Massive Kaluza-Klein Research Articles

Tree-level unitarity in gauge-Higgs unification

We numerically estimate a scale Λuni at which tree-level unitarity is violated in the SO(5) × U(1) X gauge-Higgs unification model by evaluating amplitudes for scattering of the longitudinal W bosons. The scattering amplitudes take larger values in the warped spacetime than in the flat spacetime, and take maximal values when θ H = π/2, where θ H is the Wilson line phase along the extra dimension. We take into account not only the elastic scattering but also possible inelastic scatterings in order to estimate Λuni. We found that Λuni ≃ 1.3m KK in the warped spacetime, and Λuni ≃ 140m KK in the flat spacetime, where m KK is the Kaluza-Klein mass scale. The tree-level unitarity is violated at \( \mathcal{O}\left( {1\,{\text{TeV}}} \right) \) for θ H = π/2 in the former case due to the vanishing WWH coupling.

Relaxing constraints from lepton flavor violation in 5D flavorful theories

We propose new mechanisms for ameliorating the constraints on the Kaluza-Klein (KK) mass scale from charged lepton flavor violation in the framework of the Standard Model (SM) fields propagating in a warped extra dimension, especially in models accounting for neutrino data. These mechanisms utilize the extended five-dimensional (5D) electroweak gauge symmetry [SU(2)_L x SU(2)_R x U(1)_X] which is already strongly motivated in order to satisfy electroweak precision tests in this framework. New choices of representations for leptons under this symmetry (naturally) can allow small mixing angles for left-handed (LH) charged leptons and simultaneously large mixing angles for their SU(2)_L partners, i.e., the LH neutrinos, with the neutrino data being accounted for by the latter mixings. Enhancement of charged lepton flavor violation by the large mixing angle observed in leptonic charged currents, which is present for the minimal choice of representations where the LH charged lepton and neutrino mixing angles are similar, can thus be avoided in these models. This idea might also be useful for suppressing the contributions to B_{d, s} mixing in this framework and in order to suppress flavor violation from superpartners (instead of from KK modes) in 5D "flavorful supersymmetry" models. Additionally, the less minimal representations can provide custodial protection for shifts in couplings of fermions to Z and, in turn, further suppress charged lepton flavor-violation from tree-level Z exchange in the warped extra-dimensional scenario. As a result, ~O(3) TeV KK mass scale can be simultaneously consistent with charged lepton flavor violation and neutrino data, even without any particular structure in the 5D flavor parameters in the framework of a warped extra dimension.

Higgs boson phenomenology and vacuum expectation value shift in the Randall-Sundrum scenario

In the framework of warped extra dimension models addressing the gauge hierarchy problem, we consider the Randall-Sundrum (RS) scenario under the usual hypothesis of a bulk custodial symmetry. It is shown in detail that there can exist large corrections to the Higgs boson vacuum expectation value (VEV) induced by mixings of the gauge bosons with their Kaluza-Klein (KK) excitations. The connection with electroweak precision tests is developed. A noteworthy result is that the correct treatment of the Higgs VEV leads to an increase of the lower limit at 95% C.L. on KK masses that can reach $+30%$ (from usually accepted values). For a Higgs mass $120\ensuremath{\le}{m}_{h}\ensuremath{\le}150\text{ }\text{ }\mathrm{GeV}$, the obtained limit (from updated precision data) on the first KK gauge boson mass lies in the range 3.3--4.0 TeV. The VEV corrections also play a central role in the corrections to the Higgs couplings. We find possibly substantial RS corrections to the various Higgs couplings able to affect its phenomenology, starting with a Higgs discovery at the LHC more challenging than in the standard model (SM). The deviations to the Higgs production/decay rates found in RS will be testable at the ILC as well as at LHC. Such RS signatures could even be used at the ILC to discriminate among several models beyond the SM. Finally, the possibility of a light Higgs boson (${m}_{h}\ensuremath{\simeq}99\text{ }\text{ }\mathrm{GeV}$) interpreting the excess at $2.3\ensuremath{\sigma}$ observed at LEP2 is pointed out.

Localization and mass spectra of fermions on symmetric and asymmetric thick branes

A three-parameter (positive odd integer $s$, thickness factor $\ensuremath{\lambda}$, and asymmetry factor $a$) family of asymmetric thick brane solutions in five dimensions were constructed from a two-parameter ($s$ and $\ensuremath{\lambda}$) family of symmetric ones in by R. Guerrero, R. O. Rodriguez, and R. Torrealba in [Phys. Rev. D 72, 124012 (2005).]. The values $s=1$ and $s\ensuremath{\ge}3$ correspond to single branes and double branes, respectively. These branes have very rich inner structure. In this paper, by presenting the mass-independent potentials of Kaluza-Klein (KK) modes in the corresponding Schr\odinger equations, we investigate the localization and mass spectra of fermions on the symmetric and asymmetric thick branes in an anti-de Sitter background. In order to analyze the effect of gravity-fermion interaction (i.e., the effect of the inner structure of the branes) and scalar-fermion interaction to the spectrum of fermion KK modes, we consider three kinds of typical kink-fermion couplings. The spectra of left chiral fermions for these couplings consist of a bound zero mode and a series of gapless continuous massive KK modes, some discrete bound KK modes including zero mode (exist mass gaps), and a series of continuous massive KK modes, infinite discrete bound KK modes, respectively. The structures of the spectra are investigated in detail.

Simple flavor protection for the Randall-Sundrum model

We present a simple variation of warped flavor models where the hierarchies of fermion masses and mixings are still explained but dangerous flavor-violating effects in the Kaon sector are greatly reduced. The key new ingredients are two horizontal $U(1)$ symmetries. These symmetries forbid flavor violation in the down-quark sector (with the exception of IR brane localized kinetic mixing terms for the left-handed quarks) while allowing for flavor violation in the up-quark sector. The leading flavor constraints come from ${D}^{0}\ensuremath{-}{\overline{D}}^{0}$ mixing, and are safely satisfied for the Kaluza-Klein mass scale of order 3 TeV. Our analysis of the flavor constraints includes the effects of the (usually ignored) brane localized kinetic terms. We also comment on the effects of the additional $U(1)$ gauge bosons that are present if the horizontal symmetries are gauged.

Nonminimal universal extra dimensions

In this paper, we investigate the phenomenological implications of boundary localized terms (BLTs) in the model of universal extra dimensions (UED). In particular, we study the electroweak Kaluza-Klein mass spectrum resulting from BLTs and their effect on electroweak symmetry breaking via the five-dimensional Higgs mechanism. We find that the addition of BLTs to massive five-dimensional fields induces a nontrivial extra-dimensional profile for the zero and nonzero Kaluza-Klein (KK) modes. Hence BLTs generically lead to a modification of standard model parameters and are therefore experimentally constrained, even at tree level. We study standard model constraints on three representative nonminimal UED models in detail and find that the constraints on BLTs are weak. On the contrary, nonzero BLTs have a major impact on the spectrum and couplings of nonzero KK modes. For example, there are regions of parameter space where the lightest Kaluza-Klein particle is either the Kaluza-Klein Higgs boson or the first KK mode of the ${W}^{3}$.

Bulk matters on symmetric and asymmetric de Sitter thick branes

An asymmetric thick domain wall solution with de Sitter(dS) expansion in five dimensions can be constructed from asymmetric one by using a same scalar (kink) with differentpotentials. In this paper, by presenting the mass-independentpotentials of Kaluza-Klein (KK) modes in the correspondingSchrödinger equations, we investigate the localization andmass spectra of various bulk matter fields on the symmetric andasymmetric dS thick branes. For spin 0 scalars and spin 1vectors, the potentials of KK modes in the correspondingSchrödinger equations are the modified Pöschl-Tellerpotentials, and there exist a mass gap and a series of continuousspectrum. It is shown that the spectrum of scalar KK modes on thesymmetric dS brane contains only one bound mode (the masslessmode). However, for the asymmetric dS brane with a largeasymmetric factor, there are two bound scalar KK modes: a zeromode and a massive mode. For spin 1 vectors, the spectra of KKmodes on both dS branes consist of a bound massless mode and aset of continuous ones, i.e., the asymmetric factor does notchange the number of the bound vector KK modes. For spin 1/2fermions, two types of kink-fermion couplings are investigated indetail. For the usual Yukawa coupling ηϕΨ,there exists no mass gap but a continuous gapless spectrum of KKstates. For the scalar-fermion coupling ηsin(ϕ/ϕ0)cos−δ(ϕ/ϕ0)Ψ witha positive coupling constant η, there exist some discretebound KK modes and a series of continuous ones. The total numberof bound states increases with the coupling constant η. Forthe case of the symmetric dS brane and positive η, thereare NL(NL ⩾ 1) left chiral fermion bound states (includingzero mode and massive KK modes) and NL−1 right chiral fermionbound states (including only massive KK modes). For the asymmetricdS brane scenario, the asymmetric factor a reduces the numberof the bound fermion KK modes. For large enough a, there wouldnot be any right chiral fermion bound mode, but at least one leftchiral fermion zero mode.

Natural neutrino masses and mixings from warped geometry

We demonstrate that flavor symmetries in warped geometry can provide a natural explanation for large mixing angles and economically explain the distinction between the quark and lepton flavor sectors. We show how to naturally generate Majorana neutrino masses assuming a gauged a U(1)B−L symmetry broken in the UV that generates see-saw masses of the right size. This model requires lepton minimal flavor violation (LMFV) in which only Yukawa matrices (present on the IR brane) break the flavor symmetries. The symmetry-breaking is transmitted to charged lepton bulk mass parameters as well to generate the hierarchy of charged lepton masses. With LMFV, a GIM-like mechanism prevents dangerous flavor-changing processes for charged leptons and permits flavor-changing processes only in the presence of the neutrino Yukawa interaction and are therefore suppressed when the overall scale for the neutrino Yukawa matrix is slightly smaller than one in units of the curvature. In this case the theory can be consistent with a cutoff of 10 TeV and 3 TeV Kaluza-Klein masses.

The Standard Model in a Soft-Wall Warped Dimension

We show that the Standard Model can be formulated in a warped extra dimension with a soft wall. The infrared boundary is replaced with a smoothly varying dilaton field that provides a dynamical spacetime cutoff, generalising the usual hard-wall warped dimension. This allows a more general spacing for the Kaluza-Klein mass spectrum of bulk fields, including the possibility of Regge-like behaviour. Moreover the usual features of hard-wall setups can be reproduced where electroweak symmetry is now broken with a bulk Higgs condensate.

The soft-wall standard model

We explore the possibility of modeling electroweak physics in a warped extra dimension with a soft wall. The infrared boundary is replaced with a smoothly varying dilaton field that provides a dynamical spacetime cutoff. We analyze gravity, gauge fields, and fermions in the soft-wall background and obtain a discrete spectrum of Kaluza-Klein states which can exhibit linear Regge-like behavior. Bulk Yukawa interactions give rise to nonconstant fermion mass terms, leading to fermion localization in the soft-wall background and a possible explanation of the standard model flavor structure. Furthermore we construct electroweak models with custodial symmetry, where the gauge symmetry is broken with a bulk Higgs condensate. The electroweak constraints are not as stringent as in hard-wall models, allowing Kaluza-Klein masses of order the TeV scale.

Kaluza–Klein towers in warped spaces with metric singularities

The version of the warp model that we proposed to explain the mass scale hierarchy has been extended by the introduction of one or more singularities in the metric. We restricted ourselves to a real massless scalar field supposed to propagate in a five-dimensional bulk with the extra dimension being compactified on a strip or on a circle. With the same emphasis on the hermiticity and commutativity properties of the Kaluza–Klein operators, we have established all the allowed boundary conditions to be imposed on the fields. From them, for given positions of the singularities, one can deduce either mass eigenvalues building up a Kaluza–Klein tower, or a tachyon, or a zero mass state. Assuming the Planck mass to be the high mass scale and by a choice, unique for all boundary conditions, of the major warp parameters, the low lying mass eigenvalues are of the order of the TeV, in this way explaining the mass scale hierarchy. In our model, the physical masses are related to the Kaluza–Klein eigenvalues, depending on the location of the physical brane which is an arbitrary parameter of the model. Illustrative numerical calculations are given to visualize the structure of Kaluza–Klein mass eigenvalue towers. Observation at high energy colliders like LHC of a mass tower with its characteristic structure would be the fingerprint of the model.

Localization and mass spectrum of matters on Weyl thick branes

In this paper, we study localization and mass spectrum of various matter fields on a family of thick brane configurations in a pure geometric Weyl integrable 5-dimensional space time, a non-Riemannian modification of 5-dimensional Kaluza--Klein (KK) theory. We present the shape of the mass-independent potential of the corresponding Schr\{o}dinger problem and obtain the KK modes and mass spectrum, where a special coupling of spinors and scalars is considered for fermions. It is shown that, for a class of brane configurations, there exists a continuum gapless spectrum of KK modes with any $m^2>0$ for scalars, vectors and ones of left chiral and right chiral fermions. All of the corresponding massless modes are found to be normalizable on the branes. However, for a special of brane configuration, the corresponding effective Schr\{o}dinger equations have modified P\{o}schl-Teller potentials. These potentials suggest that there exist mass gap and a series of continuous spectrum starting at positive $m^2$. There are one bound state for spin one vectors, which is just the normalizable vector zero mode, and two bound KK modes for scalars. The total number of bound states for spin half fermions is determined by the coupling constant $\eta$. In the case of no coupling ($\eta=0$), there are no any localized fermion KK modes including zero modes for both left and right chiral fermions. For positive (negative) coupling constant, the number of bound states of right chiral fermions is one less (more) than that of left chiral fermions. In both cases ($\eta>0$ and $\eta<0$), only one of the zero modes for left chiral fermions and right chiral fermions is bound and normalizable.

Dangerous angular Kaluza-Klein/glueball relics in string theory cosmology

The presence of Kaluza-Klein (KK) particles in the universe is a potential manifestation of string theory cosmology. In general, they can be present in the high temperature bath of the early universe. In particular examples, string theory inflation often ends with brane-antibrane annihilation followed by the energy cascading through massive closed string loops to KK modes which then decay into lighter standard model particles. However, massive KK modes in the early universe may become dangerous cosmological relics if the inner manifold contains warped throat(s) with approximate isometries. In the complimentary picture, in the AdS/CFT dual gauge theory with extra isometries, massive glueballs of various spins become the dangerous cosmological relics. The decay of these angular KK modes/glueballs, located around the tip of the throat, is caused by isometry breaking which results from gluing the throat to the compact Calabi-Yau (CY) manifold. We address the problem of these angular KK particles/glueballs, studying their interactions and decay channels, from the theory side, and the resulting cosmological constraints on the warped compactification parameters, from the phenomenology side. The abundance and decay time of the long-lived nonrelativistic angular KK modes depend strongly on the parameters of the warped geometry, so that observational constraints rule out a significant fraction of the parameter space. In particular, the coupling of the angular KK particles can be weaker than gravitational.

Mass gap for gravity localized on Weyl thick branes

We consider thick brane configurations in a pure geometric Weyl integrable 5D space-time, a non-Riemannian generalization of Kaluza-Klein (KK) theory involving a geometric scalar field. Thus, the 5D theory describes gravity coupled to a self-interacting scalar field which gives rise to the structure of the thick branes. We continue the study of the properties of a previously found family of solutions which is smooth at the position of the brane but involves naked singularities in the fifth dimension. Analyzing their graviton spectrum, we find that a particularly interesting situation arises for a special case in which the 4D graviton is separated from the KK gravitons by a mass gap. The corresponding effective Schr\odinger equation has a modified P\oschl-Teller potential and can be solved exactly. Apart from the massless 4D graviton, it contains one massive KK bound state, and the continuum spectrum of delocalized KK modes. We also discuss the mass hierarchy problem, and explicitly compute the corrections to Newton's law in the thin brane limit.

Stable skyrmions from extra dimensions

We show that skyrmions arising from compact five dimensional models have stable sizes. We numerically obtain the skyrmion configurations and calculate their size and energy. Although their size strongly depends on the magnitude of localized kinetic-terms, their energy is quite model-independent ranging between 50 - 65 times F-pi(2)/m(rho), where F-pi is the Goldstone decay constant and m(rho) the lowest Kaluza-Klein mass. These skyrmion configurations interpolate between small 4D YM instantons and 4D skyrmions made of Goldstones and a massive vector boson. Contrary to the original 4D skyrmion and previous 5D extensions, these configurations have sizes larger than the inverse of the cutoff scale and therefore they are trustable within our effective 5D approach. Such solitonic particles can have interesting phenomenological consequences as they carry a conserved topological charge analogous to baryon number.

Unified Gauge Theories and Reduction of Couplings: from Finiteness to Fuzzy Extra Dimensions

Finite Unified Theories (FUTs) are N = 1 supersymmetric Grand Unified Theories, which can be made all-loop finite, both in the dimensionless (gauge and Yukawa couplings) and dimensionful (soft supersymmetry breaking terms) sectors. This remarkable property, based on the reduction of couplings at the quantum level, provides a drastic reduc- tion in the number of free parameters, which in turn leads to an accurate prediction of the top quark mass in the dimensionless sector, and predictions for the Higgs boson mass and the supersymmetric spectrum in the dimensionful sector. Here we examine the predictions of two such FUTs. Next we consider gauge theories defined in higher dimensions, where the extra dimensions form a fuzzy space (a finite matrix manifold). We reinterpret these gauge theo- ries as four-dimensional theories with Kaluza-Klein modes. We then perform a generalized ` la Forgacs-Manton dimensional reduction. We emphasize some striking features emerging such as (i) the appearance of non-Abelian gauge theories in four dimensions starting from an Abelian gauge theory in higher dimensions, (ii) the fact that the spontaneous symmetry breaking of the theory takes place entirely in the extra dimensions and (iii) the renormaliza- bility of the theory both in higher as well as in four dimensions. Then reversing the above approach we present a renormalizable four dimensional SU(N) gauge theory with a suitable multiplet of scalar fields, which via spontaneous symmetry breaking dynamically develops extra dimensions in the form of a fuzzy sphere S 2 N. We explicitly find the tower of massive Kaluza-Klein modes consistent with an interpretation as gauge theory on M 4 ◊ S 2 , the scalars being interpreted as gauge fields on S 2 . Depending on the parameters of the model the low-energy gauge group can be SU(n), or broken further to SU(n1) ◊ SU(n2) ◊ U(1). Therefore the second picture justifies the first one in a renormalizable framework but in addition has the potential to reveal new aspects of the theory.

Localization of matters on pure geometrical thick branes

In the literatures, several types of thick smooth brane configurations in a pure geometric Weyl integrable 5-dimensional space time have been presented. The Weyl geometry is a non-Riemannian modification of 5-dimensional Kaluza-Klein (KK) theory. All these thick brane solutions preserve 4-dimensional Poincaré invariance, and some of them break Z2-symmetry along the extra dimension. In this paper, we study localization of various matter fields on these pure geometrical thick branes, which also localize the graviton. We present the shape of the potential of the corresponding Schrödinger problem and obtain the lowest KK mode. It is shown that, for both spin 0 scalars and spin 1 vectors, there exists a continuum gapless spectrum of KK states with m2 > 0. But only the massless mode of scalars is found to be normalizable on the brane. However, for the massless left or right chiral fermion localization, there must be some kind of Yukawa coupling. For a special coupling, there exist a series of discrete massive KK modes with m2 > 0. It is also showed that for a given coupling constant only one of the massless chiral modes is localized on the branes.

CERN LHC signals for warped electroweak neutral gauge bosons

We study signals at the Large Hadron Collider (LHC) for Kaluza-Klein (KK) excitations of the electroweak gauge bosons in the framework with the standard model (SM) gauge and fermion fields propagating in a warped extra dimension. Such a framework addresses both the Planck-weak and flavor hierarchy problems of the SM. Unlike the often studied ${Z}^{\ensuremath{'}}$ cases, in this framework, there are three neutral gauge bosons due to the underlying $SU(2{)}_{L}\ifmmode\times\else\texttimes\fi{}SU(2{)}_{R}\ifmmode\times\else\texttimes\fi{}U(1{)}_{X}$ gauge group in the bulk. Furthermore, couplings of these KK states to light quarks and leptons are suppressed, whereas those to top and bottom quarks are enhanced compared to the SM gauge couplings. Therefore, the production of light quark and lepton states is suppressed relative to other beyond the SM constructions, and the fermionic decays of these states are dominated by the top and bottom quarks, which are, though, overwhelmed by KK gluons dominantly decaying into them. However, as we emphasize in this paper, decays of these states to longitudinal $W$, $Z$ and Higgs are also enhanced similarly to the case of top and bottom quarks. We show that the $W$, $Z$ and Higgs final states can give significant sensitivity at the LHC to $\ensuremath{\sim}2(3)\text{ }\text{ }\mathrm{TeV}$ KK scale with an integrated luminosity of $\ensuremath{\sim}100\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ ($\ensuremath{\sim}1\text{ }\text{ }{\mathrm{ab}}^{\ensuremath{-}1}$). Since current theoretical framework(s) favor KK masses $\ensuremath{\gtrsim}3\text{ }\text{ }\mathrm{TeV}$, a luminosity upgrade of LHC is likely to be crucial in observing these states.

Chiral asymmetry from a 5D Higgs mechanism

An intriguing feature of the Standard Model is that the representations of the unbroken gauge symmetries are vector-like whereas those of the spontaneously broken gauge symmetries are chiral. Here we provide a toy model which shows that a natural explanation of this property could emerge in higher dimensional field theories and discuss the difficulties that arise in the attempt to construct a realistic theory. An interesting aspect of this type of models is that the 4D low energy effective theory is not generically gauge invariant. However, the non-invariant contributions to the observable quantities are very small, of the order of the square of the ratio between the light particle mass scale and the Kaluza-Klein mass scale. Remarkably, when we take the unbroken limit both the chiral asymmetry and the non-invariant terms disappear. © SISSA 2007.

Probing RS scenarios of flavour at the LHC via leptonic channels

We study a purely leptonic signature of the Randall-Sundrum scenario with Standard Model fields in the bulk at LHC: the contribution from the exchange of Kaluza- Klein (KK) excitations γ (n) , Z (n) of gauge bosons to the clear Drell-Yan reaction pp → γ/Z → l + l − . We show that, even with the low luminosities of the LHC initial regime, this contribution is detectable with the ATLAS apparatus for KK masses around the TeV scale and for sufficiently large lepton couplings to KK gauge bosons . Such large couplings can be compatible with electroweak precision data on the Z ¯ ff coupling in the framework of the custodial O(3) symmetry recently proposed, for specific configurations of lepton local- izations along the extra dimension. These configurations can simultaneously reproduce the correct lepton masses, while generating acceptably small flavour changing neutral current effects.