The grand unified theories are theoretically well motivated, but they typically have less direct indications on the low energy physics and it is not easy to test them. Here, we discuss a scenario of them which naturally solves the so-called doublet-triplet splitting problem and, at the same time, generally predicts characteristic collider phenomenology. Then, we may get a hint on the breaking of the grand unified symmetry at the on-going and next-generation collider experiments.
We discuss renormalization group equations for gauge coupling constants in gauge-Higgs grand unification on five-dimensional Randall-Sundrum warped space. We show that all the four-dimensional Standard Model gauge coupling constants are asymptotically free and are effectively unified in $SO(11)$ gauge-Higgs grand unified theories on 5D Randall-Sundrum warped space.
The effective Higgs theories at the TeV scale in supersymmetric $SU(5)$ grand unification models are systematically derived. Restricted to extensions on $\mathbf{5}_{H}$ containing the Higgs sector we show that only two types of real (vector-like) models and one type of chiral model are found to be consistent with perturbative grand unification. While the chiral model has been excluded by the LHC data, the fate of perturbative unification will be uniquely determined by the two classes of vector-like models.
4D Higgs field is identified with the extra-dimensional component of gauge potentials in the gauge-Higgs unification scenario. $SO(5) \times U(1)$ gauge-Higgs EW unification in the Randall-Sundrum warped space is successful at low energies. The Higgs field appears as an Aharonov-Bohm phase $θ_H$ in the fifth dimension. Its mass is generated at the quantum level and is finite. The model yields almost the same phenomenology as the standard model for $θ_H < 0.1$, and predicts $Z'$ bosons around 6 - 10 TeV with very broad widths. The scenario is genelarized to $SO(11)$ gauge-Higgs grand unificatio…
The supersymmetric grand unified theory with the Hosotani mechanism predicts the existence of adjoint chiral supermultiplets at the SUSY breaking scale. In particular, the SU(2) triplet and the singlet chiral superfields affect the Higgs sector. We investigate the contributions from these adjoint chiral multiplets to the masses of the Higgs sector particles and their couplings to the standard model particles. We show that the predicted values of the Higgs sector parameters deviate from the standard model and the minimal supersymmetric standard model by O(1)% - O(10)%.
The supersymmetric SU(5) grand unified theory with the gauge symmetry broken by the Hosotani mechanism naturally solves the mass hierarchy problem between the colored Higgs triplet and the electroweak Higgs doublet, and predicts the existence of adjoint chiral superfields with masses of the order of the supersymmetry breaking scale as a byproduct. In addition to the two SU(2)_L Higgs doublets of the minimal supersymmetric standard model, the Higgs sector is extended by an SU(2)_L triplet chiral supermultiplet with hypercharge zero and a neutral singlet one. Such new triplet and singlet chiral …
Grand gauge-Higgs unification of five dimensional $SU(6)$ gauge theory on an orbifold $S^1/Z_2$ is discussed. The Standard model (SM) fermions are introduced on one of the boundaries and some massive bulk fields are also introduced so that they couple to the SM fermions through the mass terms on the boundary. Integrating out the bulk fields generates the SM fermion masses with exponentially small bulk mass dependences. The SM fermion masses except for top quark are shown to be reproduced by mild tuning the bulk masses. One-loop Higgs potential is calculated and it is shown that the electroweak…
We discuss how a model for the electroweak interactions without a Higgs could be embedded into a grand unified theory. The requirement of a non-trivial fixed point in the SU(2) sector of the weak interactions together with the requirement of the numerical unification of the gauge couplings leads to a prediction for the value of the SU(2) gauge coupling in the fixed point regime. The fixed point regime must be in the TeV region to solve the unitarity problem in the elastic scattering of W bosons. We find that the unification scale is at about 10^{14} GeV. Viable grand unified theories must thus…
In the supersymmetric SU(5) grand unified theory whose gauge symmetry is broken by virtue of the Hosotani mechanism, the huge mass splitting between the colored Higgs triplet and the electroweak Higgs doublet superfields is naturally realized. As a byproduct, the existence of adjoint chiral superfields with masses of the order of the supersymmetry breaking scale is predicted, leading to the Higgs sector that contains an SU(2)_L triplet chiral multiplet with hypercharge zero and a neutral singlet one in addition to the two SU(2)_L doublets of the minimal supersymmetric standard model. We focus …
The supersymmetric grand unified theory where the SU(5) gauge symmetry is broken by the Hosotani mechanism predicts the existence of adjoint chiral superfields whose masses are at the supersymmetry breaking scale. The Higgs sector is extended with the SU(2)_L triplet with hypercharge zero and neutral singlet chiral multiplets from that in the minimal supersymmetric standard model. Since the triplet and singlet chiral multiplets originate from a higher-dimensional vector multiplet, this model is highly predictive. Properties of the particles in the Higgs sector are characteristic and can be dif…
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 one of the boundaries and some massive bulk fermions coupling to the SM fermions on the boundary are introduced, so that they respect an SU(5) symmetry structure. The SM fermion masses including top quark are reproduced by mild tuning the bulk masses and parameters of the localized gauge kinetic terms. Gauge coupling universality is not guaranteed by the presence of the localized gauge kinetic terms and it severely cons…
The supersymmetric grand unified theory where the $SU(5)$ gauge symmetry is broken by the Hosotani mechanism provides a natural solution to the so-called doublet-triplet splitting problem. At the same time, this model derives a general and distinctive prediction that is testable at TeV scale collider experiments. To be more concrete, adjoint chiral supermultiplets with masses around TeV scale appear. Since these additional fields originate from a higher-dimensional gauge supermultiplet, our model is highly predictive. We study especially the Higgs sector and show that our model is discriminati…
We investigate models of supersymmetric grand unification based on the gauge group SU(5). We consider models with non-universal gaugino masses and confront them with low energy constraints, including the Higgs boson mass and the Dark Matter relic density. We also discuss fine-tuning and show the effect of not including the mu-parameter into fine tuning determinations. With this relaxation, we find viable scenarios with low fine tuning and study some model choices for gaugino mass ratios. We demonstrate that some orbifold inspired models may provide low fine-tuning and the preferred relic abund…
We present a minimal viable Gauge-Higgs Grand Unification scenario in warped space based on a $SU(6)$ bulk symmetry - unifying the gauge symmetries of the SM and their breaking sector. We show how the issue of light exotic new states is eliminated by appropriately breaking the gauge symmetry on the UV and IR boundaries by either brane scalars or gauge boundary conditions. The SM fermion spectrum is naturally reproduced including Dirac neutrinos and we compute the Higgs potential at one-loop, finding easily solutions with a realistic $m_h \sim 125$ GeV. The problem of proton decay is addressed …
We propose a novel way to break grand unified gauge symmetries via the Hosotani mechanism in models that can accommodate chiral fermions. Adjoint scalar fields are realized through the so-called diagonal embedding method which is often used in the heterotic string theory. We calculate the one-loop effective potential of the adjoint scalar field in a five dimensional model compactified on an S^1/Z_2 orbifold, as an illustration. It turns out that the potential is basically the same as the one in an S^1 model, and thus the results in literatures, in addition to the chiral fermions, can be realiz…
$SO(11)$ gauge-Higgs grand unification is formulated in the six-dimensional hybrid warped space in which the fifth and sixth dimensions play as the electroweak and grand-unification dimensions. Fermions are introduced in ${\bf 32}$, ${\bf 11}$ and ${\bf 1}$ of $SO(11)$. Small neutrino masses naturally emerge as a result of a new seesaw mechanism in the gauge-Higgs unification which is characterized by a $3 \times 3$ mass matrix.
Gauge-Higgs grand unification is formulated. By extending $SO(5) \times U(1)_X$ gauge-Higgs electroweak unification, strong interactions are incorporated in $SO(11)$ gauge-Higgs unification in the Randall-Sundrum warped space. Quarks and leptons are contained in spinor and vector multiplets of $SO(11)$. Although the KK scale can be as low as $10 $ TeV, proton decay is forbidden by a conserved fermion number in the absence of Majorana masses of neutrinos.
We study gauge symmetry breaking patterns of the five-dimensional $SU(5)$ grand gauge-Higgs unification compactified on an orbifold $S^1/{\mathbb Z}_2$ with the Hosotani mechanism in the framework of the diagonal embedding method. We find matter contents that lead to the $SU(3)\times SU(2)\times U(1)$ gauge symmetry on the global minimum of the effective potential and also present examples of matter content for which each regular subgroup of $SU(5)$ is realized as vacuum configuration. The finite temperature phase transitions for the models with the gauge symmetry of the standard model at zero…
We study grand unified models in the five-dimensional space-time where the extra dimension is compactified on $S^1/Z_2$. 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 $E_6$ 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 …
The combination of flavor symmetries with grand unification is considered: GUT $ \times$ flavor . To accommodate three generations the flavor group SO(3) is used. All fermions transform as 3-vectors under this group. The Yukawa couplings are obtained from vacuum expectation values of flavon fields. For the flavon fields (singlets with respect to the GUT group) and the Higgs fields (singlets with respect to the generation group) a simple form for the effective potentials is postulated. It automatically leads to spontaneous symmetry breaking for these scalar fields. Discrete S4 transformations r…
$SO(11)$ gauge-Higgs grand unification in the Randall-Sundrum warped space is proposed. Orbifold boundary conditions and one brane scalar field reduce $SO(11)$ to the standard model symmetry, which is further broken to $SU(3)_C \times U(1)_{EM}$ by the Hosotani mechanism. In a minimal model quarks and leptons are contained in a multiplet in ${\bf 32}$ of $SO(11)$ in each generation. Proton decay is naturally suppressed by a conserved fermion number.
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.
We investigate the possibility of obtaining sizeable R-parity breaking interactions violating baryon number but not lepton number within supersymmetric grand unified theories. Such a possibility allows to ameliorate the naturalness status of supersymmetry while maintaining successful gauge coupling unification, one of its main phenomenological motivations. We show that this can be achieved without fine-tuning or the need of large representations in simple SO(10) models.
The mass spectra of the standard model particles are reproduced in the $SO(11)$ gauge-Higgs grand unification in the six-dimensional warped space without introducing exotic light fermions. Light neutrino masses are explained by the gauge-Higgs seesaw mechanism. We evaluate the effective potential of the 4d Higgs boson appearing as a fluctuation mode of the Aharonov-Bohm phase $θ_H$ in the extra-dimensioal space, and show that the dynamical electroweak symmetry breaking takes place with the Higgs boson mass $m_H \sim 125\,$GeV and $θ_H \sim 0.1$. The Kaluza-Klein mass scale in the fifth dimensi…
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. The number of the bulk fermions is reduced compared to the previous model, which reproduces the generation mixing of the SM fermions in addition to the SM fermion mass hierarchy by mild tuning the bulk masses and parameters of the localized gauge kinetic terms.
A possibility for grand unification and non-Higgs mass generation in a Nambu-Jona-Lasinio-like theory of fermions interacting with current metric field
