In warped models that solve the hierarchy problem, there is generally no dynamical relation between the size of the fifth dimension and the scale of electroweak symmetry breaking (EWSB). The establishment of such a relation, without fine-tuning, requires that Casimir contributions to the radion potential not exceed the energy density associated with EWSB. Here, we examine the use of supersymmetry for controlling the Casimir energy density and making quantum contributions calculable. We compute the effects of supersymmetry breaking at the UV and IR boundaries of warped backgrounds, in the presence of brane localized kinetic terms. Various limits of supersymmetry breaking are examined. We find that when supersymmetry is broken on the UV brane, vacuum contributions to the radion potential can be controlled (as likely necessary for EWSB to govern the radion potential) via small soft masses as well as a "double volume suppression." Our formalism can also provide a setup for radion stabilization by bulk fields, when supersymmetry is broken on both the UV and the IR branes.
We analyze the flavor violation in warped extra dimension due to radion mediation. We show that ΔS=2 and ΔB=2 flavor violating processes impose stringent constraints on radion mass, m_ϕand the scale Λ_ϕ. In particular, for Λ_ϕ~ O(1) TeV, B_d^0-\bar{B}^0_d implies that m_ϕ~ 65 GeV. We also study radion contributions to lepton flavor violating processes: τ-> (e,μ) ϕ, τ-> eμ^+μ^- and B -> l_i l_j. We show that BR(B_s -> μ^+ μ^-) can be of order 10^{-8}, which is reachable at the LHCb. The radion search at LHC, through the flavor violation decays into τμor top-charm quarks, is also considered.
We study constraints on the radion mass and couplings in the Randall-Sundrum model from the recent LHC data on the Standard Model (SM) Higgs boson searches. When the radion is heavy enough so that it can decay into a pair of on-shell Z-bosons, we find that the ZZ channel gives a stringent constraint. For example, if the radion mass m_ϕis 200 GeV, the scale Λ_ϕwhich characterizes the interactions of the radion with the SM fields must be larger than 5 TeV. Even for m_ϕ=1 TeV, we find that the lower bound on Λ_ϕis 2 TeV.
We derive the Lagrangian and Feynman rules up to bilinear scalar fields for the mixed Higgs-radion eigenstates interacting with Standard Model particles confined to a 3-brane in Randall-Sundrum warped geometry. We use the results to compute precision electroweak observables and compare theory predictions with experiment. We characterize the interesting regions of parameter space that simultaneously enable a very heavy Higgs mass and a very heavy radion mass, both masses being well above the putative Higgs boson mass limit in the Standard Model derived from the constraints of precision electrow…
We investigate the phenomenology of the Randall-Sundrum radion in realistic models of electroweak symmetry breaking with bulk gauge and fermion fields, since the radion may turn out to be the lightest particle in such models. We calculate the coupling of the radion in such scenarios to bulk fermion and gauge modes. Special attention needs to be devoted to the coupling to massless gauge fields (photon, gluon), since it is well known that loop effects may be important for these fields. We also present a detailed explanation of these couplings from the CFT interpretation. We then use these coupli…
We consider the Kaluza-Klein (KK) graviton and its decays in the presence of the light radion, the modulus of extra dimension, appearing naturally light due to classical scale invariance in warped gravity. Due to the presence of a sizable wavefunction overlap in the extra dimension between the KK graviton and the radion, the KK graviton can decay largely into a pair of radions, each of which decays into a pair of collimated photons or photon-jets. Focusing on the setup where the KK graviton has suppressed couplings to the Higgs boson and fermions, we discuss the bounds on the light radion in t…
We study radion phenomenology in the context of flavor shining in warped extra dimension models. In this unique setup, originally proposed by Rattazzi and Zaffaroni, solutions to the gauge hierarchy problem and the new physics flavor problem are unified. A special role is played by the vacuum energy on the branes, that naturally allows for flavon stabilization and parametrically raises the radion mass. We note that the radion mass squared is suppressed only by the log of the weak-Planck hierarchy, and it is in the favored range of the standard model Higgs. We emphasize that the radion to di-ph…
In the usual 5-dimensional Randall-Sundrum scenario with warped geometry of the extra compact dimension, the Goldberger-Wise mechanism for stabilisation of the radius of compactification can lead to a scalar field called the radion. The radion can have implications in TeV-scale physics, which can be especially noticeable if its vacuum expectation value (vev) is not far above a TeV. However a large mass of the first graviton excitation, which seems to be suggested by recent search limit, tends to make the radion vev, far too large in the minimal model. We show that this is not the case if a Gau…
A recently proposed warped top-condensation model generally predicts a light radion ϕ, with a mass of a few GeV or less, whose interactions are suppressed by a scale of order 100 TeV. In this talk, we present existing constraints and potential signals from the process b \to s ϕ, in the context of such a model. Astrophysical bounds, applicable to very light radions, are also briefly discussed.
The radion scalar field might be the lightest new particle predicted by extra-dimensional extensions of the Standard Model, thus possibly leading to the first signatures of new physics at the LHC. We perform a study of its production in association with a $Z$ boson in the custodially protected warped model with a brane-localised Higgs boson addressing the gauge hierarchy problem, with Higgs-radion mixing effects included. While the considered radion production at the LHC would constrain some parts of the parameter space, it is only the ILC program that will be able to cover a significant part …
The radion scalar field might be the lightest new particle predicted by extra-dimensional extensions of the Standard Model. It could thus lead to the first signatures of new physics at the LHC collider. We perform a complete study of the radion production in association with the Z gauge boson in the custodially protected warped model with a brane-localised Higgs boson addressing the gauge hierarchy problem. Radion-Higgs mixing effects are present. Such a radion production receives possibly resonant contributions from the Kaluza-Klein excitations of the Z boson as well as the extra neutral gaug…
Warped scenarios offer an appealing solution to the hierarchy problem. We consider a non-trivial deformation of the basic Randall-Sundrum framework that has a KK-parity symmetry. This leads to a stable particle beyond the Standard Model, that is generically expected to be the first KK-parity odd excitation of the radion field. We consider the viability of the KK-radion as a DM candidate in the context of thermal and non-thermal production in the early universe. In the thermal case, the KK-radion can account for the observed DM density when the radion decay constant is in the natural multi-TeV …
We study implications of generalized non-zero Dirichlet boundary condition along with the ordinary Neumann one on a bulk scalar in the Randall-Sundrum warped compactification. First we show profiles of vacuum expectation value of the scalar under the general boundary conditions. We also investigate Goldberger-Wise mechanism in several setups with the general boundary conditions of the bulk scalar field and find that the mechanism can work under non-zero Dirichlet boundary conditions with appropriate vacuum expectation values. Especially, we show that $SU(2)_R$ triplet Higgs in the bulk left-ri…
We consider the Higgs-radion mixing in the context of warped space extra dimensional models with custodial symmetry and investigate the prospects of detecting the mixed radion. Custodial symmetries allow the Kaluza-Klein excitations to be lighter, and protect Zbb to be in agreement with experimental constraints. We perform a complementary study of discovery reaches of the Higgs-radion mixed state at the 13 and 14 TeV LHC and at the 500 and 1000 GeV ILC. We carry out a comprehensive analysis of the most significant production and decay modes of the mixed radion in the 80 GeV - 1 TeV mass range,…
Theories beyond the Standard Model often contain mass scales hierarchically different from the electroweak scale and the Planck scale. It has been shown that such hierarchical mass scales can be realized as typical energy scales of multiple 3-branes in a 5D warped spacetime. We present a mechanism for stabilizing the intervals between the multiple 3-branes in the warped extra dimension, by introducing a single 5D scalar field with brane-localized potentials. We discuss the radion stabilization by solving the Einstein equation and the scalar field equation of motion so that a backreaction effec…
We examine the soft supersymmetry breaking parameters in supersymmetric theories on a slice of AdS_5 which generate the hierarchical Yukawa couplings by dynamically localizing the bulk matter fields in extra dimension. Such models can be regarded as the AdS dual of the recently studied 4-dimensional models which contain a supersymmetric CFT to generate the hierarchical Yukawa couplings. In such models, if supersymmetry breaking is mediated by the bulk radion superfield and/or some brane chiral superfields, potentially dangerous flavor-violating soft parameters can be naturally suppressed, ther…
We show that the radion in a warped geometry bounded by two branes can have a potential suitable for inflation. Our construction is based upon a solution known in string theory as the linear dilaton, in which the back-reaction from a bulk scalar Φis exactly accounted for. The radion, stabilized by Φ, is much heavier than the TeV scale and its couplings to the standard model are much more suppressed than in the usual Randall-Sundrum solution. We present a new formalism for obtaining approximate time-dependent solutions, based on perturbing the exact solution to the coupled Einstein and scalar f…
We point out that the light radion phi in a recently proposed Warped Top-Condensation Model, can provide distinct signatures in b -> s phi, where the on-shell phi can decay with displaced vertices. We find that some of the parameter space of these models is constrained by B-meson and astrophysical data. Future B-decay measurements can lead to the discovery of the WTCM.
We study a generalization of the Randall-Sundrum mechanism for generating the weak/Planck hierarchy, which uses two rather than one warped extra dimension, and which requires no negative tension branes. A 4-brane with one exponentially large compact dimension plays the role of the Planck brane. We investigate the dynamical stability with respect to graviton, graviphoton and radion modes. The radion is shown to have a tachyonic instability for certain models of the 4-brane stress-energy, while it is stable in others, and massless in a special case. If stable, its mass is in the milli-eV range, …
A warped space model with a constant boundary superpotential has been an efficient model both to break supersymmetry and to stabilize the radius, when hypermultiplet, compensator and radion multiplet are taken into account. In such a model of the radius stabilization, the radion and moduli masses, the gravitino mass and the induced soft masses are studied. We find that a lighter physical mode composed of the radion and the moduli can have mass of the order of a TeV and that the gravitino mass can be of the order of 10$^7$ GeV. It is also shown that soft mass induced by the anomaly mediation ca…
Precision data generally require the threshold for physics beyond the Standard Model to be at the deca-TeV (10 TeV) scale or higher. This raises the question of whether there are interesting deca-TeV models for which the LHC may find direct clues. A possible scenario for such physics is a 5D warped model of fermion masses and mixing, with Kaluza-Klein masses m_KK ~ 10 TeV, allowing it to avoid tension with stringent constraints, especially from flavor data. Discovery of a Standard-Model-like Higgs boson, for which there are some hints at ~125 GeV at the LHC, would also require the KK masses to…
Supersymmetry breaking and radius stabilization by constant superpotentials localized at boundaries is studied in a supersymmetric warped space model where a hypermultiplet, a compensator and a radion multiplet are taken into account. Soft mass induced by the anomaly mediation can be of the order of 100GeV and can be dominant compared to that mediated by bulk fields. A lighter physical mode composed of the radion and the moduli can have mass of the order of a TeV and the gravitino mass can be of the order of 10^7 GeV. The radius is stabilized by the presence of the constant boundary superpoten…
In the context of higher dimensional braneworld scenario, the stabilisation of extra dimensional modulus is an essential requirement for resolving the gauge hierarchy problem in the context of Standard Model of elementary particle Physics. For Randall-Sundrum (RS) warped extra dimensional model, Goldberger and Wise (GW) proposed a much useful mechanism to achieve this using a scalar field in the bulk spacetime ignoring the effects of backreaction of the scalar field on the background metric. In this article we examine the influence of the backreaction of the stabilising field on the stabilisat…
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…
We present an N=1 superfield formulation of supersymmetric gauge theories with a compact extra dimension. The formulation incorporates the radion superfield and allows to write supersymmetric theories on warped gravitational backgrounds. We apply it to study the breaking of supersymmetry by the F-term of the radion, and show that, for flat extra dimensions, this leads to the same mass spectrum as in Scherk-Schwarz models of supersymmetry breaking. We also consider scenarios where supersymmetry is broken on a boundary of a warped extra dimension and compare them with anomaly mediated models.
We investigate coupled gravity and a bulk scalar field on a slice of AdS_5 bulk with special BPS branes at the two ends. With the special scalar potentials on the branes the scalar field does not stabilize the size of the orbifold. With a careful treatment of the general coordinate invariance the complete tensor-scalar spectrum is presented. There are two massless zero modes in the scalar sector, the radion and a dilatonic zero mode. The scalar KK modes acquire masses at the order of the warped mass scale. The four dimensional effective action is of tensor-scalar type.
We present a possible explanation for the smallness of the observed cosmological constant using a variant of the Randall-Sundrum(RS)- Goldberger-Wise paradigm for a warped extra dimension. In contrast to RS, we imagine that we are living on the positive tension Planck brane, or on a zero-tension TeV brane. In our model there are two solutions for the scalar field in the bulk and the corresponding brane separations, one of which is tuned to have zero cosmological constant. We show that in the other solution, which is a false vacuum state, the 4-D cosmological constant can be naturally small, du…
We examine the cosmology and hierarchy of scales in models with branes immersed in a five-dimensional curved spacetime subject to radion stabilization. When the radion field is time-independent and the inter-brane spacing is stabilized, the universe can naturally find itself in the radiation-dominated epoch. This feature is independent of the form of the stabilizing potential. We recover the standard Friedmann equations without assuming a specific form for the bulk energy-momentum tensor. In the models considered, if the observable brane has positive tension, a solution to the hierarchy proble…
A radion in a scenario with a warped extra dimension can be lighter than the Higgs boson, even if the Kaluza-Klein excitation modes of the graviton turn out to be in the multi-TeV region. The discovery of such a light radion would be gateway to new physics. We show how the two-photon mode of decay can enable us to probe a radion in the mass range 60 - 110 GeV. We take into account the diphoton background, including fragmentation effects, and include cuts designed to suppress the background to the maximum possible extent. Our conclusion is that, with an integrated luminosity of 3000 $\rm fb^{-1…
Recently (arXiv:1608.00526), a new framework for warped higher-dimensional compactifications with "bulk" standard model (SM) was proposed: in addition to the UV (Planck scale) and IR (a couple of TeV) branes, there is an intermediate brane, taken to be around 10 TeV. The SM matter and Higgs fields propagate from the UV brane down to this intermediate brane only, while gauge and gravity fields propagate in the entire bulk. Such a configuration renders the lightest gauge Kaluza-Klein (KK) states within LHC reach, simultaneously satisfying flavor and CP constraints. In addition, the usual leading…
We revisit the case of scalar dark matter interacting just gravitationally with the Standard Model (SM) particles in an extra-dimensional Randall-Sundrum scenario. We assume that both, the dark matter and the Standard Model, are localized in the TeV brane and only interact via gravitational mediators, namely the graviton Kaluza-Klein modes and the radion. We analyze in detail the dark matter annihilation channel into two on-shell KK-gravitons, and contrary to previous studies which overlooked this process, we find that it is possible to obtain the correct relic abundance for dark matter masses…
We explore, within the warped extra dimensional framework, the possibility of finding anti-matter signals in cosmic rays (CRs) from dark matter (DM) annihilation. Exchange of order 100 GeV radion, an integral part of our setup, generically results in Sommerfeld enhancement of the annihilation rate for TeV DM mass. No dark sector is required to obtain boosted annihilation cross sections. A mild hierarchy between the radion and DM masses can be natural due to the pseudo-Goldstone boson nature of the radion. Implications of Sommerfeld enhancement in warped grand unified theory (GUT) models, where…
We analyze signals at the Large Hadron Collider (LHC) from production and decay of Kaluza-Klein (KK) gravitons in the context of "extended" warped extra-dimensional models, where the standard model (SM) Higgs and fermion fields are restricted to be in-between the usual ultraviolet/Planck brane and a $\sim O(10)$ TeV (new, "intermediate") brane, whereas the SM gauge fields (and gravity) propagate further down to the $\sim O( \hbox{TeV} )$ infrared brane. Such a framework suppresses flavor violation stemming from KK particle effects, while keeping the KK gauge bosons and gravitons accessible to …
We study the spin-dependence of Dark Matter (DM) particles which interact gravitationally with the Standard Model (SM) in an extra-dimensional Randall-Sundrum scenario. We assume that both the Dark Matter and the Standard Model are confined to the TeV (Infra-red) brane and only interact via gravitational mediators, namely Kaluza-Klein gravitons and the radion. We analyze the different DM annihilation channels and find that it is possible to achieve the presently observed relic abundance of Dark Matter, $Ω_{\rm DM}$, within the freeze-out mechanism for DM particles of spin 0, 1/2 and 1. We stud…
Supersymmetry breaking by constant (field independent) superpotentials localized at boundaries is studied in a supersymmetric warped space model. We calculate the Kaluza-Klein mass spectrum of the hypermultiplet. We take into account of the radion and the compensator supermultiplets, as well as the bulk mass $c$ for the hypermultiplet. The mass splitting is similar to that of the Scherk-Schwarz supersymmetry breaking (in flat space) for large $|c|$, and has an interesting dependence on the bulk mass parameter $c$. We show that the radius is stabilized by the presence of the constant boundary s…
We show that in brane-world scenarios with warped extra dimensions, the Casimir force due to bulk matter fields may be sufficient to stabilize the radion field $ϕ$. In particular, we calculate one loop effective potential for $ϕ$ induced by bulk gravitons and other possible massless bulk fields in the Randall-Sundrum background. This potential has a local extremum, which can be a maximum or a minimum depending on the detailed bulk matter content. If the parameters of the background are chosen so that the hierarchy problem is solved geometrically, then the radion mass induced by Casimir correct…
We study an effective 4-dimensional scalar-tensor field theory, originated from an underlying brane-bulk warped geometry, to explore the scenario of inflation. It is shown that the inflaton potential naturally emerges from the radion energy-momentum tensor which in turn results into an inflationary model of the Universe on the visible brane that is consistent with the recent results from the Planck's experiment. The dynamics of modulus stabilization from the inflaton rolling condition is demonstrated. The implications of our results in the context of recent BICEP2 results are also discussed.
We study whether modification of gravity at large distances is possible in warped backgrounds with two branes and a brane-induced term localized on one of the branes. We find that there are three large regions in the parameter space where the theory is weakly coupled up to high energies. In one of these regions gravity on the brane is four-dimensional at arbitrarily large distances, and the induced Einstein term results merely in the renormalization of the 4d Planck mass. In the other two regions the behavior of gravity changes at ultra-large distances; however, radion becomes a ghost. In part…
In the warped space model, the inter-brane distance can be stabilized by the Goldberger-Wise mechanism. Of particular importance, the stabilization potential calls for a proper identification of the dynamical degree of freedom. In this paper, we provided a complete calculation of the effective Lagrangian till the quadratic order that is generic for the Randall-Sundrum model and its $N$-brane $(N \geq 4)$ extensions. By applying the variation principle to a specific perturbation field, we derived the equations of motion and orthogonal conditions for decoupling the graviton. This approach is dem…
Supersymmetric models with a warped fifth spatial dimension can solve the hierarchy problem, avoiding some shortcomings of non-supersymmetric constructions, and predict a plethora of new phenomena at typical scales Lambda not far from the electroweak scale (Lambda ~ a few TeV). In this paper we derive the low-energy effective theories of these models, valid at energies below Lambda. We find that, in general, such effective theories can deviate significantly from the Minimal Supersymmetric Standard Model (MSSM) or other popular extensions of it, like the NMSSM: they have non-minimal Kaehler pot…
We implement soft leptogenesis in a warped five dimensional scenario with two branes on the orbifold boundaries coming from an S^{1}/Z_{2} symmetry, and supersymmetry broken on the IR brane. The SM hypermultiplet fields (fermions and Higgs) live in the UV brane and we allow the vector supermultiplets corresponding to the gauge bosons and a hypermultiplet corresponding to the right handed neutrino to live in the bulk. We assume that there are Majorana mass terms for the right handed neutrino superfield fixed on each brane and that there is a Yukawa term involving the right handed neutrino, the …
We study the Friedmann equation for the warped codimension-two braneworld background which most closely resembles the Randall-Sundrum model. Extra matter on the (Planck) 4-brane, with equation of state p_θ=(α-1)ρfor the azimuthal pressure, is required to satisfy the junction conditions. For 1 < α< 5, we show that there are two static solutions to the Einstein equations for given values of the brane stress-energies. Close to the static solutions, the relation between Hubble expansion rate H and brane tension reproduces the standard 4D result for small H, but exhibits unusual deviations when H i…
Braneworld models in extra dimensions can be tested in laboratory by the coupling of the radion to the Standard Model fields. The identification of the radion as a canonically normalized field involves a careful General Relativity treatment: if a bulk scalar is responsible for the stabilization of the system, its fluctuations are entangled with the perturbations of the metric and they also have to be taken into account (similarly to the well-developed theory of scalar metric perturbations in 4D cosmology with a scalar field). Extracting a proper dynamical variable in a warped geometry/scalar s…
We investigate scalar perturbations from inflation in braneworld cosmologies with extra dimensions. For this we calculate scalar metric fluctuations around five dimensional warped geometry with four dimensional de Sitter slices. The background metric is determined self-consistently by the (arbitrary) bulk scalar field potential, supplemented by the boundary conditions at both orbifold branes. Assuming that the inflating branes are stabilized (by the brane scalar field potentials), we estimate the lowest eigenvalue of the scalar fluctuations - the radion mass. In the limit of flat branes, we re…
Using a five-dimensional warped model including a scalar potential with an exponential behavior in the infrared, and strong back-reaction over the metric, we study the electroweak phase transition, and explore parameter regions that were previously inaccessible. The model exhibits gravitational waves and predicts a stochastic gravitational wave background observable, both at the Laser Interferometer Space Antenna and at the Einstein Telescope. Moreover, concerning the collider signatures predictions, the radion evades current constraints but may show up in future LHC runs.
We study the cosmological transition of 5D warped compactifications, from the high-temperature black-brane phase to the low-temperature Randall-Sundrum I phase. The transition proceeds via percolation of bubbles of IR-brane nucleating from the black-brane horizon. The violent bubble dynamics can be a powerful source of observable stochastic gravitational waves. While bubble nucleation is non-perturbative in 5D gravity, it is amenable to semiclassical treatment in terms of a "bounce" configuration interpolating between the two phases. We demonstrate how such a bounce configuration can be smooth…
We give a full nonlinear numerical treatment of time-dependent 5d braneworld geometry, which is determined self-consistently by potentials for the scalar field in the bulk and at two orbifold branes, supplemented by boundary conditions at the branes. We describe the BraneCode, an algorithm which we designed to solve the dynamical equations numerically. We applied the BraneCode to braneworld models and found several novel phenomena of the brane dynamics. Starting with static warped geometry with de Sitter branes, we found numerically that this configuration is often unstable due to a tachyonic …
