A bound on Universal Extra Dimension Models from up to 2fb^{-1} of LHC Data at 7TeV

The recent up to 2fb^{-1} of data from the ATLAS and CMS experiments at the CERN Large Hadron Collider at 7TeV put an upper bound on the production cross section of a Higgs-like particle. We translate the results of the H ->WW ->l nu l nu and H ->gamma gamma as well as the combined analysis by the ATLAS and CMS into an allowed region for the Kaluza-Klein (KK) mass M_{KK} and the Higgs mass $M_H$ for all the known Universal Extra Dimension (UED) models in five and six dimensions. Our bound is insensitive to the detailed KK mass splitting and mixing and hence complementary to all other known signatures.


Introduction
The ATLAS and CMS experiments at the CERN Large Hadron Collider (LHC) have presented their latest results for the 2 fb −1 of data at the center of mass energy 7 TeV at the XXV International Symposium on Lepton Photon Interactions at High Energies (Lepton Photon 11), Mumbai, India, 22-27 August 2011. One of the most remarkable among them is the bound on the Higgs mass in the Standard Model (SM). A combined analysis of the ATLAS experiment excludes the existence of the SM Higgs in mass ranges 146 GeV < M H < 232 GeV, 256 GeV < M H < 282 GeV, and 296 GeV < M H < 466 GeV within the 95% Confidence Level (CL) based on 1.0-2.3 fb −1 data [1] and that of the CMS experiment excludes 145 GeV < M H < 216 GeV, 226 GeV < M H < 288 GeV, and 310 GeV < M H < 400 GeV within the 95% CL based on 1.1-1.7 fb −1 data [2]. Further the production cross section of a Higgs-like particle, a particle that decays the same way as the SM Higgs, is severely constrained by these data in the still-allowed regions, namely light 115 GeV < M H < 145 GeV, middle 288 GeV < M H < 296 GeV, and heavy M H > 466 GeV windows.
One of the biggest advantages of the UED models is the existence of a natural Dark Matter (DM) candidate, the Lightest KK Particle (LKP) [13]. The 6D UED models have further advantages of the requirement of the number of generations to be (zero modulo) three [14] and the assurance of the proton stability [15].
There exist several bounds on the 5D mUED model, within which the brane-localized interactions are assumed to be vanishing at the 5D Ultra-Violet (UV) cutoff scale Λ 5D . The latest analysis on DM relic abundance including the effects from second KK resonances gives the preferred KK scale at around M KK ∼ 1.3 TeV [16]. It is noted that the first KK charged Higgs becomes the LKP when M H 240-300 GeV, depending on the KK scale [17]. The electroweak precision data suggests that the KK scale should be M KK 800 GeV (300 GeV M KK 400 GeV) at the 95% CL for M H = 115 (700) GeV [18,19,20]. The observed branching ratio of B d → X s γ confines the KK scale as M KK > 600 GeV [21] at the 95% CL. Recent study puts a constraint M KK > 600 GeV for 10 < Λ 5D /M KK < 40 at the 95% CL {} [22], from the ATLAS SUSY search result in multijet+E miss T with 1 fb −1 data [23]. 2 We see that current LHC bound from jets plus missing E T is not severe even for the most constraint mUED. This is because we have typically smaller mass splitting between the LKP and other new particles than the one between the lightest supersymmetric particle and other sparticle in the minimal supersymmetric standard model.
We note that all of these bounds are strongly dependent on the mass splitting and mixing within the first KK level and therefore on the boundary mass structure which is derived from the above-mentioned assumption that all of them are zero at the 5D UV cutoff scale. The bound on the KK scale put in this Letter is complementary to them in the sense that this is depending only on the Higgs mass. That is, our bound is insensitive to the boundary masses if they are smaller than the KK scale, as is necessary to have a higher dimensional picture at all. 1 In [11] the terminology "real projective plane" is employed for a sphere with its antipodal points being identified. In order to distinguish [11] from [9], we call the former the Projective Sphere (PS). We note that the PS and S 2 UED models have no orbifold fixed point and hence no localized interaction on it.
2 Inclusion of the decay channel into KK Higgs, if allowed, might significantly affect the result. We thank K. Tobioka on this point.

Procedure to obtain the bound
The ATLAS and CMS groups have shown the results for the combined analyses for the ratio σ 95% pp→H /σ SM pp→H as a function of the Higgs mass M H , where σ 95% pp→H is an upper bound on the production cross section of a particle that decays the same as the SM Higgs, at the 95% CL [1,2]. In our case the constrained production cross section is that of the UED Higgs. In UED models, a process can be affected by KK-loops when it is loop-induced in the SM. In particular, the dominant Higgs production channel via the gluon fusion process can be greatly enhanced, see [12] and references therein. For middle and heavy Higgs mass regions, the constraint is mainly from the H → W W and ZZ channels, which are dominated by the tree-level SM processes and therefore the result of the combined analysis can be applied directly.
For the light Higgs mass region, the severest bound on σ 95% pp→H /σ SM pp→H comes from H → W W → lνlν or H → γγ. The latter is loop-induced in the SM and can be affected by the KKloops. Further, the loop-induced decay into gluons is not negligible in this region in computation of the total decay width. Therefore, we cannot trust the combined analysis which assumes that the branching ratios are not changed from the SM. In the light mass range, we apply the CMS bounds on σ 95% pp→H→γγ /σ SM pp→H→γγ and σ 95% pp→H→W W /σ SM pp→H→W W [2]. For the Higgs production, we focus on the the gluon fusion process via the (KK) top quark loops, which is the dominant Higgs production channel in the SM and the UED models [12,24,25,26]. The parton level cross section of each modelσ model gg→H iŝ whereŝ is the parton level center-of-mass-energy-squared and Γ model H→gg is the partial decay width into a pair of gluons in each model: where α s is the QCD coupling strength and v EW is the Higgs vacuum expectation value 246 GeV and K is the K-factor to take into account the higher order QCD corrections, whose NNLO value is 1.9 at the relevant energies, see e.g. Ref. [27]. When we consider a ratio such as σ 95% pp→H /σ SM pp→H from the gluon fusion process, the overall K-factor does not influence the result. However it contributes to the decay branching ratios of the light Higgs boson non-negligibly. For each model, the loop function J model t describes the contributions of all the zero and KK modes for the top quark in the triangle loops: where I andĨ are given by the n model (j) counts the number of degeneracy: n S 2 /Z2 (j) = j + 1, j, n PS even (j) = 2j + 1, 0, n PS odd (j) = 0, for j = even, 2j + 1, for j = odd, and we write the KK top and W masses (X = t, W ) with M KK being the first KK mass: M KK = 1/R for the S 1 /Z 2 (mUED), an interval (DH), and T 2based compactifications (namely T 2 /Z 2 , T 2 /(Z 2 × Z 2 ), T 2 /Z 4 and RP 2 ) and being M KK = √ 2/R for the S 2 -based ones (namely S 2 /Z 2 , PS and S 2 ). The range of the KK summation reflects the structure of each extra dimensional background. 3 The factor √ 2ε 1 in Eq. (5) is equal to 2 √ 2/π ∼ 0.90. Readers who want more explanations on the above expressions should consult Ref. [12].
As is mentioned above, we compute the decay rate into a photon pair, following [26]. The result is 3 The origin of the factor 2 in front of each KK summation is the fact that there are both left and right handed (namely, vector-like) KK modes for each chiral quark zero mode corresponding to a SM quark. where with L(a, b, c, d, e; λ 1 , The  Table 1. Let us briefly explain this treatment hereafter. For more details, see Ref. [12]. Since the electroweak symmetry is broken by the Higgs mechanism in the SM and UED models (except for the DH model), the gluon fusion process is described by a dimension-six operator at lowest in 4D point of view after KK expansion. This means that the calculation is UV logarithmic-divergent (convergent) in six (five) dimensions. 4 Therefore we need to put an upper limit of the summation over KK indices in 6D. We do it by adopting the NDA. In both the T 2 and S 2 -based geometries, the most stringent bound turns out to be the one from the perturbativity of the U (1) Y gauge interaction, which results in the following allowed regions of KK indices [12]: where the index m for the S 2 -case discriminates the degenerate states of each j-th level. The cutoff scale of 6D UED theory Λ 6D must be lower than that in Eq. (28) or (29). In Table 1, we list the values that we take. Based on the knowledge sketched above, we can evaluate the total cross section of the Higgs production of the UED models σ model pp→H and the ratio to that of the SM σ model pp→H /σ SM pp→H to be compared to the experimental result.

Results
First, we show our results for the light region: 115 GeV < M H < 145 GeV. We apply the CMS bounds on H → γγ and H → W W channels that are dominant in this range. In Fig. 1, we list the contour plots for the excluded region in the M KK -M H plane for various UED models in 5 and 6 dimensions. Plots for the maximum and minimum choices of the UV cutoff scale are presented for the 6D UED models. In general, UED models enhance Higgs production via gluon fusion and reduce the Higgs decay into a pair of photons. Therefore, σ UED pp→H→γγ receives nontrivial contributions from such effects. Typically, the enhancement of Higgs production cross section overcomes the suppression of the di-photon branching ratio in the H → γγ excluded range (with orange and red colors), whereas the region for smaller M KK is not excluded because of the suppression of the di-phton branching ratio. (For example, in the case of S 2 UED, the di-photon cross section is suppressed for M KK 400 GeV.) We find that all the suppressed region is already excluded by W W channel. It is natural that the lower the cutoff scale becomes, the more the allowed parameter region is enlarged since smaller numbers of KK tops contribute to the process. In 6D, we have more light KK top quarks running in the loop, and get stronger constraints than in 5D. The BR(H → W W ) is also affected by the enhancement of the total Higgs decay rate due to the increase of H → gg.
Second, we move on to the middle region: 288 GeV < M H < 296 GeV. The Standard Model is still allowed in this range whereas we find that all the UED models below M KK = 1.4 TeV is excluded.
Finally, let us discuss the heavy region: M H > 446 GeV. We choose severer bound on σ 95% pp→H /σ SM pp→H between ATLAS and CMS data for each M H . That is, we use ATLAS and CMS bounds for M H < 500 GeV and M H ≥ 500 GeV, respectively. In Fig. 2 we plot our results. We note that in all the allowed region, we get M H < 2M KK and hence the Higgs does not decay into a pair of KK particles. Now let us comment on the DH model. In this model, the bound is put only on M KK (= M H ) and the theoretical value of the ratio σ DH pp→H /σ SM pp→H decreases when one increases M KK , while the experimental upper bound σ 95% /σ SM is an increasing function of M H in the high-mass region. The cross-over occurs at M KK = 480 GeV which gives σ DH pp→H /σ SM pp→H 1.2 and we conclude that the allowed parameter region of M KK is: In the M KK region of 110 GeV < M KK < 149 GeV and 206 GeV < M KK < 300 GeV, the value of σ DH pp→H /σ SM pp→H grows significantly and thereby these regions are rejected by the CMS result at the 95% CL. Noting that the indirect electroweak constraint gives 430 GeV < M KK < 500 GeV at the 90% CL [4], the allowed region of M KK roughly lies between 480 GeV M KK 500 GeV.

Summary and Discussions
In this Letter we have constrained the UED models in 5D and 6D by use of the latest ATLAS and CMS bounds on the Higgs production cross section. The bound on 6D UED is severer than that on 5D UED because 6D KK mass spectrum is denser than that in 5D and therefore the KK top modes contribute to the gluon fusion process larger. The KK (Higgs) mass of the Dirichlet Higgs model is pinned down at around 500 GeV.
In the light mass range 115 GeV < M H < 145 GeV, one of the dominant constrains on the Higgs production cross section is coming from the H → γγ decay, which is reduced when KK scale is not large, due to the interference between the SM gauge boson and KK top loops, with some corrections from SM top and KK gauge bosons. We have taken into account the CMS constraints from H → γγ and H → W W → lνlν instead of the combined analysis. We find in this light region that the Higgs mass above 140 GeV is already excluded in the 5D and 6D T 2 /Z 4 UED models, while the mass above 130 GeV is ruled out in other 6D UED models, both within a reasonably small KK scale < 1.4 TeV.
Our analyses on the 6D UED models cannot evade ambiguities from the NDA, but the plots in Figs. 1 and 2 imply that the dependence on the cutoff is rather mild 10%. For a low cutoff scale, there can also be contributions from higher dimensional operators that must be taken into account. We have ignored these possible contributions in our analysis.
In both 5D and 6D cases, the bound is insensitive to the detailed boundary mass structure. In this sense this constraint is complementary to other ones such as the relic abundance of the LKP and the M T 2 analysis of the decay of the colored KK into the LKP.
When the KK scale is not much heavier than the weak scale 246 GeV, the UED models tend to prefer much heavier Higgs mass than in the SM in order to cancel the KK top loops in the T -parameter. (This contribution has the same origin as the gluon fusion process discussed in this Letter.) In this regard it would be important to put an experimental bound for the Higgs mass beyond 600 GeV.
There is the triviality bound if the Higgs is heavy and the UED scale is light which are being studied by the authors, along with the vacuum stability bound for the case of light Higgs, and will be presented in a separate publication.