Kaluza-Klein Excitations Research Articles

The hierarchy problem and [formula omitted] supergravity

We introduce a new scenario to solve the hierarchy problem based on N=2, five-dimensional supergravity compactified on Calabi–Yau threefold down from D=11 supergravity. When modeling the universe as a 3-brane embedded in a five-dimensional bulk, the background metric is proportional to one of the hypermultiplets fields, namely the dilaton, the volume modulus of the Calabi–Yau space. When solving the dilaton field equation, we find that it is dependent on the extra dimension. We solve the modified Friedmann equations and find the implications of the model on the relation between the effective four-dimensional gravity scale in the brane and the Planck scale of the fifth extra dimension (M). A couple of different scales are considered for the extra dimension, the first where the extra dimension is in range of the solar system and M is of order of the electroweak scale, and the second where the scale of the extra dimension is of order μm and the higher dimensional Planck scale M∼1013GeV. In both cases, the signatures of Kaluza–Klein excitations are quite distinct from the signatures of any previous extra dimensions model.

A 4D IIB flux vacuum and supersymmetry breaking. Part II. Bosonic spectrum and stability

We recently constructed type-IIB compactifications to four dimensions depending on a single additional coordinate, where a five-form flux Φ on an internal torus leads to a constant string coupling. Supersymmetry is fully broken when the internal manifold includes a finite interval of length ℓ, which is spanned by a conformal coordinate in a finite range 0 < z < zm. Here we examine the low-lying bosonic spectra and their classical stability, paying special attention to self-adjoint boundary conditions. Special boundary conditions result in the emergence of zero modes, which are determined exactly by first-order equations. The different sectors of the spectrum can be related to Schrödinger operators on a finite interval, characterized by pairs of real constants μ and μ~\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\overset{\\sim }{\\mu } $$\\end{document}, with μ equal to 1/3 or 2/3 in all cases and different values of μ~\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\overset{\\sim }{\\mu } $$\\end{document}. The potentials behave as μ2−1/4z2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\frac{\\mu^2-1/4}{z^2} $$\\end{document} and μ~2−1/4zm−z2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\frac{{\\overset{\\sim }{\\mu}}^2-1/4}{{\\left({z}_m-z\\right)}^2} $$\\end{document} near the ends and can be closely approximated by exactly solvable trigonometric ones. With vanishing internal momenta, one can thus identify a wide range of boundary conditions granting perturbative stability, despite the intricacies that emerge in some sectors. For the Kaluza-Klein excitations of non-singlet vectors and scalars the Schrödinger systems couple pairs of fields, and the stability regions, which depend on the background, widen as the ratio Φ/ℓ4 decreases.

Mathcal{N} = 1 S-fold spectroscopy

We analyse the spectrum of Kaluza-Klein excitations above three distinct families of mathcal{N} = 1 AdS4 solutions of type IIB supergravity of typically non-geometric, S-fold type that have been recently found. For all three families, we provide the complete algebraic structure of their spectra, including the content of OSp(4|1) multiplets at all Kaluza-Klein levels and their charges under the residual symmetry groups. We also provide extensive results for the multiplet dimensions using new methods derived from exceptional field theory, including complete, analytic results for one of the families. All three spectra show periodicity in the moduli that label the corresponding family of solutions. Finally, the compactness of these moduli is verified in some cases at the level of the fully-fledged type IIB uplifted solutions.

Anomaly flow by an Aharonov–Bohm phase

Abstract In gauge-Higgs unification (GHU), gauge symmetry is dynamically broken by an Aharonov–Bohm (AB) phase, θH, in the fifth dimension. We analyze SU(2) GHU with an SU(2) doublet fermion in the flat M4 × (S1/Z2) spacetime and in the Randall–Sundrum (RS) warped space. With orbifold boundary conditions the U(1) part of gauge symmetry remains unbroken at θH = 0 and π. The fermion multiplet has chiral zero modes at θH = 0, which become massive at θH = π. In other words, chiral fermions are transformed to vector-like fermions by the AB phase θH. The chiral anomaly at θH = 0 continuously varies as θH, and vanishes at θH = π. We demonstrate this intriguing phenomenon in the RS space in which no level crossing occurs in the mass spectrum and everything varies smoothly. The flat spacetime limit is singular as the anti-de Sitter curvature of the RS space diminishes, and reproduces the result in the flat spacetime. Anomalies appear for various combinations of Kaluza–Klein excitation modes of gauge fields as well. Although the magnitude of the anomalies depends on θH and the warp factor of the RS space, it does not depend on the bulk mass parameter of the fermion field controlling its mass and wave function at general θH.

Addendum to “Leptophilic U(1) massive vector bosons from large extra dimensions: Reexamination of constraints from LEP data” [Phys. Lett. B 820 (2021) 136585

Very recently, we proposed an explanation of the discrepancy between the measured anomalous magnetic moment of the muon and the Standard Model (SM) prediction in which the dominant contribution to (g−2)μ originates in Kaluza-Klein (KK) excitations (of the lepton gauge boson) which do not mix with quarks (to lowest order) and therefore can be quite light avoiding LHC constraints. In this addendum we reexamine the bounds on 4-fermion contact interactions from precise electroweak measurements and show that the constraints on KK masses and couplings are more severe than earlier thought. However, we demonstrate that our explanation remains plausible if a few KK modes are lighter than LEP energy, because if this were the case the contribution to the 4-fermion scattering from the internal propagator would be dominated by the energy and not by the mass. To accommodate the (g−2)μ discrepancy we assume that the lepton number L does not partake in the hypercharge and propagates in one extra dimension (transverse to the SM branes): for a mass of the lowest KK excitation of 60 GeV (lower than the LEP energy), the string scale is roughly 10 TeV while the L gauge coupling is of order ∼10−1.

High quality axion via a doubly composite dynamics

We explore a new framework that furnishes a mechanism to simultaneously address the electroweak naturalness problem and the axion high quality problem. The framework is based on a doubly composite dynamics where the second confinement takes place after the CFT encounters the first confinement and the theory flows into another conformal fixed point. For a calculable example, we present a holographic dual description of the 4D model via a warped extra dimension model with three 3-branes. While the hierarchy problem is taken cared of by the localization of the Higgs fields on the TeV brane just as in the original Randall-Sundrum model, the Peccei-Quinn (PQ) symmetry is realized as a gauge symmetry in the bulk of the extra dimension to solve the axion quality problem. We introduce a 5D scalar field whose potential at the intermediate brane drives spontaneous breaking of the PQ symmetry. Then, the PQ breaking scale is given by the scale of the intermediate brane and is naturally small compared to the Planck scale. The axion bulk profile is significantly suppressed around the UV brane, which protects the axion from gravitational violations of the PQ symmetry on the UV brane. Our model genuinely predicts the existence of the Kaluza-Klein excitations of the QCD axion at around the TeV scale and relatively light extra Higgs bosons.

Gauge symmetry restoration by Higgs condensation in flux compactifications on coset spaces

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 and restore (a part of) the gauge symmetries which are broken by gauge field backgrounds. We particularly consider compactifications on ${S}^{2}$ with monopolelike fluxes and also on ${\mathbb{CP}}^{2}$ with instanton and monopolelike fluxes. In some cases, the gauge symmetry is fully restored, as argued in previous literatures. In other cases, there is a stable vacuum with a partial restoration of the gauge symmetry after Higgs condensation. Topological structure of the gauge field configurations prevent the gauge symmetries from being restored.

Leptophilic U(1) massive vector bosons from large extra dimensions

We demonstrate that the discrepancy between the anomalous magnetic moment measured at BNL and Fermilab and the Standard Model prediction could be explained within the context of low-scale gravity and large extra-dimensions. The dominant contribution to (g−2)μ originates in Kaluza-Klein (KK) excitations (of the lepton gauge boson) which do not mix with quarks (to lowest order) and therefore can be quite light avoiding LHC constraints. We show that the KK contribution to (g−2)μ is universal with the string scale entering as an effective cutoff. The KK tower provides a unequivocal distinctive signal which will be within reach of the future muon smasher.

Muon Discrepancy Within D‐brane String Compactifications

AbstractVery recently, the Muon g − 2 experiment at Fermilab has confirmed the E821 Brookhaven result, which hinted at a deviation of the muon anomalous magnetic moment from the Standard Model (SM) expectation. The combined results from Brookhaven and Fermilab show a difference with the SM prediction δaμ = (251 ± 59) × 10−11 at a significance of 4.2σ, strongly indicating the presence of new physics. Motivated by this new result we reexamine the contributions to δaμ from both: (i) the ubiquitous U(1) gauge bosons of D‐brane string theory constructions and (ii) the Regge excitations of the string. We show that, for a string scale , the contribution from anomalous U(1) gauge bosons which couple to hadrons could help to reduce (though not fully eliminate) the discrepancy reported by the Muon g − 2 Collaboration. Consistency with null results from LHC searches of new heavy vector bosons imparts the dominant constraint. We demonstrate that the contribution from Regge excitations is strongly suppressed as it was previously conjectured. We also comment on contributions from Kaluza‐Klein (KK) modes, which could help resolve the δaμ discrepancy. In particular, we argue that for 4‐stack intersecting D‐brane models, the KK excitations of the U(1) boson living on the lepton brane would not couple to hadrons and therefore can evade the LHC bounds while fully bridging the δaμ gap observed at Brookhaven and Fermilab.

Spin-dependence of gravity-mediated dark matter in warped extra-dimensions

We study the possibility that Dark Matter (DM) particles of spin 0, 1/2 or 1 may interact gravitationally with Standard Model (SM) particles within the framework of a warped Randall–Sundrum (RS) model. Both the Dark Matter and the Standard Model particles are assumed to be confined to the infra-red (IR) brane and only interchange Kaluza–Klein excitations of the graviton and the radion (adopting the Goldberger–Wise mechanism to stabilize the size of the extra-dimension). We analyze the different DM annihilation channels and find that the presently observed Dark Matter relic abundance, Omega _{mathrm{DM}}, can be obtained within the freeze-out mechanism for DM particles of all considered spins. This extends our first work concerning scalar DM in RS scenarios (Folgado et al., in JHEP 01:161. https://doi.org/10.1007/JHEP01(2020)161, 2020) and put it on equal footing with our second work in which we studied DM particles of spin 0, 1/2 and 1 in the framework of the Clockwork/Linear Dilaton (CW/LD) model (Folgado et al., in JHEP 20:036. https://doi.org/10.1007/JHEP04(2020)036, 2020). We study the region of the model parameter space for which Omega _{mathrm{DM}} is achieved and compare it with the different experimental and theoretical bounds. We find that, for DM particles mass m_{mathrm{DM}} in [1,15] TeV, most of the parameter space is excluded by the current constraints or will be excluded by the LHC Run III or by the LHC upgrade, the HL-LHC. The observed DM relic abundance can still be achieved for DM masses m_{mathrm{DM}} in [4,15] TeV and m_{G_1} < 10 TeV for scalar and vector boson Dark Matter. On the other hand, for spin 1/2 fermion Dark Matter, only a tiny region with m_{mathrm{DM }} in [4, 15] TeV, m_{G_1} in [5,10] TeV and Lambda > m_{G_1} is compatible with theoretical and experimental bounds. We have also studied the impact of the radion in the phenomenology, finding that it does not modify significantly the allowed region for DM particles of any spin (differently from the CW/LD case, where its impact was quite significant in the case of scalar DM). We, eventually, briefly compare results in RS with those obtained in the CW/LD model.

Kinetic mixing, dark photons and extra dimensions. Part III. Brane localized dark matter

Extra dimensions have proven to be a very useful tool in constructing new physics models. In earlier work, we began investigating toy models for the 5-D analog of the kinetic mixing/vector portal scenario where the interactions of dark matter, taken to be, e.g., a complex scalar, with the brane-localized fields of the Standard Model (SM) are mediated by a massive U(1)D dark photon living in the bulk. These models were shown to have many novel features differentiating them from their 4-D analogs and which, in several cases, avoided some well-known 4-D model building constraints. However, these gains were obtained at the cost of the introduction of a fair amount of model complexity, e.g., dark matter Kaluza-Klein excitations. In the present paper, we consider an alternative setup wherein the dark matter and the dark Higgs, responsible for U(1)D breaking, are both localized to the ‘dark’ brane at the opposite end of the 5-D interval from where the SM fields are located with only the dark photon now being a 5-D field. The phenomenology of such a setup is explored for both flat and warped extra dimensions and compared to the previous more complex models.

A warped scalar portal to fermionic dark matter

We argue that extensions of the SM with a warped extra dimension, together with a new {mathbb {Z}}_2-odd scalar singlet, provide a natural explanation not only for the hierarchy problem but also for the nature of fermion bulk masses and the observed dark matter relic abundance. In particular, the Kaluza-Klein excitations of the new scalar particle, which is required to naturally obtain fermion bulk masses through Yukawa-like interactions, can be the leading portal to any fermion propagating into the bulk of the extra dimension and playing the role of dark matter. Moreover, such scalar excitations will necessarily mix with the Higgs boson, leading to modifications of the Higgs couplings and branching ratios, and allowing the Higgs to mediate the coannihilation of the fermionic dark matter. We study these effects and explore the viability of fermionic dark matter in the presence of these new heavy scalar mediators both in the usual freeze-out scenario and in the case where the freeze-out happens during an early period of matter domination.

Radiatively corrected Kaluza-Klein masses in an aether compactification

We address the issue of radiative corrections to Kaluza-Klein (KK) masses in five-dimensional QED supplemented by aether Lorentz-violating terms. Specifically, we compute the corrections to the KK photon masses from one fermion loop. In general, the KK masses receive radiative corrections due to breaking the five-dimensional Lorentz invariance by compactification. As we show, the presence of the additional Lorentz violating factor - an aether background, leads to the non-trivial modification of these corrections. This model may be of interest in addressing important phenomenological issues such as the relation between radiative corrected KK mass splitting of a particular mode and uncertainties in the measurements and/or possible spatial variation of the fine-structure constant. For the recent data on the fine-structure constant, we find a KK mass splitting of magnitude $\sim 0.01$ MeV for the first excited Kaluza-Klein gauge boson at TeV scale. On the other hand, the large KK modes limit displays a very interesting phenomenon, showing the very special role of the aether in protecting the higher modes from the quantum corrections.

Diphoton Higgs signal strength in universal extra dimensions

The signal strength of the gg → H → γγ reaction in pp collisions at the Large Hadron Collider is studied within the context of the standard model with universal extra dimensions (UED). The impact of an arbitrary number n of UED on both the gg → H and H → γγ subprocesses is studied. The one-loop contribution of Kaluza–Klein excitations on these subprocesses are proportional to discrete and continuous sums, , which can diverge. By implementing the dimensional regularization scheme, it is shown that discrete regularized sums can naturally be expressed as multidimensional Epstein functions, and that divergences, if exist, emerge through the poles of these functions. It is found that continuous sums converge, but the discrete ones diverge, with the exception of the n = 1 case, in which the one-dimensional Epstein function converges. It is argued that divergences that arise from discrete sums for n ⩾ 2 are genuine ultraviolet divergences, since they correspond to short-distance effects in the compact manifold. Then, the amplitudes are renormalized in a modern sense by incorporating interactions of canonical dimension higher than four that allow us to generate the required counterterms, which are determined using a -like renormalization scheme. We find that the gg → H subprocess is quite sensitive to both the size and the dimension of the compact manifold, but the Standard Model prediction for H → γγ subprocess is practically unchanged. It is found that the experimental limit on leads to lower bounds for the compactification scale given by R−1 ⩾ 1.26, 1.55, 2.45, 3.57, 5.10, 7.25 TeVs for n = 1, 2, 4, 6, 8, 10, respectively.

Search for resonant pair production of Higgs bosons in the bbZZ channel in proton-proton collisions at s=13 TeV

A search for the production of a narrow-width resonance decaying into a pair of Higgs bosons decaying into the bbZZ channel is presented. The analysis is based on data collected with the CMS detector during 2016, in proton-proton collisions at the LHC, corresponding to an integrated luminosity of 35.9 fb−1. The final states considered are the ones where one of the Z bosons decays into a pair of muons or electrons, and the other Z boson decays to either a pair of quarks or a pair of neutrinos. Upper limits at 95% confidence level are placed on the production of narrow-width spin-0 or spin-2 particles decaying to a pair of Higgs bosons, in models with and without an extended Higgs sector. For a resonance mass range between 260 and 1000 GeV, limits on the production cross section times branching fraction of a spin-0 and spin-2 resonance range from 0.1 to 5.0 pb and 0.1 to 3.6 pb, respectively. These results set limits in parameter space in bulk Randall-Sundrum radion, Kaluza-Klein excitation of the graviton, and next-to-minimal two-Higgs doublet models (N2HDMs). For specific choices of parameters the N2HDM can be excluded in a mass range between 360 and 620 GeV for a resonance decaying to two Higgs bosons. This is the first search for Higgs boson resonant pair production in the bbZZ channel.Received 11 June 2020Accepted 15 July 2020DOI:https://doi.org/10.1103/PhysRevD.102.032003Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.© 2020 CERN, for the CMS CollaborationPhysics Subject Headings (PhySH)Research AreasParticle decaysPhysical SystemsBottom quarkHiggs bosonsTechniquesHadron collidersParticles & Fields

Proof of dispersion relations for the amplitude in theories with a compactified space dimension

The analyticity properties of the scattering amplitude in the nonforward direction are investigated for a field theory in the manifold R3,1 ⨂ S1. The theory is obtained from a massive, neutral scalar field theory of mass m0 defined in flat five dimensional spacetime upon compactification on a circle, S1. The resulting theory is endowed with a massive scalar field which has the lowest mass, m0, as of the original five dimensional theory and a tower of massive Kaluza-Klein states. We derive nonforward dispersion relations for scattering of the excited Kaluza-Klein states in the Lehmann-Symanzik-Zimmermann formulation of the theory. In order to accomplish this object, first we generalize the Jost-Lehmann-Dyson theorem for a relativistic field theory with a compact spatial dimension. Next, we show the existence of the Lehmann-Martin ellipse inside which the partial wave expansion converges. The scattering amplitude satisfies fixed-t dispersion relations when |t| lies within the Lehmann-Martin ellipse.

Massive spin-2 scattering amplitudes in extra-dimensional theories

In this paper we describe in detail the computation of the scattering amplitudes of massive spin-2 Kaluza-Klein excitations in a gravitational theory with a single compact extra dimension, whether flat or warped. These scattering amplitudes are characterized by intricate cancellations between different contributions: although individual contributions may grow as fast as ${\cal O}(s^5)$, the full results grow only as ${\cal O}(s)$. We demonstrate that the cancellations persist for all incoming and outgoing particle helicities and examine how truncating the computation to only include a finite number of intermediate states impacts the accuracy of the results. We also carefully assess the range of validity of the low energy effective Kaluza-Klein theory. In particular, for the warped case we demonstrate directly how an emergent low energy scale controls the size of the scattering amplitude, as conjectured by the AdS/CFT correspondence.

Limits on Kaluza\u2013Klein dark matter annihilation in the Sun from recent IceCube results

We interpret recent IceCube results on searches for dark matter accumulated in the Sun in terms of the lightest Kaluza–Klein excitation (assumed here to be the Kaluza–Klein photon, B^1), obtaining improved limits on the annihilation rate in the Sun, the resulting neutrino flux at the Earth and on the B^1-proton cross-sections, for B^1 masses in the range 30–3000 GeV. These results improve previous results from IceCube in its 22-string configuration by up to an order of magnitude, depending on mass, but also extend the results to B^1 masses as low as 30 GeV.

Soft theorems from compactification

We analyze the single subleading soft graviton theorem in (d + 1) dimensions under compactification on S1. This produces the single soft theorems for the graviton, vector and scalar fields in d dimension. For the compactification of 11-dimensional supergravity theory, this gives the soft factorization properties of the single graviton, dilaton and RR 1-form fields in type IIA string theory in ten dimensions. For the case of the soft vector field, we also explicitly check the result obtained from compactification by computing the amplitudes with external massive spin two and massless finite energy states interacting with soft vector field. The former are the Kaluza-Klein excitations of the d + 1 dimensional metric. Describing the interaction of the KK-modes with the vector field at each level by the minimally coupled Fierz-Pauli Lagrangian, we find agreement with the results obtained from the compactification if the gyromagnetic ratio in the minimally coupled Fierz-Pauli Lagrangian is taken to be g = 1.

Gravitational waves and higher dimensions: Love numbers and Kaluza-Klein excitations

Gravitational-wave (GW) observations provide a wealth of information on the nature and properties of black holes. Among these, tidal Love numbers or the multipole moments of the inspiralling and final objects are key to a number of constraints. Here, we consider these observations in the context of higher-dimensional scenarios, with flat large extra dimensions. We show that -- as might be anticipated, but not always appreciated in the literature -- physically motivated set-ups are unconstrained by gravitational-wave data. Dynamical processes that do not excite the Kaluza-Klein (KK) modes lead to a signal identical to that in four-dimensional general relativity in vacuum . In addition, any possible excitation of the KK modes is highly suppressed relative to the dominant quadrupolar term; given existing constraints on the extra dimensions and the masses of the objects seen in gravitational-wave observations, KK modes appear at post-Newtonian order $\sim 10^{11}$. Finally, we re-compute the tidal Love numbers of spherical black holes in higher dimensions. We confirm that these are different from zero, but comparing with previous computations we find a different magnitude and sign.