain three generations of quarks and leptons after symmetry breaking of the larger family unified gauge group. A prescription of constructing a six-dimensional SU(N) grand gauge-Higgs unification model including a five-dimensional SU(7) grand gauge-Higgs unification after compactifying the sixth dimension on an orbifold S1/Z2 is given. We find a six-dimensional SU(14) grand gauge-Higgs unification model with a set of representations containing three generations of quarks and leptons. Published by the American Physical Society 2024

Probing gauge-Higgs unification models at the ILC with quark–antiquark forward–backward asymmetry at center-of-mass energies above the Z mass

The International Linear Collider (ILC) will allow the precise study of e-e+→qq¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$e^{-}e^{+} \\rightarrow q\\bar{q}$$\\end{document} interactions at different center-of-mass energies from the Z\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Z$$\\end{document}-pole to 1 TeV. In this paper, we discuss the experimental prospects for measuring differential observables in e-e+→bb¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$e^{-}e^{+} \\rightarrow b\\bar{b}$$\\end{document} and e-e+→cc¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$e^{-}e^{+} \\rightarrow c\\bar{c}$$\\end{document} at the ILC baseline energies, 250 and 500 GeV. The study is based on full simulation and reconstruction of the International Large Detector (ILD) concept. Two gauge-Higgs unification models predicting new high-mass resonances beyond the Standard Model are discussed. These models predict sizable deviations of the forward–backward observables at the ILC running above the Z mass and with longitudinally polarized electron and positron beams. The ability of the ILC to probe these models via high-precision measurements of the forward–backward asymmetry is discussed. Alternative scenarios at other energies and beam polarization schemes are also discussed, extrapolating the estimated uncertainties from the two baseline scenarios.

Model building by coset space dimensional reduction scheme using eight-dimensional coset spaces

We investigate the twelve-dimensional gauge-Higgs unification models with an eight- dimensional coset space as the extra space. For each model, we apply the coset space dimensional reduction procedure and examine the particle contents of the resulting four-dimensional theory. All combinations of inputs to the procedure are exhaustively analyzed under several assumptions. As a result, some twelve-dimensional SO(18) gauge theories lead to models of the SO(10) × U(1) grand unified theory in four dimensions, where fermions of the Standard Model appear in multiple generations along with scalars that may break the electroweak symmetry. The representations of the obtained scalars and fermions are summarized.

UV completion of extradimensional Yang-Mills theory for Gauge-Higgs unification

The SU(N)SU(N) Yang-Mills theory in \mathbb R^4\times S^1ℝ4×S1 spacetime is studied as a simple toy model of Gauge-Higgs unification. The theory is perturbatively nonrenormalizable but could be formulated as an asymptotically safe theory, namely a nonperturbatively renormalizable theory. We study the fixed point structure of the Yang-Mills theory in \mathbb R^4\times S^1ℝ4×S1 by using the functional renormalization group in the background field approximation. We derive the functional flow equations for the gauge coupling and the background gauge-field potential. There exists a nontrivial fixed point for both couplings at finite compactification radii. At the fixed point, gauge coupling and vacuum energy are both relevant. The renormalization group flow of the gauge coupling describes the smooth transition between the ultraviolet asymptotically safe regime and the strong interacting infrared limit.

Bhabha scattering in the gauge-Higgs unification

We examine effects of $Z'$ bosons in gauge-Higgs unification (GHU) models at $\mathrm{e}^{+}\mathrm{e}^{-}\to \mathrm{e}^{+}\mathrm{e}^{-}$ Bhabha scatterings. We evaluate differential cross sections in Bhabha scatterings including $Z'$ bosons in two types of $\mathrm{SO}(5) \times \mathrm{U}(1) \times \mathrm{SU}(3)$ GHU models. We find that deviations of differential cross sections in the GHU models from those in the SM can be seen at $\sqrt{s} = 250\,\mathrm{GeV}$. With $80\%$-longitudinally polarized electron and $30\%$-longitudinally polarized positron beams, the left-right asymmetries in the GHU A- and B-models are resolved at more than $3\,\sigma$ at $L_{\rm int} =250\,\mathrm{fb}^{-1}$. We also show that Bhabha scattering with scattering angle less than 100 mrad can be safely used as luminosity measurements in $\mathrm{e}^{+}\mathrm{e}^{-}$ colliders since the effects of $Z'$ bosons are well suppressed for small scattering angle. We propose a new observable which can be measured at future TeV-scale $\mathrm{e}^{+} \mathrm{e}^{-}$ linear colliders.

Signals of W′ and Z′ bosons at the LHC in the SU(3)×SO(5)×U(1) gauge-Higgs unification

The $pp\to \{W, W'\} \to l\nu$ and $pp\to \{\gamma, Z, Z'\} \to l^+l^-$ ($l=e,\mu$) processes in the $SU(3)_C\times SO(5)\times U(1)_X$ gauge-Higgs unification (GHU) models are studied, where $W'$ and $Z'$ bosons are Kaluza-Klein (KK) exited states of the electroweak gauge bosons. From the experimental data collected at the Large Hadron Collider, constraints on the KK mass scale and the Aharonov-Bohm phase are obtained. One can explore the KK mass scale in the GUT inspired GHU model up to 18 TeV for the luminosity 300 fb$^{-1}$ and 22 TeV for the luminosity 3000 fb$^{-1}$ at $\sqrt{s}=14$ TeV.

Dirac gaugino from grand gauge-Higgs unification

Abstract We show that models of the Dirac gaugino can naturally be embedded into a kind of grand unified theory (GUT), the grand gauge-Higgs unification (gGHU) model, with the gauge group $SU(5)\times SU(5)/\mathbb {Z}_2$ on an $S^1/\mathbb {Z}_2$ orbifold. The supersymmetric gGHU is known to possess a light chiral adjoint supermultiplet after the GUT breaking, thanks to the exchange symmetry of two SU(5) groups. Identifying the “predicted” adjoint fermion with the Dirac partner of the gaugino, we argue that the supersoft term, responsible for the Dirac gaugino mass, can be obtained from the supersymmetric Chern–Simons (CS)-like term in the gGHU setup. Although the latter term does not respect the exchange symmetry, we propose a novel way to introduce its breaking effect within a consistent orbifold construction. We also give a concrete setup of fermion field contents (bulk and boundary-localized fermions) that induce the requisite CS-like term, and calculate its coefficient from the bulk profile of chiral fermion zero modes. Our gGHU setup may be regarded as an extra-dimensional realization of the Goldstone gaugino scenario that was proposed before as a solution to the problem of adjoint scalar masses.

Are low-energy data already hinting at five dimensions?

Low-energy data, combined with renormalization group (RG) equations, can predict new physics at far higher energy scales. In this paper, we consider the possibility that the measured Higgs boson mass and top quark mass hint at a five-dimensional gauge-Higgs unification (5D GHU) model at a scale above TeV. We note that the vanishing of the Higgs quartic coupling and the proximity of the top quark Yukawa coupling and weak gauge coupling at high scales, inferred from the experimental data, are in harmony with 5D GHU, because in 5D GHU models the Higgs quartic coupling is forbidden by the 5D gauge symmetry and the Yukawa couplings and the weak gauge coupling originate from a common 5D gauge coupling. Based on the above insight, we propose a 5D GHU model where the Standard Model fermions are embedded in 5D fermions in a way to tightly relate the top Yukawa coupling with the weak gauge coupling. Also, the model predicts the presence of vector-like fermions (other than the Kaluza-Klein modes), which can affect the RG evolutions of the 4D theory and reconcile the scale of vanishing Higgs quartic coupling and that of equality of the top Yukawa and weak gauge couplings, thereby achieving a successful matching of the 4D theory with 5D GHU. We predict the vector-like fermion mass and the compactification scale of 5D GHU from the conditions for the successful matching.

Higgs potential in gauge-Higgs unification with a flat extra dimension

We analyze the structure of the Higgs potential in gauge-Higgs unification with a flat extra dimension. As a concrete model, we first consider the cases where the Standard Model Higgs doublet is embedded into a higher-dimensional SU(3)w gauge multiplet with five-dimensional Lorentz symmetry relaxed. In this SU(3)w model with Lorentz violation, the deviation of the resulting triple Higgs boson coupling from its SM prediction is shown to be less than 10% when the compactification scale is larger than the experimental lower bound, which is around 5 TeV. Next, we examine the Higgs potential in other similar gauge-Higgs unification models with a flat extra dimension. It is pointed out that even in such models the shape of the Higgs potential around the vacuum quickly approaches that of the minimal Higgs potential with one Higgs doublet as the compactification scale of the extra dimension increases. An observable deviation of the triple Higgs boson coupling at planned lepton colliders will necessitate significant extensions of such gauge-Higgs unification models.

Strong first order electroweak phase transition in gauge-Higgs unification at finite temperature

We analyze the electroweak phase transition at finite temperature in a model of gauge-Higgs unification where the fermion mass hierarchy including top quark mass, a viable electroweak symmetry breaking and an observed Higgs mass are successfully reproduced. To study the phase transition, we derive the general formula of the 1-loop effective potential at finite temperature by using the $\zeta$ function regularization method. It is remarkable that the functions determining the Kaluza-Klein mass spectrum have only to be necessary in calculations. This potential can be applicable to any higher dimensional theory in flat space where one extra spatial dimension is compactified. Applying to our model of gauge-Higgs unification, the strong first phase transition compatible with 125 GeV Higgs mass is found to happen.

To be, or not to be finite? The Higgs potential in Gauge-Higgs Unification

In this paper, we investigate the finiteness of the Higgs effective potential in an SU( mathcal{N} ) Gauge-Higgs Unification (GHU) model defined on M4× S1. We obtain the Higgs effective potential at the two-loop level and find that it is finite. We also discuss that the Higgs effective potential is generically divergent for three- or higher-loop levels. As an example, we consider an SU( mathcal{N} ) gauge theory on M5× S1, where the one-loop corrections to the four-Fermi operators are divergent. We find that the Higgs effective potential depends on their counter terms at the three-loop level.

Forward\u2013backward asymmetry in the gauge-Higgs unification at the International Linear Collider

The signals of the SO(5)times U(1) gauge-Higgs unification model at the International Linear Collider are studied. In this model, Kaluza–Klein modes of the neutral gauge bosons affect fermion pair productions. The deviations of the forward–backward asymmetries of the e^+e^-rightarrow bar{b}b, bar{t}t processes from the standard model predictions are clearly seen by using polarised beams. The deviations of these values are predicted for two cases, the bulk mass parameters of quarks are positive and negative case.

Unification of gauge and Yukawa couplings

In this talk we describe how unification of gauge and Yukawa couplings can be obtained in gauge-Higgs unification models in extra-dimensions using a toy model. It is usually considered that such unification is difficult to obtain using simple group theory arguments. We consider a toy model based on the SU(3) symmetry and show that including the renormalisation group running at one loop for the couplings improve the result. The gauge couplings unify asymptotically at high energies, and this may result from the presence of an UV fixed point. The Yukawa coupling is enhanced at low energies, showing that a genuine unification of gauge and Yukawa couplings may be achieved. Some other arguments and directions of study are also mentioned to tackle the problem of producing a scalar potential allowing to accommodate the measured Higgs mass at 125 GeV.

GUT inspired SO(5)×U(1)×SU(3) gauge-Higgs unification

$SO(5) \times U(1) \times SU(3)$ gauge-Higgs unification model inspired by $SO(11)$ gauge-Higgs grand unification is constructed in the Randall-Sundrum warped space. The 4D Higgs boson is identified with the Aharonov-Bohm phase in the fifth dimension. Fermion multiplets are introduced in the bulk in the spinor, vector and singlet representations of $SO(5)$ such that they are implemented in the spinor and vector representations of $SO(11)$. The mass spectrum of quarks and leptons in three generations is reproduced except for the down quark mass. The small neutrino masses are explained by the gauge-Higgs seesaw mechanism which takes the same form as in the inverse seesaw mechanism in grand unified theories in four dimensions.

Fermionic minimal dark matter in 5D gauge-Higgs unification

We propose a Minimal Dark Matter (MDM) scenario in the context of a simple gauge-Higgs Unification (GHU) model based on the gauge group SU(3) x U(1)' in 5-dimensional Minkowski space with a compactification of the 5th dimension on S^1/Z_2 orbifold. A pair of vector-like SU(3) multiplet fermions in a higher-dimensional representation is introduced in the bulk, and the DM particle is identified with the lightest mass eigenstate among the components in the multiplets. In the original model description, the DM particle communicates with the Standard Model (SM) particles only through the bulk gauge interaction, and hence our model is the GHU version of the MDM scenario. There are two typical realizations of the DM particle in 4-dimensional effective theory: (i) the DM particle is mostly composed of the SM SU(2)_L multiplets, or (ii) the DM is mostly composed of the SM SU(2)_L singlets. Since the case (i) is very similar to the original MDM scenario, we focus on the case (ii), which is a realization of the Higgs-portal DM scenario in the context of the GHU model. We identify an allowed parameter region to be consistent with the current experimental constraints, which will be fully covered by the direct dark matter detection experiments in the near future. In the presence of the bulk multiplet fermions in higher-dimensional $SU(3)$ representations, we reproduce the 125 GeV Higgs boson mass through the renormalization group evolution of Higgs quartic coupling with the compactification scale of 10-100 TeV.

Unification of gauge and Yukawa couplings

The unification of gauge and top Yukawa couplings is an attractive feature of gauge-Higgs unification models in extra-dimensions. This feature is usually considered difficult to obtain based on simple group theory analyses. We reconsider a minimal toy model including the renormalisation group running at one loop. Our results show that the gauge couplings unify asymptotically at high energies, and that this may result from the presence of an UV fixed point. The Yukawa coupling in our toy model is enhanced at low energies, showing that a genuine unification of gauge and Yukawa couplings may be achieved.

27pSD-1 LHC実験によるゲージヒッグス統一模型への制限

27pSD-1 LHC実験によるゲージヒッグス統一模型への制限

The standard model gauge symmetry from higher-rank unified groups in grand gauge-Higgs unification models

We study grand unified models in the five-dimensional space-time where the extra dimension is compactified on S1/ℤ2. The spontaneous breaking of unified gauge symmetries is achieved via vacuum expectation values of the extra-dimensional components of gauge fields. We derive one-loop effective potentials for the zero modes of the gauge fields in SU(7), SU(8), SO(10), and E6 models. In each model, the rank of the residual gauge symmetry that respects the boundary condition imposed at the orbifold fixed points is higher than that of the standard model. We verify that the residual symmetry is broken to the standard model gauge symmetry at the global minima of the effective potential for certain sets of bulk fermion fields in each model.

Proton decay prediction from a gauge-Higgs unification scenario in five dimensions

The Higgs boson mass and top quark mass imply that the Higgs quartic coupling vanishes around the scale of $10^9 - 10^{13}$ GeV, depending on the precise value of the top quark mass. The vanishing quartic coupling can be naturally addressed if the Higgs field originates from a 5-dimensional gauge field and the 5th dimension is compactified at the scale of the vanishing Higgs quartic coupling, which is a scenario based on gauge-Higgs unification. We present a general prediction of the scenario on the proton decay process $p \to \pi^0 e^+$. In many gauge-Higgs unification models, the 1st generation fermions are localized towards an orbifold fixed point in order to realize the realistic Yukawa couplings. Hence, four-fermion operators responsible for the proton decay can appear with a suppression of the 5-dimensional Planck scale (not the 4-dimensional Planck scale). Since the 5-dimensional Planck scale is connected to the compactification scale, we have a correlation between the proton partial decay width and the top quark mass. We show that the future Hyper-Kamiokande experiment may discover the proton decay if the top quark pole mass is larger than about 172.5 GeV.

Extra-dimensional models on the lattice

In this review we summarize the ongoing effort to study extra-dimensional gauge theories with lattice simulations. In these models the Higgs field is identified with extra-dimensional components of the gauge field. The Higgs potential is generated by quantum corrections and is protected from divergences by the higher dimensional gauge symmetry. Dimensional reduction to four dimensions can occur through compactification or localization. Gauge-Higgs unification models are often studied using perturbation theory. Numerical lattice simulations are used to go beyond these perturbative expectations and to include nonperturbative effects. We describe the known perturbative predictions and their fate in the strongly-coupled regime for various extra-dimensional models.