We consider the compactification of a Yang-Mills theory on a three-dimensional nilmanifold. The compactification generates a Yang-Mills theory in four space-time dimensions, coupled to a specific scalar sector. The compactification geometry gives rise to masses for the zero-modes, proportional to the twist parameter of the nilmanifold. We study the simple example of an SU (3) model broken by a non-trivial vacuum of the scalar potential which generates three mass scales, two being at tree level, and the third one at loop level. We point out the relevance of general twisted geometries for model building and in particular for gauge-Higgs type models, as the twist generates tree-level mass hierarchies useful for grand unification and for the Higgs sector in electroweak symmetry breaking.
We present a method to obtain a scalar potential at tree level from a pure gauge theory on nilmanifolds, a class of negatively-curved compact spaces, and discuss the spontaneous symmetry breaking mechanism induced in the residual Minkowski space after compactification at low energy. We show that the scalar potential is completely determined by the gauge symmetries and the geometry of the compact manifold. In order to allow for simple analytic calculations we consider three extra space dimensions as the minimal example of a nilmanifold, therefore considering a pure Yang-Mills theory in seven di…
We study a two-loop finiteness of an effective potential for a Higgs boson that is the fifth component of a gauge field in an $U(1)$ gauge theory coupled to quantum gravity on the five-dimensional space-time $M^4\times S^1$. There are two types of diagrams including quantum gravitational corrections. We find that only one type of diagram contributes to the effective potential for the Higgs boson in fact and its magnitude is finite.
We propose a gauge-invariant description for the Higgs mechanism by which a gauge boson acquires the mass. We do not need to assume spontaneous breakdown of gauge symmetry signaled by a non-vanishing vacuum expectation value of the scalar field. In fact, we give a manifestly gauge-invariant description of the Higgs mechanism in the operator level, which does not rely on spontaneous symmetry breaking. For concreteness, we discuss the gauge-Higgs models with $U(1)$ and $SU(2)$ gauge groups explicitly. This enables us to discuss the confinement-Higgs complementarity from a new perspective.
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.
In the general Two-Higgs Doublet Model it has been shown that the Higgs potential can be expressed in terms of gauge-independent quantities. In particular, stability, electroweak symmetry breaking, and CP symmetry can be understood in a concise way, avoiding unphysical gauge degrees of freedom. We complete this program and show how all the masses, the trilinear and quartic scalar interactions, the gauge-boson-Higgs interactions, as well as the Yukawa couplings in the general THDM can be expressed in a gauge-invariant way.
We study the possibility that the Higgs and the inflaton are the same single field or cousins arising from the extra space components of some higher-dimensional gauge field. We take 5D supersymmetric gauge theory with a matter compactified on S^1 as a toy model and evaluate the one-loop contribution to the Higgs-inflaton potential. Our gauge-Higgs-inflaton unification picture applied to the gauge field of intermediate energy scale (\sim 10^{13} GeV) can explain the observed inflation parameters without fine-tuning.
The physical process of Higgs decaying to two photons is the most important mode in the discovery of the Higgs particle. Theoretical calculation of $H\rightarrowγγ$ amplitude therefore provides us with an avenue to explore the underlying theory. Yet some confusion has arisen over the gauge invariant property of $H\rightarrowγγ$ in the standard model. In this paper, we show that if dimensional regularization is adopted, the on-shell 1-loop $H\rightarrowγγ$ amplitude calculated in the standard model is gauge invariant. In particular, we prove that the physical amplitude calculated in the unitary…
$SO(11)$ 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.
In the gauge-Higgs unification with multiple extra spaces, the Higgs self-coupling is of the order of $g^2$ and Higgs is predicted to be light, being consistent with the LHC results. When the gauge group is simple, the weak mixing angle is also predictable. We address a question whether there exists a model of gauge-Higgs unification in 6-dimensional space-time, which successfully predicts the mass ratios of the Higgs boson and weak gauge bosons. First, by use of a useful formula we give a general argument on the condition to get a realistic prediction of the weak mixing angle $sin^{2}theta_{W…
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.
Extra-dimensional components of gauge fields in higher-dimensional gauge theories will play a role of the Higgs field and become tachyonic after Kaluza-Klein compactifications on internal spaces with (topologically nontrivial) gauge field backgrounds. Its condensation is then expected to break gauge symmetries spontaneously. But, contrary to the expectation, some models exhibit restoration of gauge symmetries. In this paper, by considering all the massive Kaluza-Klein excitations of gauge fields, we explicitly show that some of them indeed become massless at the minimum of the Higgs potential …
We discuss the gauge-Higgs unification in a framework of Lifshitz type gauge theory. We study a higher dimensional gauge theory on R^{D-1}\times S^{1} in which the normal second (first) order derivative terms for scalar (fermion) fields in the action are replaced by higher order derivative ones for the direction of the extra dimension. We provide some mathematical tools to evaluate a one-loop effective potential for the zero mode of the extra component of a higher dimensional gauge field and clarify how the higher order derivative terms affect the standard form of the effective potential. Our …
We present a gauge mediation principle for BSM theories where exact UV scale invariance is broken in a hidden sector. The relevant configurations are those in which the Standard Model and a hidden sector emanate from a scale invariant pair of UV theories that communicate only via gauge interactions. We compute the radiatively induced Higgs potential which contains logarithmic mass-squared terms that lead to unusual Higgs self-couplings. Its other couplings are unchanged.
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.
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…
We propose a novel description for the Higgs mechanism by which a gauge boson acquires the mass. We do not assume spontaneous breakdown of gauge symmetry signaled by a non-vanishing vacuum expectation value of the scalar field. In fact, we give a manifestly gauge-invariant description of the Higgs mechanism in the operator level, which does not rely on spontaneous symmetry breaking. This enables us to discuss the confinement-Higgs complementarity from a new perspective. The "Abelian" dominance in quark confinement of the Yang-Mills theory is understood as a consequence of the gauge-invariant H…
e have investigated the gauge parameter dependence of the Higgs pole masses in the multi-Higgs model in two different types of the gauge fixing conditions. It turns out that the Higgs pole masses of the multi-Higgs model when expressed in terms of the Lagrangian parameters, are independent of the gauge parameter for both cases.
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.
In the gauge-Higgs unification the 4D Higgs field becomes a part of the extra-dimensional component of the gauge potentials. In the $SO(5) \times U(1)$ gauge-Higgs unification in the Randall-Sundrum warped spacetime the electroweak symmetry is dynamically broken through the Hosotani mechanism. The Higgs bosons become absolutely stable, and become the dark matter of the universe. The mass of the Higgs boson is determined from the WMAP data to be about 70 GeV.
We consider the triple coupling of the Higgs boson in the context of the gauge-Higgs unification scenario. We show that the triple coupling of the Higgs boson in this scenario generically deviates from SM prediction since the Higgs potential in this scenario has a periodicity. We calculate the coupling in the five-dimensional $SU(3)$ x $U(1)_X$ gauge-Higgs unification model and obtain 70% deviation from the SM prediction.
Static quark-antiquark states in QCD, at finite quark separation, have a spectrum of metastable states corresponding to string-like excitations of the gauge field. In this article I suggest that there may also exist an excitation spectrum of heavy fermions in some gauge Higgs theories deep in the Higgs phase. In this situation there are no color electric flux tubes connecting quarks with antiquarks. There may, nonetheless, exist stable excitations of the bosonic fields surrounding an isolated fermion, below the particle production threshold. I present numerical evidence indicating the existenc…
We study the dynamics of $SU(2)_L$ times $U(1)_Y$ electroweak gauge fields during and after Higgs inflation. In particular, we investigate configurations of the gauge fields during inflation and find the gauge fields remain topologically non-trivial. We also find that the gauge fields grow due to parametric resonances caused by oscillations of a Higgs field after inflation. We show that the Chern-Simons number also grows significantly. Interestingly, the parametric amplification gives rise to sizable magnetic fields after the inflation whose final amplitudes depend on the anisotropy survived d…
We study the deviation of yukawa coupling in the gauge-Higgs unification scenario from the Standard Model one. Applying the obtained results to the tau and bottom yukawa couplings, we numerically calculate the signal strength of $gg \to H \to \bar b b, \bar τ τ$in the gauge-Higgs unification.
We study the parametrization and gauge dependences in the Higgs field coupled to gravity in the context of asymptotic safety. We use the exponential parametrization to derive the fixed points for the cosmological constant, Planck mass, Higgs mass and its coupling, keeping arbitrary gauge parameters $α$ and $β$, and compare the results with the linear split. We find that the beta functions for the Higgs potential are expressed in terms of redefined Planck mass such that the apparent gauge dependence is absent. Only the trace mode of the gravity fluctuations couples to the Higgs potential and it…
The Higgs boson is unified with gauge fields in the gauge-Higgs unification. The $SO(5) \times U(1)$ gauge-Higgs electroweak unification in the Randall-Sundrum warped space yields almost the same phenomenology at low energies as the standard model, and gives many predictions for the Higgs couplings and new $W', Z'$ bosons around $6 \sim 8$ TeV, which can be tested at 14 TeV LHC. The gauge-Higgs grand unification is achieved in $SO(11)$ gauge theory. It suggests the existence of the sixth dimension (GUT dimension) in addition to the fifth dimension (electroweak dimension). The proton decay is n…
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 Hig…
In the context of gauge-Higgs unification scenario in a 5-dimensional flat spacetime, we investigate Higgs boson production via gluon fusion and its diphoton decay mode at the LHC. We show that the signal strength of the Higgs diphoton decay mode observed at ATLAS and CMS, which is considerably larger than the Standard Model expectation, can be explained by a simple gauge-Higgs unification model with color-singlet bulk fermions to which a half-periodic boundary condition is assigned. The bulk fermions also play a crucial role in reproducing the observed Higgs boson mass around 125 GeV.
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…
We study the phase structure of the gauge theories in the space-time with one compact dimension, where the gauge symmetry can be broken by the Hosotani mechanism. As the extra dimension, we consider the SO(5) x U(1) gauge-Higgs unification in the Randall-Sundrum space-time which reproduce the 126 GeV Higgs mass. It is found that the thermal phase transition of the electroweak symmetry is almost second order and the critical temperature is around 160 GeV for z_L < 10^7 and n_F=3.
Gauge coupling unification is studied within the framework where there are extra Higgs doublets and $E_6$ exotic fields. Supersymmetric models and nonsupersymmetric models are investigated, and a catalog of models with gauge coupling unification is presented.
