Kaluza-Klein Number Research Articles

Radiative corrections to masses and couplings in universal extra dimensions

Models with an orbifolded universal extra dimension receive important loop-induced corrections to the masses and couplings of Kaluza-Klein (KK) particles. The dominant contributions stem from so-called boundary terms which violate KK number. Previously, only the parts of these boundary terms proportional to ln(ΛR) have been computed, where R is the radius of the extra dimension and Λ is cut-off scale. However, for typical values of ΛR ∼ 10 · · · 50, the logarithms are not particularly large and non-logarithmic contributions may be numerically important. In this paper, these remaining finite terms are computed and their phenomenological impact is discussed. It is shown that the finite terms have a significant impact on the KK mass spectrum. Furthermore, one finds new KK-number violating interactions that do not depend on ln(ΛR) but nevertheless are non-zero. These lead to new production and decay channels for level-2 KK particles at colliders.

Constraints on universal extra dimensions fromW′searches

We obtain constraints on three universal extra-dimensional models utilizing limits from the CMS Collaboration on ${W}^{\ensuremath{'}}$ production and decay into a single-top-quark final state. We find a weak constraint on the minimal universal extra-dimensional model due to small Kaluza-Klein number violating terms. In contrast, the ${W}^{\ensuremath{'}}$ search puts a strong limit on the size of the Dirac mass term of the quarks in split universal extra-dimension models. In nonminimal universal extra-dimension models, the ${W}^{\ensuremath{'}}$ search constrains the splitting between the boundary-localized kinetic terms of the gauge bosons and the quarks. Each of these bounds can be translated into constraints on the mass splitting between the Kaluza-Klein excitations of the $SU(2)$ charged quarks and the Klauza-Klein excitations of the $W$ boson.

Closed string transport coefficients and the membrane paradigm

I discuss a correspondence between a fictitious fluid in the black hole membrane paradigm and highly excited closed string states according to the black hole correspondence principle. I calculate the membrane transport coefficients of an electric NS-NS 2-charged black hole and transport coefficients of the highly excited closed string states which possess a Kaluza-Klein number and a winding number. Comparing both the transport coefficients at the correspondence point, I show that, except for the bulk viscosity, the membrane transport coefficients are of the same order as the transport coefficients of the closed string states on the stretched horizon. Also, I show that, except for the bulk viscosity, both the dimensionless transport coefficients, which are defined by dividing the transport coefficients by the entropy density, are exactly equal if the central charge is 6.

Minimal universal extra dimensions in CalcHEP/CompHEP

We present an implementation of the model of minimal universal extra dimensions (MUED) in CalcHEP/CompHEP. We include all level-1 and level-2 Kaluza–Klein (KK) particles outside the Higgs sector. The mass spectrum is automatically calculated at one loop in terms of the two input parameters in MUED: the inverse radius R-1 of the extra dimension and the cut-off scale of the model Λ. We implement both the KK number conserving and the KK number violating interactions of the KK particles. We also account for the proper running of the gauge coupling constants above the electroweak scale. The implementation has been extensively cross-checked against known analytical results in the literature and numerical results from other programs. Our files are publicly available and can be used to perform various automated calculations within the MUED model.

Productions of second Kaluza-Klein gauge bosons in the minimal universal extra dimension model at LHC

We calculate the production rates of the second Kaluza-Klein (KK) photon ${\ensuremath{\gamma}}^{(2)}$ and $Z$ boson ${Z}^{(2)}$ at the LHC including all significant processes in the minimal universal extra dimension (MUED) model. For discrimination of the MUED model from other TeV scale models at the LHC, ${\ensuremath{\gamma}}^{(2)}$ and ${Z}^{(2)}$ play a crucial role. In order to discuss the discrimination and calculate their production rates, we derive KK number violating operators including the contribution of the top Yukawa coupling. Using these operators, we accurately calculate branching ratios of second KK particles. In addition we find that these KK number violating operators provide new processes for ${\ensuremath{\gamma}}^{(2)}$ and ${Z}^{(2)}$ productions, such as cascade decay from second KK quarks produced through these operators. They have large contributions to their total production rates. In particular, these production processes give the dominant contribution for ${\ensuremath{\gamma}}^{(2)}$ production for $1/R\ensuremath{\gtrsim}800\text{ }\text{ }\mathrm{GeV}$. As a result, with an integrated luminosity of $100\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$, the number of produced ${\ensuremath{\gamma}}^{(2)}$ and ${Z}^{(2)}$ are estimated as ${10}^{6}--{10}^{2}$ for the compactification scale between 400 and 2000 GeV.

One universal extra dimension in Pythia

The Universal Extra Dimensions model has been implemented in the Pythia generator from version 6.4.18 onwards, in its minimal formulation with one TeV −1-sized extra dimension. The additional possibility of gravity-mediated decays, through a variable number of eV −1-sized extra dimensions into which only gravity extends, is also available. The implementation covers the lowest lying Kaluza–Klein (KK) excitations of Standard Model particles, except for the excitations of the Higgs fields, with the mass spectrum calculated at one loop. 2 → 2 tree-level production cross sections and unpolarized KK number conserving 2-body decays are included. Mixing between iso-doublet and -singlet KK excitations is neglected thus far, and is expected to be negligible for all but the top sector. New version summary Program title: PYTHIA Version number: 6.420 Catalogue identifier: ACTU_v2_1 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ACTU_v2_1.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 79 362 No. of bytes in distributed program, including test data, etc.: 590 900 Distribution format: tar.gz Programming language: Fortran 77 Computer: CERN lxplus and any other machine with a Fortran 77 compiler Operating system: Linux Red Hat RAM: about 800 K words Word size: 32 bits Classification: 11.2 Catalogue identifier of previous version: ACTU_v2_0 Journal reference of previous version: Comput. Phys. Comm. 135 (2001) 238 Does the new version supersede the previous version?: Yes Nature of problem: At high energy collisions between elementary particles, physics beyond the Standard Model is searched for. Many models are being investigated, namely extra-dimensional models. Solution method: The Universal Extra Dimension model is implemented in the PYTHIA event generator. Reasons for new version: The Universal Extra Dimensions model has been implemented in the PYTHIA generator from version 6.4.18 onwards, in its minimal formulation with one TeV −1-sized extra dimension. The additional possibility of gravity-mediated decays, through a variable number of eV −1-sized extra dimensions into which only gravity extends, is also available. The implementation covers the lowest lying Kaluza–Klein (KK) excitations of Standard Model particles, except for the excitations of the Higgs fields, with the mass spectrum calculated at one loop. 2 → 2 tree-level production cross sections and unpolarized KK number conserving 2-body decays are included. Mixing between iso-doublet and -singlet KK excitations is neglected thus far, and is expected to be negligible for all but the top sector. Running time: 10–1000 events per second, depending on the process studied.

PRODUCTION RATE OF SECOND KK GAUGE BOSONS IN UED MODELS AT LHC

We calculate the production rates of the second Kaluza-Klein (KK) photon γ(2) and Z boson Z(2) at the LHC including all significant processes in the minimal universal extra dimension (MUED) model. For discrimination of the MUED model from other TeV scale models in hadron collider experiments, γ(2) and Z(2) play a crucial role. In order to discuss the discrimination and calculate their production rates, we derive effective Lagrangian containing KK number violating operators. We show that KK number violating processes are extremely important for the compactification scale larger than 800 GeV. We find that, with an integrated luminosity of 100 fb-1, γ(2) and Z(2) are produced 106 - 102 for the compactification scale between 400 GeV and 2000 GeV.

Exploring the universal extra dimension at the LHC

Besides supersymmetry, the other prime candidate of physics beyond the Standard Model (SM), crying out for verification at the CERN Large Hadron Collider (LHC), is extra-dimension. To hunt for effects of Kaluza–Klein (KK) excitations of known fermions and bosons is very much in the agenda of the LHC. These KK states arise when the SM particles penetrate in the extra space-like dimension(s). In this paper, we consider a 5d scenario, called ‘Universal Extra Dimension’, where the extra space coordinate, compactified on an orbifold S 1 / Z 2 , is accessed by all the particles. The KK number ( n) is conserved at all tree level vertices. This entails the production of KK states in pairs and renders the lightest KK particle stable, which leaves the detector carrying away missing energy. The splitting between different KK flavors is controlled by the zero mode masses and the bulk- and brane-induced one-loop radiative corrections. We concentrate on the production of an n = 1 KK electroweak gauge boson in association with an n = 1 KK quark. This leads to a signal consisting of only one jet, one or more leptons and missing p T . For definiteness we usually choose the inverse radius of compactification to be R − 1 = 500 GeV , which sets the scale of the lowest lying KK states. We show on a case-by-case basis (depending on the number of leptons in the final state) that with 10 fb −1 integrated luminosity at the LHC with s = 14 TeV this signal can be detected over the SM background by imposing appropriate kinematic cuts. We record some of the expectations for a possible intermediate LHC run at s = 10 TeV and also exhibit the integrated luminosity required to obtain a 5 σ signal as a function of R −1 .

Universal extra dimension: Violation of Kaluza-Klein parity

The minimal universal extra dimension (mUED) model respects the Kaluza-Klein (KK) parity $(\ensuremath{-}1{)}^{n}$, where $n$ is the KK number. However, it is possible to have interactions located at only one of the two fixed points of the ${S}_{1}/{\mathcal{Z}}_{2}$ orbifold. Such asymmetric interactions violate the KK parity. This kills the cold dark matter component of UED but also removes the upper bound on the inverse compactification radius, and thus nonobservation of the KK excitations even at the Large Hadron Collider does not necessarily invalidate the model. Apart from the decay of the lightest $n=1$ KK excitation, this leads to collider signals which are markedly different from those in the mUED scenario. The phenomenological consequences of such KK-parity violating terms are explored.

A mechanism for Kaluza–Klein number violation in UED and implications for LHC

We extend our previous analysis on a model where the Higgs does not propagate into an otherwise universal extra dimension. Previously, we computed the cross section for the pair production of Kaluza–Klein excitations of the top quark based on mixing in the Yukawa interactions between the zero-mode top quark and its lowest-lying Kaluza–Klein excitations. In this work, we show that there is also violation of tree-level Kaluza–Klein number conservation in the gauge sector. This allows Kaluza–Klein excitations of the fermions to be produced singly, and opens up new decay channels in the gauge sector. Here, we compute the cross section for the production of the lowest-lying Kaluza–Klein excitations of the top and bottom quarks in the non-universal Higgs model at the Large Hadron Collider, and consider their subsequent decays, including effects from mixing in the gauge sector. The effect is quite large: for example, the pair production of Kaluza–Klein excitations of the bottom quark leads to a pair of top quarks plus a pair of charged weak gauge bosons. Since the production is via the strong interaction, such final states stand out well against the Standard Model background, and are observable at the LHC for a wide range of compactification scales.

Collider implications of a nonuniversal Higgs boson

We consider in detail the possibility that the Higgs is wholly or partially excluded from propagating into one otherwise universal extra dimension. This exclusion of the Higgs from propagating into an otherwise universal extra dimension violates tree-level Kaluza-Klein number conservation in the Yukawa interactions. As a consequence, there is inter-mode mixing between fermions. For example, zero-mode fermions mix with their associated Kaluza-Klein excitations. This is in contrast to the original universal extra dimensions scenario, in which conservation of Kaluza-Klein number prohibits such inter-mode mixing. Inter-mode mixing is especially significant for the top quark, since its mass ($171.4\ifmmode\pm\else\textpm\fi{}2.1\text{ }\text{ }\mathrm{GeV}$) is approximately one-half the current Tevatron mass bound ($\ensuremath{\sim}350\char21{}400\text{ }\text{ }\mathrm{GeV}$) for Kaluza-Klein excitations of quarks propagating into universal extra dimensions. We compute the effects that mixing among the zero-modes and lowest-lying Kaluza-Klein excitations has on the lightest third-generation charge $2/3$ quark mass eigenvalue in the nonuniversal Higgs model with one otherwise universal extra dimension. Another consequence of the inter-mode mixing is that the Kaluza-Klein excitations of the fermions can decay to a zero-mode Higgs and a corresponding zero-mode fermion. As a result, the pair production of Kaluza-Klein excitations of the top quark would lead to two zero-mode Higgs bosons plus a zero-mode top quark/antiquark pair. We compute the cross section that the nonuniversal Higgs model contributes to Higgs production at the Large Hadron Collider. The effect is quite large: For example, the Kaluza-Klein contribution to Higgs production is comparable to or larger than the Standard Model contribution, depending on the Higgs mass, for compactification scales up to about 600 GeV.

THE PHENOMENOLOGY OF UNIVERSAL EXTRA DIMENSIONS AT HADRON COLLIDERS

Theories with extra dimensions of inverse TeV size (or larger) predict a multitude of signals which can be searched for at present and future colliders. In this paper, we review the different phenomenological signatures of a particular class of models, universal extra dimensions, where all matter fields propagate in the bulk. Such models have interesting features, in particular Kaluza–Klein (KK) number conservation, which makes their phenomenology similar to that of supersymmetric theories. Thus, KK excitations of matter are produced in pairs, and decay to a lightest KK particle (LKP), which is stable and weakly interacting, and therefore will appear as missing energy in the detector (similar to a neutralino LSP). Adding gravitational interactions which can break KK number conservation greatly expands the class of possible signatures. Thus, if gravity is the primary cause for the decay of KK excitations of matter, the experimental signals at hadron colliders will be jets + missing energy, which is typical of supergravity models. If the KK quarks and gluons decay first to the LKP, which then decays gravitationally, the experimental signal will be photons and/or leptons (with some jets), which resembles the phenomenology of gauge mediated supersymmetry breaking models.

Monojet and single photon signals from universal extra dimensions

The usual universal extra dimensions scenario does not allow for single production of first level Kaluza-Klein (KK) excitations of matter due to the KK number conservation. However, if the matter fields are localized on a fat brane embedded in a higher dimensional space, matter-gravitation interactions violate KK number, and the production of single KK excitations becomes possible. In this paper we analyze the production of a single KK matter excitation together with a graviton in the final state, and study the potential for discovery at the Tevatron and Large Hadron Collider.

Non-Perturbative Aspects of Kaluza--Klein Modes in Five-Dimensional Supersymmetric QCD on S1

We study the stability of Kaluza-Klein (KK) modes in five-dimensional N=1 supersymmetric QCD compactified on S^1 using the D3-brane probe realization. We find a phenomenon in which the quark KK mode with the KK number n=1 decays while other KK modes are stable. This is contrary to the ordinary assumption that the state with n=1 is the most stable in quark KK modes. In addition, we show that a massive gauge singlet state carrying the KK number exists stably. This provides a proper candidate for dark matter.

Is the lightest Kaluza–Klein particle a viable dark matter candidate?

In models with universal extra dimensions (i.e., in which all Standard Model fields, including fermions, propagate into compact extra dimensions) momentum conservation in the extra dimensions leads to the conservation of Kaluza–Klein (KK) number at each vertex. KK number is violated by loop effects because of the orbifold imposed to reproduce the chiral Standard Model with zero modes, however, a KK parity remains at any order in perturbation theory which leads to the existence of a stable lightest KK particle (LKP). In addition, the degeneracy in the KK spectrum is lifted by radiative corrections so that all other KK particles eventually decay into the LKP. We investigate cases where the Standard Model lives in five or six dimensions with compactification radius of TeV −1 size and the LKP is the first massive state in the KK tower of either the photon or the neutrino. We derive the relic density of the LKP under a variety of assumptions about the spectrum of first tier KK modes. We find that both the KK photon and the KK neutrino, with masses at the TeV scale, may have appropriate annihilation cross sections to account for the dark matter, Ω M∼0.3 .

New signal for universal extra dimensions

In the universal extra dimensions (UED) scenario, the tree level masses of the first level Kaluza–Klein (KK) excitations of Standard Model particles are essentially degenerate. Radiative corrections will, however, lift this degeneracy, allowing the first level excitations to decay to the lightest KK particle (LKP), which is the γ∗. KK number conservation implies that the LKP is stable. Then, since the SM particles radiated during these decays are rather soft, the observation of KK excitations production and decay in collider experiments will be quite difficult. We propose to add to this model KK number violating interactions mediated by gravity, which allow the γ∗ to decay to a photon and a KK graviton. For a variety a models and a large range of parameters, these decays will occur within the detector. Thus, pair production of KK excitations will give rise to a striking collider signal, consisting of two hard photons plus large missing energy (due to escaping gravitons). We evaluate the cross-section for these signals at the Tevatron and LHC, and derive the reach of these colliders in the search for universal extra dimensions.

Bosonic supersymmetry? Getting fooled at the CERN LHC

We define a minimal model with universal extra dimensions, and begin to study its phenomenology. The collider signals of the first Kaluza-Klein (KK) level are surprisingly similar to those of a supersymmetric model with a nearly degenerate superpartner spectrum. The lightest KK particle (LKP) is neutral and stable because of KK parity. KK excitations cascade decay to the LKP yielding missing energy signatures with relatively soft jets and leptons. Level 2 KK modes may also be probed via their KK number violating decays to standard model particles. In either case we provide initial estimates for the discovery potential of the Fermilab Tevatron and the CERN Large Hadron Collider.

Probes of universal extra dimensions at colliders

In the universal extra dimensions model of Appelquist, Cheng, and Dobrescu, all of the standard model fields are placed in the bulk and thus have Kaluza-Klein (KK) excitations. These KK states can only be pair produced at colliders due to the tree-level conservation of the KK number, with the lightest of them being stable and possibly having a mass as low as $\ensuremath{\simeq}350--400 \mathrm{GeV}.$ After calculating the contribution to $g\ensuremath{-}2$ in this model we investigate the production cross sections and signatures for these particles at both hadron and lepton colliders. We demonstrate that these signatures critically depend upon whether the lightest KK states remain stable or are allowed to decay by any of a number of new physics mechanisms. These mechanisms which induce KK decays are studied in detail.

Bounds on universal extra dimensions

We show that the bound from the electroweak data on the size of extra dimensions accessible to all the standard model fields is rather loose. These "universal" extra dimensions could have a compactification scale as low as 300 GeV for one extra dimension. This is because the Kaluza-Klein number is conserved and thus the contributions to the electroweak observables arise only from loops. The main constraint comes from weak-isospin violation effects. We also compute the contributions to the S parameter and the $Zb\bar{b}$ vertex. The direct bound on the compactification scale is set by CDF and D0 in the few hundred GeV range, and the Run II of the Tevatron will either discover extra dimensions or else it could significantly raise the bound on the compactification scale. In the case of two universal extra dimensions, the current lower bound on the compactification scale depends logarithmically on the ultra-violet cutoff of the higher dimensional theory, but can be estimated to lie between 400 and 800 GeV. With three or more extra dimensions, the cutoff dependence may be too strong to allow an estimate.