gauge-Higgs Unification Research Articles

New models of SU(6) grand gauge-Higgs unification

Abstract A five dimensional SU(6) grand gauge-Higgs unification compactified on S1/Z2 is discussed. We propose new sets of the SU(6) representations where the quarks and leptons in one generation are embedded and there is no extra massless exotic fermions absent in the Standard Model. The correct electroweak symmetry breaking pattern can be realized by introducing some adjoint fermions. We also analyze whether a viable Higgs mass can be obtained.

Correction to: Coupling sum rules and oblique corrections in gauge-Higgs unification

Correction to: Coupling sum rules and oblique corrections in gauge-Higgs unification

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

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

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.

Fermion mass hierarchy and mixing in simplified grand gauge–Higgs unification

Grand gauge–Higgs unification of five-dimensional SU(6) gauge theory on an orbifold S 1/Z 2 with localized gauge kinetic terms is discussed. The Standard Model (SM) fermions on the boundaries and some massive bulk fermions coupling to the SM fermions are introduced. Compared to the previous model, the number of bulk fermions is reduced, which reproduces the generation mixing of SM fermions and SM fermion mass hierarchy by mildly tuning the bulk masses and parameters of the localized gauge kinetic terms.

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.

Mass spectrum in a six-dimensional SU(n) gauge theory on a magnetized torus

We examine six-dimensional SU(n) gauge theories compactified on a two-dimensional torus with a constant magnetic flux background to obtain a comprehensive low-energy mass spectrum. We introduce general background configurations including the magnetic flux and continuous Wilson line phases, consistent with classical equations of motion. Under the standard gauge fixing procedure, the complete mass spectrum in low-energy effective theory for the SU(n) case is newly presented without imposing restrictions on the gauge fixing parameter. Our analysis confirms the inevitable existence of tachyonic modes, which neither depend on the background configurations of Wilson line phases nor are affected by the gauge fixing parameter. Masses for some low-energy modes exhibit dependence on the gauge fixing parameter, and these modes are identified as would-be Goldstone bosons that are absorbed by massive four-dimensional vector fields. We discuss the phenomenological implications associated with stabilization or condensation of the tachyonic states. Various mass spectra and symmetry-breaking patterns are expected with flux backgrounds in the SU(n) case. They are helpful for constructing phenomenologically viable models beyond the standard model, such as gauge-Higgs unification and grand unified theories.

Coupling sum rules and oblique corrections in gauge-Higgs unification

Abstract In grand-unified-theory-inspired SO(5) × U(1)X × SU(3)C gauge-Higgs unification (GHU) in the Randall–Sundrum warped spacetime, the W- and Z-couplings of all 4D fermion modes become nontrivial. The W- and Z-couplings of zero-mode quarks and leptons slightly deviate from those in the SM, and the couplings take the matrix form in the space of Kaluza–Klein (KK) states. In particular, the 4D couplings and mass spectra in the KK states depend on the Aharonov–Bohm phase θH in the fifth dimension. Nevertheless there emerge three astonishing sum rules among those coupling matrices, which guarantees the finiteness of certain combinations of corrections to vacuum polarization tensors. We confirm by numerical evaluation that the equality in the sum rules holds with 5- to 7-digit accuracy. Based on the sum rules we propose improved oblique parameters in GHU. Oblique corrections due to fermion 1-loop diagrams are found to be small.

Single Higgs boson production at electron-positron colliders in gauge-Higgs unification

Single Higgs boson production at electron-positron colliders in gauge-Higgs unification

SU(6) gauge-Higgs grand unification: minimal viable models and flavor

Gauge-Higgs grand unification theories are models of gauge-Higgs unification that extend the electroweak group into a simple group that includes the color symmetry. The minimal option is a gauge-Higgs grand unification based on the SU(6) gauge group, mirroring SU(5) grand unification in 4D while providing a solution to the hierarchy problem. We explore different minimal and realistic novel incarnations of SU(6) gauge-Higgs grand unification. We submit the setup to the various flavor hierarchies observed in nature and, utilizing the power of the fifth dimension, identify an embedding that provides a compelling model of quarks and leptons that naturally explains the mass hierarchies and the CKM/PMNS structure. We perform a detailed study of quark- and lepton-flavor constraints (which are intimately related due to the GUT nature) together with an analysis of the Higgs potential which arises at the loop level. Electroweak precision constraints on the model are discussed and the rich scalar sector is analyzed. Future flavor constraints from upcoming experiments will provide a stringent test for this class of models, while a scalar singlet and leptoquark provide unique targets for current and future collider experiments to probe this solution to various open questions in nature.

Gauge coupling unification in simplified grand gauge-Higgs unification

Grand gauge-Higgs unification of five dimensional SU(6) gauge theory on an orbifold $S^1/Z_2$ with localized gauge kinetic terms is discussed. The Standard model (SM) fermions on the boundaries and some massive bulk fermions coupling to the SM fermions on the boundary are introduced. Taking the power-law running contributions from the bulk fields into account, perturbative gauge coupling unification is shown to be realized at around $10^{14}$ GeV, which is a few order smaller than the unification scale of four dimensional grand unified theories.

On the vacuum structure of gauge–Higgs unification models

Abstract We discuss the vacuum structure of the gauge–Higgs unification theory, which is one of the attractive candidates for physics beyond the standard model. This scenario has a remarkable feature: it has infinitely degenerate vacua due to the characteristic periodic potential of the Higgs field, to be identified with the extra space component of the higher-dimensional gauge field. We address the question of whether forming the superposition of such degenerate vacua, like the θ-vacuum in quantum chromodynamics (QCD), is necessary or not, in order to realize the true vacuum state of the theory. We derive a gauge field configuration which describes the transition between neighboring vacua, like the instanton (or anti-instanton) solution in QCD, and the corresponding Euclidean action in two models. In a simplified two-dimensional U(1) model, the derived configuration to describe the transition is shown to have finite Euclidean action, and accordingly the “θ-vacuum” and the resultant “θ-term” are formulated. In a realistic five-dimensional U(1) model, however, the gauge field configuration to describe the transition is shown to have infinite Euclidean action, and therefore the tunneling probability between the degenerate vacua vanishes. Thus, superposition of the degenerate vacua is not necessary.

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.

Anomaly flow by an Aharonov–Bohm phase

Abstract In gauge-Higgs unification (GHU), gauge symmetry is dynamically broken by an Aharonov–Bohm (AB) phase, θH, in the fifth dimension. We analyze SU(2) GHU with an SU(2) doublet fermion in the flat M4 × (S1/Z2) spacetime and in the Randall–Sundrum (RS) warped space. With orbifold boundary conditions the U(1) part of gauge symmetry remains unbroken at θH = 0 and π. The fermion multiplet has chiral zero modes at θH = 0, which become massive at θH = π. In other words, chiral fermions are transformed to vector-like fermions by the AB phase θH. The chiral anomaly at θH = 0 continuously varies as θH, and vanishes at θH = π. We demonstrate this intriguing phenomenon in the RS space in which no level crossing occurs in the mass spectrum and everything varies smoothly. The flat spacetime limit is singular as the anti-de Sitter curvature of the RS space diminishes, and reproduces the result in the flat spacetime. Anomalies appear for various combinations of Kaluza–Klein excitation modes of gauge fields as well. Although the magnitude of the anomalies depends on θH and the warp factor of the RS space, it does not depend on the bulk mass parameter of the fermion field controlling its mass and wave function at general θH.

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.

Electroweak and left-right phase transitions in SO(5)×U(1)×SU(3) gauge-Higgs unification

The electroweak phase transition in GUT inspired $SO(5)\times U(1) \times SU(3)$ gauge-Higgs unification is shown to be weakly first order and occurs at $T = T_c^{\rm EW} \sim 163\,$GeV, which is very similar to the behavior in the standard model in perturbation theory. A new phase appears at higher temperatures. $SU(2)_L \times U(1)_Y$ ($\theta_H=0$) and $SU(2)_R \times U(1)_{Y'}$ ($\theta_H=\pi$) phases become almost degenerate above $T \sim m_{\rm KK}$ where $m_{\rm KK}$ is the Kaluza-Klein mass scale typically around 13$\,$TeV and $\theta_H$ is the Aharonov-Bohm phase along the fifth dimension. The two phases become degenerate at $T = T_c^{\rm LR} \sim m_{\rm KK}$. As the temperature drops in the evolution of the early Universe the $SU(2)_R \times U(1)_{Y'}$ phase becomes unstable. The tunneling rate from the $SU(2)_R \times U(1)_{Y'}$ phase to the $SU(2)_L \times U(1)_Y$ phase becomes sizable and a first-order phase transition takes place at $T=2.5 \sim 2.6\,$TeV. The amount of gravitational waves produced in this left-right phase transition is small, far below the reach of the sensitivity of Laser Interferometer Space Antenna (LISA). A detailed analysis of the $SU(2)_R \times U(1)_{Y'}$ phase is also given. It is shown that the $W$ boson, $Z$ boson and photon, with $\theta_H$ varying from 0 to $\pi$, are transformed to gauge bosons in the $SU(2)_R \times U(1)_{Y'}$ phase. Gauge couplings and wave functions of quarks, leptons and dark fermions in the $SU(2)_R \times U(1)_{Y'}$ phase are determined.

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.