KK Mass Research Articles

On the cosmological constant, the KK mass scale, and the cut-off dependence in the dark dimension scenario

In this short note we comment on the relation between the cosmological and the Kaluza–Klein mass scale in the dark dimension scenario [1], also in view of some recent claims [2] that would raise some doubts about the validity of this scenario. Here we argue that these claims have serious flaws and cannot be trusted.

Harmonic functions and gravity localization

In models with extra dimensions, matter particles can be easily localized to a ‘brane world’, but gravitational attraction tends to spread out in the extra dimensions unless they are small. Strong warping gradients can help localize gravity closer to the brane. In this note we give a mathematically rigorous proof that the internal wave-function of the massless graviton is constant as an eigenfunction of the weighted Laplacian, and hence is a power of the warping as a bound state in an analogue Schrödinger potential. This holds even in presence of singularities induced by thin branes.We also reassess the status of AdS vacuum solutions where the graviton is massive. We prove a bound on scale separation for such models, as an application of our recent results on KK masses. We also use them to estimate the scale at which gravity is localized, without having to compute the spectrum explicitly. For example, we point out that localization can be obtained at least up to the cosmological scale in string/M-theory solutions with infinite-volume Riemann surfaces; and in a known class of N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 4 models, when the number of NS5- and D5-branes is roughly equal.

Deviation of Yukawa coupling in gauge-Higgs unification

We study the deviation of yukawa coupling in the gauge-Higgs unification scenario from the Standard Model one. Taking into account the brane mass terms necessary for generating the flavor mixing and removing the exotic massless fermions, we derive an analytic formula determining the KK mass spectrum and yukawa coupling. Applying the obtained results to the tau and bottom yukawa couplings, we numerically calculate the ratio of the yukawa couplings in the gauge-Higgs unification and in the Standard Model.

Universal spin-1/2 fermion field localization on a 5D braneworld

In this letter we have proposed a natural way of determine the Yukawa coupling $F(z)\bar\Psi \Psi$ for the 5D bulk action, the form of the $F(z)$ function allows us to localize the spin--$\frac{1}{2}$ fermionic fields in the paradigm of the 5D braneworld scenarios. The structure acquired by the $V_{L,R}$ potentials is induced by the ansatz for the $F(z)$ function and we show that this choice allows the localization of the left-- or right--chiral KK zero modes $L_{0}(z)$, $R_{0}(z)$ and excludes the tachyonic modes of the KK mass spectrum $m_{L_{n}}$ and $m_{R_{n}}$. The proposal for the function $F(z)$ leaves behind other speculative proposals since it is independent of the braneworld model, hence the form for the Yukawa coupling here presented is the most natural choice. This is shown most evidently if we set $M=\pm 3/2$, which is a more phenomenologically viable ansatz. This choice allows for a direct relation between the localization of the ground state for the left-- or right--chiral KK mass spectrum and the localization of the zero mode for the 4D graviton in the brane. As a bonus, we include a brief discussion about the existence of a left-- or right--chiral KK zero mode decoupled from the corresponding continuous KK mass spectrum, as well as the possible existence of a mass gap, due to the asymptotic nature of the potentials $V_{R,L}$.

Bulk stabilization, the extra-dimensional Higgs portal and missing energy in Higgs events

To solve the hierarchy problem, extra-dimensional models must explain why the new dimensions stabilize to the right size, and the known mechanisms for doing so require bulk scalars that couple to the branes. Because of these couplings the energetics of dimensional stabilization competes with the energetics of the Higgs vacuum, with potentially observable effects. These effects are particularly strong for one or two extra dimensions because the bulk-Higgs couplings can then be super-renormalizable or dimensionless. Experimental reach for such extra-dimensional Higgs `portals' are stronger than for gravitational couplings because they are less suppressed at low-energies. We compute how Higgs-bulk coupling through such a portal with two extra dimensions back-reacts onto properties of the Higgs boson. When the KK mass is smaller than the Higgs mass, mixing with KK modes results in an invisible Higgs decay width, missing-energy signals at high-energy colliders, and new mechanisms of energy loss in stars and supernovae. Astrophysical bounds turn out to be complementary to collider measurements, with observable LHC signals allowed by existing constraints. We comment on the changes to the Higgs mass-coupling relationship caused by Higgs-bulk mixing, and how the resulting modifications to the running of Higgs couplings alter vacuum-stability and triviality bounds.

Tensor gauge field localization on a string-like defect

This work is devoted to the study of tensor gauge fields on a string-like defect in six dimensions. This model is very successful in localizing fields of various spins only by gravitational interaction. Due to problems of field localization in membrane models we are motivated to investigate if a string-like defect localizes the Kalb–Ramond field. In contrast to what happens in Randall–Sundrum and thick brane scenarios we find a localized zero mode without the addition of other fields in the bulk. Considering the local string defect we obtain analytical solutions for the massive modes. Also, we take the equations of motion in a supersymmetric quantum mechanics scenario in order to analyze the massive modes. The influence of the mass as well as the angular quantum number in the solutions is described. An additional analysis on the massive modes is performed by the Kaluza–Klein decomposition, which provides new details about the KK masses.

Flavour physics in the soft wall model

We extend the description of flavour that exists in the Randall-Sundrum (RS) model to the soft wall (SW) model in which the IR brane is removed and the Higgs is free to propagate in the bulk. It is demonstrated that, like the RS model, one can generate the hierarchy of fermion masses by localising the fermions at different locations throughout the space. However, there are two significant differences. Firstly the possible fermion masses scale down, from the electroweak scale, less steeply than in the RS model and secondly there now exists a minimum fermion mass for fermions sitting towards the UV brane. With a quadratic Higgs VEV, this minimum mass is about fifteen orders of magnitude lower than the electroweak scale. We derive the gauge propagator and despite the KK masses scaling as $$ m_n^2 \sim n $$ , it is demonstrated that the coefficients of four fermion operators are not divergent at tree level. FCNC’s amongst kaons and leptons are considered and compared to calculations in the RS model, with a brane localised Higgs and equivalent levels of tuning. It is found that since the gauge fermion couplings are slightly more universal and the SM fermions typically sit slightly further towards the UV brane, the contributions to observables such as ε K and Δm K , from the exchange of KK gauge fields, are significantly reduced.

Higgs phenomenology in warped extra dimensions with a fourth generation

We study a warped extra-dimension scenario where the Standard Model fields lie in the bulk, with the addition of a fourth family of fermions. We concentrate on the flavor structure of the Higgs couplings with fermions in the flavor anarchy ansatz. Even without a fourth family, these couplings will be generically misaligned with respect to the SM fermion mass matrices. The presence of the fourth family typically enhances the misalignment effects and we show that one should expect them to be highly non-symmetrical in the ${(34)}$ inter-generational mixing. The radiative corrections from the new fermions and their flavor violating couplings to the Higgs affect negligibly known experimental precision measurements such as the oblique parameters and $Z\to b {\bar b}$ or $Z \to \mu^+ \mu^-$. On the other hand, $\Delta F=1,2$ processes, mediated by tree-level Higgs exchange, as well as radiative corrections to $b \to s \gamma$ and $\mu \to e\gamma$ put some generic pressure on the allowed size of the flavor violating couplings. But more importantly, these couplings will alter the Higgs decay patterns as well as those of the new fermions, and produce very interesting new signals associated to Higgs phenomenology in high energy colliders. These might become very important indirect signals for these type of models as they would be present even when the KK mass scale is high and no heavy KK particle is discovered.

Warped 5D standard model consistent with EWPT

AbstractFor a 5D Standard Model propagating in an AdS background with an IR localized Higgs, compatibility of bulk KK gauge modes with EWPT yields a phenomenologically unappealing KK spectrum (mKK< 12.5 TeV) and leads to a “little hierarchy problem”. For a bulk Higgs the solution to the hierarchy problem reduces the previous bound only by ∼ $^{1 \over 2}$. As a way out, models with an enhanced bulk gauge symmetry SU(2)R × U(1)B‐L were proposed. In this note we describe a much simpler (5D Standard) Model, where introduction of an enlarged gauge symmetry is no longer required. It is based on a warped gravitational background which departs from AdS at the IR brane and a bulk propagating Higgs. The model is consistent with EWPT for a range of KK masses within the LHC reach.

Suppressing electroweak precision observables in 5D warped models

We elaborate on a recently proposed mechanism to suppress large contributions to the electroweak precision observables in five dimensional (5D) warped models, without the need for an extended 5D gauge sector. The main ingredient is a modification of the AdS metric in the vicinity of the infrared (IR) brane corresponding to a strong deviation from conformality in the IR of the 4D holographic dual. We compute the general low energy effective theory of the 5D warped Standard Model, emphasizing additional IR contributions to the wave function renormalization of the light Higgs mode. We also derive expressions for the S and T parameters as a function of a generic 5D metric and zero-mode wave functions. We give an approximate formula for the mass of the radion that works even for strong deviation from the AdS background. We proceed to work out the details of an explicit model and derive bounds for the first KK masses of the various bulk fields. The radion is the lightest new particle although its mass is already at about 1/3 of the mass of the lightest resonances, the KK states of the gauge bosons. We examine carefully various issues that can arise for extreme choices of parameters such as the possible reintroduction of the hierarchy problem, the onset of nonperturbative physics due to strong IR curvature or the creation of new hierarchies near the Planck scale. We conclude that a KK scale of 1 TeV is compatible with all these constraints.

A six-dimensional gauge-Higgs unification model based on E 6 gauge symmetry

We construct a six-dimensional gauge-Higgs unification model with the enlarged gauge group of E 6 on S 2 / Z 2 orbifold compactification. The standard model particle contents and gauge symmetry are obtained by utilizing a monopole background field and imposing appropriate parity conditions on the orbifold. In particular, a realistic Higgs potential suitable for breaking the electroweak gauge symmetry is obtained without introducing extra matter or assuming an additional symmetry relation between the SU(2) isometry transformation on the S 2 and the gauge symmetry. The Higgs boson is a KK mode associated with the extra-dimensional components of gauge field. We also compute the KK masses of all fields at tree level.

STANDARD MODEL IN AdS SLICE WITH UV-LOCALIZED HIGGS FIELD

We discuss five-dimensional Standard Model in a slice of AdS space–time with the Higgs field residing near or on the UV brane. Allowing fermion fields to propagate in the bulk, we obtain the hierarchy of their masses and quark mixings without introducing large or small Yukawa couplings. However, the interaction of fermions with the Higgs and gauge boson KK excitations gives rise to FCNC with no built-in suppression mechanism. This strongly constrains the scale of KK masses. We also discuss neutrino mass generation via KK excitations of the Higgs field. We find that this mechanism is subdominant in the scenarios of spontaneous symmetry breaking we consider.

Viable Randall-Sundrum model for quarks and leptons withT′family symmetry

We propose a Randall-Sundrum model with a bulk family symmetry based on the double tetrahedral group, T', which generates the tri-bimaximal neutrino mixing pattern and a realistic CKM matrix, including CP violation. Unlike 4D models where the generation of mass hierarchy requires additional symmetry, the warped geometry naturally gives rise to the fermion mass hierarchy through wavefunction localization. The T' symmetry forbids tree-level flavor changing neutral currents in both the quark and lepton sectors, as different generations of fermions are unified into multiplets of T'. This results in a low first KK mass scale and thus the model can be tested at collider experiments.

ΔF= 2 observables and fine-tuning in a warped extra dimension with custodial protection

We present a complete study of ΔS = 2 and ΔB = 2 processes in a warped extra dimensional model with a custodial protection of ZbLL, including εK, ΔMK, ΔMs, ΔMd, ASLq, ΔΓq, ACP(Bd→ψKS) andACP(Bs→ψϕ). These processes are affected by tree level contributions from Kaluza-Klein gluons, the heavy KK photon, new heavy electroweak gauge bosons ZH and Z', and in principle by tree level Z contributions. We confirm recent findings that the fully anarchic approach where all the hierarchies in quark masses and weak mixing angles are geometrically explained seems implausible and we confirm that the KK mass scale MKK generically has to be at least ∼ 20 TeV to satisfy the εK constraint. We point out, however, that there exist regions in parameter space with only modest fine-tuning in the 5D Yukawa couplings which satisfy all existing ΔF = 2 and electroweak precision constraints for scales MKK ≃ 3 TeV in reach of the LHC. Simultaneously we find that ACP(Bs → ψϕ) and AsSL can be much larger than in the SM as indicated by recent results from CDF and DØ data. We point out that for Bd,s physics ΔF = 2 observables the complex (ZH,Z') can compete with KK gluons, while the tree level Z and KK photon contributions are very small. In particular we point out that the ZdiLjL couplings are protected by the custodial symmetry. As a by-product we show the relation of the RS flavour model to the Froggatt-Nielsen mechanism and we provide analytic formulae for the effective flavour mixing matrices in terms of the fundamental 5D parameters.

Minimal flavor violation in the lepton sector of the Randall–Sundrum model

We propose a realization of Minimal Flavor Violation in the lepton sector of the Randall–Sundrum model. With the MFV assumption, the only source of flavor violation are the 5D Yukawa couplings, and the usual two independent sources of flavor violation are related. In the limit of massless neutrinos, the bulk mass matrices and 5D Yukawa matrices are simultaneously diagonalized, and hence the absence of FCNCs. In the case of massive neutrinos, the contributions to FCNCs in the charged lepton sector are highly suppressed, due to the smallness of neutrino masses. In addition, the MFV assumption also allows suppressing one-loop charged current contributions to flavor changing processes by reducing the size of the Yukawa couplings, which is not possible in the generic anarchical case. We found that the first KK mass scale as low as ∼3 TeV can be allowed. In both cases, we present a set of numerical results that give rise to realistic lepton masses and mixing angles. Mild hierarchy in the 5D Yukawa matrix of O(25) in our numerical example is required to be consistent with two large and one small mixing angles. This tuning could be improved by having a more thorough search of the parameter space.

A model of lepton masses from a warped extra dimension

In order to explain the non-hierarchical neutrino mixing angles and the absence of lepton flavor violating processes in the context of warped extra dimensions one needs to introduce bulk flavor symmetries. We present a simple model of lepton masses and mixings in RS models based on the A4 non-abelian discrete symmetry. The virtues of this choice are: (i) the natural appearance of the tri-bimaximal mixing pattern; (ii) the complete absence of tree-level flavor violations in the neutral sector; (iii) the absence of flavor gauge bosons; (iv) the hierarchies in the charged lepton masses are explained via wave-function overlaps. We present the minimal field content and symmetry breaking pattern necessary to obtain a successful model of this type. The bounds from electroweak precision measurements allow the KK mass scale to be as low as 3 TeV. Tree-level lepton flavor violation is absent in this model, while the loop induced mu -> e gamma branching fraction is safely below the experimental bound.

Warped spectroscopy: localization of frozen bulk modes

We study the 10D equation of motion of dilaton-axion fluctuations in type IIB string compactifications with three-form flux, taking warping into account. Using simplified models with physics comparable to actual compactifications, we argue that the lightest mode localizes in long warped throats and takes a mass of order the warped string scale. Also, Gukov-Vafa-Witten superpotential is valid for the lightest mass mode; however, the mass is similar to the Kaluza-Klein scale, so the dilaton-axion should be integrated out of the effective theory in this long throat regime (leaving a constant superpotential). On the other hand, there is a large hierarchy between flux-induced and KK mass scales for moderate or weak warping. This hierarchy agrees with arguments given for trivial warping. Along the way, we also estimate the effect of the other 10D supergravity equations of motion on the dilaton-axion fluctuation, since these equations act as constraints. We argue that they give negligible corrections to the simplest approximation.

Gauge Theories in AdS5 and Fine-Lattice Deconstruction

The logarithmic energy dependence of gauge couplings in AdS5 emerges almost automatically when the theory is deconstructed on a coarse lattice. Here we study the theory away from the coarse-lattice limit. While we cannot analytically calculate individual KK masses for a fine lattice, we can calculate the product of all non-zero masses. This allows us to write down the gauge coupling at low energies for any lattice-spacing and curvature. As expected, the leading log behavior is corrected by power-law contributions, suppressed by the curvature. We then turn to intermediate energies, and discuss the gauge coupling and the gauge boson profile in perturbation theory around the coarse-lattice limit.

Gravitational instability of de Sitter compactifications

We consider warped compactifications in(4 + d)-dimensional theories, with four-dimensional (4d) de SitterdS4 vacua (withHubble parameter H) and with a compact internal space. After introducing a gauge-invariant formalism for the genericmetric perturbations of these backgrounds, we focus on modes which are scalar with respect todS4. The physical eigenmasses of these modes acquire a large universal tachyonic contribution−12d/(d + 2)H2, independently of the stabilization mechanism for the compact space, in additionto the usual KK masses, which instead encode the effects of the stabilization.General arguments, as well as specific examples, lead us to conjecture that, forsufficiently large dS curvature, the compactified geometry becomes gravitationallyunstable due to the tachyonic growth of the scalar perturbations. This meansthat for any stabilization mechanism the curvature of the dS geometry cannotexceed some critical value. We relate this effect to the anisotropy of the bulkgeometry and suggest the end points of the instability. Of relevance for inflationarycosmology, the perturbations of the bulk metric inevitably induce a new modulusfield, which describes the conformal fluctuations of the 4d metric. If this modeis light during inflation, the induced conformal fluctuations will be amplifiedwith a scale free spectrum and with an amplitude which is disentangled from thestandard result of slow-roll inflation. The conformal 4d metric fluctuations giverise to a very generic realization of the mechanism of modulated cosmologicalfluctuations, related to spatial variation of couplings during (p)reheating after inflation.

Radiative corrections to Kaluza-Klein masses

Extra-dimensional theories contain a number of almost degenerate states at each Kaluza-Klein level. If extra dimensional momentum is at least approximately conserved then the phenomenology of such nearly degenerate states depends crucially on the mass splittings between KK modes. We calculate the complete one-loop radiative corrections to KK masses in general 5 and 6 dimensional theories. We apply our formulae to the example of universal extra dimensions and show that the radiative corrections are essential to any meaningful study of the phenomenology. Our calculations demonstrate that Feynman diagrams with loops wrapping the extra dimensions are well-defined and cut-off independent even though higher dimensional theories are not renormalizable.