Minimal Universal Extra Dimensions

Highly degenerate spectra associated with universal extra dimensions (UED) provide an interesting phenomenology not only from the point of view of cosmology and astrophysics, but also for colliders. We study these exotic signals for the simplest case, called minimal UED, where it is natural to find slow charged particles, displaced vertices, tracks with non-vanishing impact parameters, track kinks, and even vanishing charged tracks.


Introduction
Minimal universal extra dimensions (mUED) is defined as the minimum consistent extension of the standard model (SM) with additional spatial dimensions. All the particles propagate in one flat, compact extra dimension compactified on an S 1 /Z 2 orbifold of size 10 −18 m or smaller [1] [2].
The properties of the model depend on only one new parameter at tree level, the size of the extra dimension, R. This model is non renormalizable, and one needs to introduce a cut-off, Λ, that we will fix to the standard value ΛR = 20 [3]. The other free parameter of this model is the last free parameter of the SM: the Higgs mass m h . In this model, the particle spectrum is naturally highly degenerate. Inside the allowed region of the parameter space of mEUD by standard cosmology, the lightest Kaluza-Klein (KK) particle (LKP) and the next-to-lightest KK particle (NLKP) are the KK gauge boson, B 1 , and the graviton, G 1 , with maximal mass splittings of ∼ 1GeV [4]. The LKP is completely stable by KK parity and the lifetime of the NLKP is given by the formula: where M P is the reduced Planck scale M P ≡ (8πG N ) −1/2 ≃ 2.4 × 10 18 GeV. The b factor is of order one and depends on which particle is the lightest one: b = 10 cos 2 θ W /3 ≃ 2.54 for the B 1 → G 1 γ decay, and b = 2 cos 2 θ W ≃ 1.52 for the G 1 → B 1 γ decay [5] (θ W is the weak mixing angle, cos 2 θ W ≃ 0.76). The lifetime of these NLKPs is longer than the age of the Universe for compactification scales 795 GeV < R −1 < 820 GeV. This region is particularly important for G 1 LKPs (R −1 < 809 GeV). In this region of parameter space, the thermal B 1 abundance has the preferred value observed for the non-baryonic dark matter (for Higgs masses 180 GeV < m h < 215 GeV), and it is not excluded by present observations (see Ref. [4,6] and Fig. 3).

Constraints
The size of the extra dimension has an upper bound from precision electroweak measurements: R −1 > ∼ 250 GeV [2,7], with other low energy constraints similar or weaker [8,9]. Particle physics alone does not place any lower bound on R, but the thermal relic density of LKPs grows with R −1 , and LKPs would overclose the universe for R −1 > 1.5 TeV [6,10,11,12,13,14], providing strong motivation for considering weak-scale KK particles. Direct contrains on the standard model Higgs boson mass apply to mUED requiring m h > 114.4 GeV at 95% CL [15]. In contrast, however, the indirect bounds on m h are significantly weakened relative to the standard model, requiring only m h < 900 GeV for R −1 = 250 GeV and m h < 300 GeV for R −1 = 1 TeV at 90% CL [7]. However, if m h > 245 GeV, the lightest KK particle is the charged higgs boson, whose relic abundace rules out the model unless the reheat temperature is very low.

Lightest particles
Early studies of UED focused on the line in model parameter space defined by m h = 120 GeV [16] and neglected the existence of the KK graviton G 1 [10,17]. Given these assumptions, for R −1 > ∼ 250 GeV, the LKP is the hypercharge gauge boson B 1 , and these studies therefore focused on missing energy signals at colliders and weakly-interacting massive particle (WIMP) dark matter for cosmology. These predictions are similar to those from supersymmetry with R-parity conservation. UED with KK-parity and supersymmetry with R-parity predict different collider event rates for similar spectra, and the different spins of partner particles may be distinguished through, for example, indirect dark matter detection in positrons [17]. Nevertheless, the difficulty of distinguishing UED and supersymmetry has attracted much attention and been a fertile testing ground for future experiments, especially the Large Hadron Collider (LHC) [18].
More recent studies have shown that framework of UED is far richer than indicated above. First, it was noted that the KK graviton G 1 necessarily exists in any UED model and may be the LKP, leading not to WIMP dark matter, but to superWIMP dark matter, with a completely different set of cosmological and astroparticle signatures [5,19,20]. Second, studies have now emphasized that, by relaxing the constraint m h = 120 GeV and considering higher values, KK Higgs bosons may become lighter than the B 1 . That both of these possibilities may be realized in a general UED model is, perhaps, not surprising. Remarkably, however, all of these complexities arise even in the extremely constrained framework of mUED. Any one of the G 1 , B 1 , and the charged Higgs boson H ± 1 may be the LKP, leading to many different "phases" of parameter space with qualitatively distinct signatures. The "triple point,"

Exotic collider phenomenology associated with long-lived particles
The degeneracies throughout the mUED phase diagram are typically of 1% or 0.1%. These degeneracies suppress NLKP decay widths, such that NLKPs produced in colliders may decay at points macroscopically separated from the interaction point. In fact, if we wet aside the KK graviton G 1 and cosmological considerations, mUED supports 4 distinct standard model (NLKP, LKP) combinations, or phases, as it is shown in Fig. 1. The NLKP decay lengths throughout parameter space are given in Fig. 2.
In addition, strongly-interacting KK particles may be produced with large rates at the LHC since the KK spectrum is highly degenerate. Long-lived NLKP tracks will therefore presumably be most easily identified in the cascade decays of KK quarks and gluons. Such events will be characterized by many jets and missing transverse energy, which will satisfy trigger criteria, and the jets will fix the interaction point. The possible signals are [4]: • Phase 1: Prompt decays l 1 R → B 1 l R , where l = e, µ, τ , the mass splitting between KK states is ∆m ∼ O(GeV), and the final state lepton is consequently very soft.
• Phase 2: Decays H ± 1 → B 1 ff ′ , where ff ′ = e + ν e , µ + ν µ , ud, τ + ν τ , cs, where the decay length is cτ > ∼ 100 nm (for R −1 < ∼ 1400 GeV) and may be effectively infinite for collider phenomenology. Again ∆m ∼ O(GeV), and the final state fermions are very soft. Depending on the observability of the final state fermions, the exotic signatures could include non-prompt decays producing displaced vertices, tracks with non-vanishing impact parameters, track kinks, or even disappearing charged (H ± 1 ) tracks that mysteriously vanish after passing through only part of the detector. In the parameter region where the H ± 1 is effectively stable, it may be produced at low velocities, resulting in time-of-flight anomalies and highly-ionizing tracks.
• Phase 3: Decays B 1 → H ± 1 ff ′ , where the ff ′ pairs are as in Phase 2, with decay length typically satisfying cτ > ∼ 10 mm (except in a tiny region, in which could be even shorter than 10µm), and again ∆m ∼ O(GeV), and the final state standard model fermions are very soft. The possible signatures are as above, with the exception that, since the NLKP is neutral and the LKP is charged in this case, NLKP events could instead be seen as charged (H ± 1 ) tracks that mysteriously appear somewhere in the detector. Bckg g- Figure 3: The cosmologically preferred region of the complete phase diagram of mUED. The G 1 has been included, and the dark shaded regions are excluded by the cosmological constraints on stable charged relics, the diffuse photon flux, and WIMP overproduction, as indicated. In the preferred region, the light shaded region is from Ref. [6] and shows where the B 1 thermal relic density is within 2σ of the WMAP central value for non-baryonic dark matter. Contours of constant decay length cτ = 10 µm, 100 µm, 1 mm, . . . , 1 m, 10 m are also plotted (only the lowest few are labeled) [4].

Conclusions
Taking into account these collider signatures, it is interesting to study the KK graviton, G 1 , the nature of the dark matter (DM) in the model, and the consequences of late decays in cosmology or astrophysics. It has been shown that long-lived particles [5,21] have associated a large number of possible astrophysical signatures, such as modifications of light element abundances [22,23], anomalies in the cosmic microwave background [24], deviations from the cold DM power spectrum [25,26,27], modifications in the reionization history [28] or anomalies in cosmic ray spectra [29]. The analysis of all these signals, complements other astrophysical searches [30] and related collider experiments [31,32].
One of these signals may be the first evidence of this scenario. At the same time, they introduce important constraints to the model as we have briefly commented. For a low enough reheating temperature after inflation, all 4 phases, even Phases 3 and 4 with charged LKPs, are viable. On the contrary, much of the phase diagram is excluded if one assumes a standard cosmology with reheat temperature above R −1 /25. The final results are given in Fig. 3. Phases 3 and 4 are excluded by bounds on stable charged particles, Phases 1 and 2 with R −1 < 810 GeV are excluded by bounds from the observed diffuse MeV photon flux, and Phases 1 and 2 with high R −1 are excluded XXIII International Symposium on Lepton and Photon Interactions at High Energy, Aug 13-18, 2007, Daegu, Korea because WIMPs are overproduced through thermal freeze-out.
The resulting cosmologically preferred region is bounded on all sides as it can be seen in Fig. 3. In this region the Higgs boson mass lies in the range 180 GeV < ∼ m h < ∼ 245 GeV, which is allowed and implies the "golden" 4 lepton signatures for Higgs bosons at the LHC. The compactification radius satisfies 810 GeV < ∼ R −1 < ∼ 1400 GeV and The LKP mass is approximately in this range, and the heaviest n = 1 KK particle is never heavier than 320 GeV, which means that KK particles will be copiously produced at the LHC. On the contrary, none of these new particles would be produced directly at the International Linear Collider operating at center of mass energies below 1.5 TeV. The decay H ± 1 → B 1 ff ′ has associated decay lengths cτ > ∼ 4 µm, without upper bound. Generically, then, long-lived tracks are expected at the LHC. This phenomenology is very distinctive of mUED in relation to other theories beyond the standard model such as supersymmetry, where these signatures require fine-tunning among the different parameters of the model.