Gauge-Higgs Grand Unification Research Articles

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.

Minimal SU(6) gauge-Higgs grand unification

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 by showing that baryon number is a hidden symmetry of the model. Among the phenomenological consequences, we highlight the presence of a scalar leptoquark and a scalar singlet. The usual $X,Y$ gauge bosons from $SU(5)$ GUTs are found at collider accessible masses.

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.

Electroweak symmetry breaking and mass spectra in six-dimensional gauge–Higgs grand unification

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 $\theta_H$ 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 $\theta_H \sim 0.1$. The Kaluza-Klein mass scale in the fifth dimension is approximately given by $m_{\rm KK} \sim 1.230\,{\rm TeV}/\sin \theta_H$.

Gauge-Higgs seesaw mechanism in 6-dimensional grand unification

$SO(11)$ 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.

Toward realistic gauge–Higgs grand unification

The $SO(11)$ gauge-Higgs grand unification in the Randall-Sundrum warped space is presented. The 4D Higgs field is identified as the zero mode of the fifth dimensional component of the gauge potentials, or as the fluctuation mode of the Aharonov-Bohm phase $\theta_H$ along the fifth dimension. Fermions are introduced in the bulk in the spinor and vector representations of $SO(11)$. $SO(11)$ is broken to $SO(4) \times SO(6)$ by the orbifold boundary conditions, which is broken to $SU(2)_L \times U(1)_Y \times SU(3)_C$ by a brane scalar. Evaluating the effective potential $V_{\rm eff} (\theta_H)$, we show that the electroweak symmetry is dynamically broken to $U(1)_{\rm EM}$. The quark-lepton masses are generated by the Hosotani mechanism and brane interactions, with which the observed mass spectrum is reproduced. The proton decay is forbidden thanks to the new fermion number conservation. It is pointed out that there appear light exotic fermions. The Higgs boson mass is determined with the quark-lepton masses given, which, however, turns out smaller than the observed value.

Gauge-Higgs EW and grand unification

Four-dimensional Higgs field is identified with the extra-dimensional component of gauge potentials in the gauge-Higgs unification scenario. [Formula: see text] gauge-Higgs EW unification in the Randall–Sundrum warped space is successful at low energies. The Higgs field appears as an Aharonov–Bohm phase [Formula: see text] 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 [Formula: see text], and predicts [Formula: see text] bosons around 6–10 TeV with very broad widths. The scenario is generalized to [Formula: see text] gauge-Higgs grand unification. Fermions are introduced in the spinor and vector representations of [Formula: see text]. Proton decay is naturally forbidden.

Gauge coupling unification in gauge–Higgs grand unification

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.

Gauge-Higgs grand unification

$SO(11)$ 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.