Enriching the exploration of the mUED model with event shape variables at the CERN LHC

We propose a new search strategy based on the event shape variables for new physics models where the separations among the masses of the particles in the spectrum are small. Collider signature of these models, characterised by low $p_T$ leptons/jets and low missing $p_T$, are known to be difficult to look for. The conventional search strategies involving hard cuts may not work in such situations. As a case study, we have investigated the hitherto neglected jets + missing $E_T$ signature -known to be a challenging one - arising from the pair productions and decay of $n =1$ KK-excitations of gluons and quarks in the minimal Universal Extra Dimension (mUED) model. Judicious use of the event shape variables, enables us to reduce the Standard Model backgrounds to a negligible level . We have shown that in mUED, $R^{-1}$ upto $850 ~\rm GeV$, can be explored or ruled out with 12 fb$^{-1}$ of integrated luminosity at the 7 TeV run of the LHC. We also discuss the prospects of employing these variables for searching other beyond standard model physics with compressed or partially compressed spectra.


Introduction
One of the main goals of the ongoing LHC experiment at CERN is to find out any new dynamics that could be operative at the energy scale of Tera electron volts (TeV) among the elementary particles.
Apart from the search of Higgs boson, both the ATLAS and the CMS experiments are engaged in looking for the signals of scenarios beyond the Standard Model. Among these, models defined in one or more space-like extra dimensions need special attention. These models can be divided broadly into two classes. In models proposed in [1] and [2], all the Standard Model (SM) fields are confined in a 1+3 dimensional sub-space of a larger space-time manifold, while the Gravitational interaction can perceive the full space time manifold. After compactification of the extra space like dimensions, the effective four dimensional theory consists of towers of gravitons interacting with SM fields. However, we are interested in a class of models wherein some or all of the SM fields can access the extended space-time manifold [3,4]. Such extra-dimensional scenarios could lead to a new mechanism of supersymmetry breaking [5], relax the upper limit of the lightest supersymmetric neutral Higgs [6], address the issue of fermion mass hierarchy [7], provide a cosmologically viable dark matter candidate [8], interpret the Higgs as a quark composite leading to a successful EWSB without the necessity of a fundamental scalar or Yukawa interactions [9], and lower the unification scale down to a few Tev [10,11]. Our concern here is a particularly interesting framework, called the minimal Universal Extra Dimension (mUED) scenario, characterized by a single flat extra dimension, compactified on an S 1 /Z 2 orbifold (with radius of compactification, R) [3]. This extra space like dimension is accessed by all the SM particles. From a 4-dimensional viewpoint, every field in the SM will then have an infinite tower of Kaluza-Klein (KK) modes, each mode being identified by an integer, n, called the KK-number. The zero modes (n = 0) are identified as the corresponding SM states. The orbifolding is essential to ensure that fermion zero modes have a chiral representation. But it has other consequences too. First, the physical region along the extra direction y is now smaller [0, πR] than the periodicity [0, 2πR], so the KK number (n) is no longer conserved. What remains actually conserved is the even-ness and odd-ness of the KK states, ensured through the conservation of KK parity, defined by (−1) n . Secondly, Lorentz invariance is also lost due to compactification, and as a result the KK masses receive bulk and orbifold-induced radiative corrections [4,12]. The bulk corrections are finite and nonzero only for bosons. The orbifold corrections, which vary logarithmically with the cutoff (Λ), depend on group theoretic invariants, as well as Yukawa and quartic scalar couplings of the gauge and matter KK fields and hence are flavor-dependent. This induces a mass splitting among the different flavors of the same KK level, further to what has already been caused by the different zero mode masses. The model thus can be described by two dimensionful parameters, namely the inverse of compactification radius, R −1 and the cut-off scale, Λ. We will not present the expressions for the radiatively corrected masses of the different KK-modes of the SM particles. However, these can be easily obtained from [13]. Independent of the values of the input parameters, the lightest among the n = 1 KK states turns out to be γ 1 , the n = 1 KK-excitation of photon. Typically, if R −1 = 500 GeV, mass of γ 1 is slightly above 500 GeV, just above lie the KK leptons (L 1 , ν 1 ) and weak bosons (W ±1 , Z 1 ) in the region of 500-550 GeV, further up are the KK quarks (Q 1 L,R ) near 600 GeV, and at the peak the KK gluon, G 1 , (the heaviest) hovers around 650 GeV.
Conservation of the KK-parity ensures the lightest KK particle (LKP) is stable (hence being a natural candidate for the Dark-matter [8]) and that the level-one KK-modes would be produced only in pairs. This also ensures that the KK modes do not affect electroweak processes at the tree level. And while they do contribute to higher order electroweak processes, in a loop they appear only in pairs resulting in a substantial suppression of such contributions, thereby allowing for relatively smaller KK-spacings. In spite of the infinite multiplicity of the KK states, the KK parity ensures that all electroweak observables are finite (up to one-loop) [14] 1 , and a comparison of the observable predictions with experimental data yields bounds on the compactification radius R. Constraints on the UED scenario from the measurement of the anomalous magnetic moment of the muon [15], flavour changing neutral currents [16], Z → bb decay [17], the ρ parameter [3,18], several other electroweak precision tests [19], yield R −1 ∼ > 300 GeV.
The fact that such a small value for R −1 (equivalently, small KK spacings) is still allowed, renders collider search prospects very interesting both in the context of hadronic [20,21,13,22,23] and leptonic [24,25] colliders.
At the very outset it was realized that the signatures of the mUED model at hadron colliders has an inherent problem [4]. The signature with the largest cross-section at hadron colliders is the jets + missing transverse momenta ( E T ) which is similar to the traditional squark-gluino signal in supersymmetric (SUSY) models. There is, however, an important difference.
It has been already mentioned above that the spectrum of mUED is very much compressed. As a result, the transverse momenta/energy spectra of all the visible particles -the missing transverse momenta spectrum included-are soft. Consequently the conventional search strategies to dig out the signals of mUED from the SM backgrounds using strong cuts on visible/missing p T are not very efficient. Such cuts on the other hand are the most potent tools in the arsenal of the SUSY hunter.
Subsequently the viability of jets + E T channel has never been explored in the framework of mUED, because of the general belief that the signal of mUED in this channel will be overwhelmed by the QCD background. All the earlier analyses in the context of mUED, in fact, are either based on search of n = 2 KK-excitations [21,25] of SM particles or on the n = 1 KK-excitations giving rise to multi-leptons in association with jets and E T [13,22,23]. The bulk of the collider events stemming from such model remain unexplored till date.
In this work we focus on this hitherto neglected channel. Moreover our analysis will be restricted to the search prospects at the ongoing experiments at 7 TeV. It would be important to mention here, that both the ATLAS and the CMS collaborations have looked for the above jets + E T signature [26,27] using the accumulated data of 1.04 fb −1 from the current LHC run at 7 TeV. In principle, these analyses could be used to constrain the mUED parameters. However, the CMS/ATLAS analyses are aimed for SUSY models motivated by the minimal gravity mediated SUSY breaking (mSUGRA), where, the masses of the sparticles are well separated over most of the parameter space. As a result high p T jets/leptons and a hard E T spectrum is expected in the signal. Thus the search strategies of the LHC collaborations involve hard cuts on p T and E T to suppress the huge SM backgrounds (including QCD). For example, only those events are retained which have E T greater than 100 GeV.
Moreover, the leading jet is required to have p T greater than 100 GeV.
We shall show the distributions of E T and the p T of the leading jet for a representative mUED model in a later section. They will indicate unambiguously that the signatures of this model cannot survive the hard cuts usually employed by the LHC collaborations. Thus it is quite possible that the signatures of the mUED model remain buried in current LHC data.
It should emphasized that this is a generic problem (not specific to mUED only) which confronts the search strategy for any model having a compressed mass spectrum. For example, in an unconstrained minimal supersymmetric standard model (MSSM) it is quite possible that the entire sparticle spectrum is quite compressed. Based on various theoretical motivations, models with partially compressed mass spectra have also been proposed [28,29]. It would be interesting to device an alternative search strategy for such scenarios.
In this article we will show that judicious use of the event shape variables (defined below) would be very efficient in reducing huge SM background from QCD, tt and W/Z+ jets events confronting the jets + E T signal. Using this new strategy, we could also push up the sensitivity of the current LHC experiments to the parameters of the mUED model compared to an earlier analysis using the kinematic variable M T 2 [30].
Before delving into the analysis let us briefly discuss the processes and the relevant decay cascades that contribute to the signal. We will confine to the production of n = 1 KK-level excitations only.
These particles can only be produced in pairs by the virtue of KK-parity conservation. In LHC, the colliding partons being the gluons or quarks, pair production of Q 1 L,R Q 1 L,R , G 1 G 1 , G 1 Q 1 L,R would be highly enhanced and these processes contribute to our signal significantly. Once produced, G 1 will decay to a Q 1 L,R along with a SM quark (Q 0 L,R ) with equal probabilities. Q 1 R only can decay to Q 0 R and the LKP (γ 1 ) . On the other hand, Q 1 L, decays to W ±1 or Z 1 (with Brs. 2 3 and 1 3 respectively) with a SM quark.
It may be recalled that Z 1 or W ±1 does not decay hadronically. Z 1 decay results either into ννγ 1 (with Br. of 0.5) or into l LlL γ 1 (with Br. of 0.16 for each lepton flavour). On the other hand, W 1 decays into lνγ 1 (with Brs of 0.33 for each lepton flavour). It must be emphasised here, that decay patterns and branching fractions of n = 1 KK-mode fields are independent of the mUED model parameters.
Following the above discussions one can see that the G 1 G 1 production is the source of 4 jets, while G 1 Q 1 (Q 1 Q 1 ) production leads to 3 (2) jets at the parton level. In addition, τ (coming from W 1 / Z 1 ) decay in hadronic channels will also contribute to our signal enhancing the number of jets at the parton level itself. Consequently, the pair production of n = 1 KK-gluons and quarks, would most All the previous analysis of mUED signal at the LHC were done with multi-lepton final state, which necessarily have a smaller (effective) signal cross-section. Of course, there is one advantage using the leptonic final states. The SM background rate for the multi-lepton final state is also moderate and easy to tame with more conventional kinematic cuts used in new particle searches. However, as already mentioned all kind of signals arising from a particular new physics model must be looked for. Throwing away a class of signatures which has the largest cross-section, makes the search incomplete.
In this work we have taken a strategy which remove this incompleteness and utilizes the large crosssection of jets + E T final state. The SM background in this channel (arising from QCD production of jets, tt production, W/Z + jets production) is undoubtedly challenging and orders of magnitude larger than the signal. Kinematic cuts, like lower cuts on the p T of particles in the final state or E T , which are generally used for new particle searches, are of not very effective in reducing the backgrounds. At this juncture the event shape variables, namely, α T and R T , play a crucial role in taming these huge backgrounds without affecting the signal too much.
In the next section we will in detail describe our analysis with emphasis om the event-shape variables. However, before delving into the detail, a few features on the parameters of the mUED model need our attention. Existing collider and other low energy experimental data allow values of R −1 to be higher than 300 GeV. On the other hand, the analysis of relic density of LKP dark matter sets an upper limit of 700 GeV according to [31]. However, we will not be restricted by this upper limit in the following analysis and will try to see how much one can push up the search limit with the 7 Tev run of LHC.

Analysis and Results
At the LHC, total production cross-section of G 1 G 1 , G 1 Q 1 , Q 1 Q 1 pairs are 0.03 pb, 0.66 pb and 1.21 pb respectively at the leading order (LO ) for R −1 = 700 GeV with ΛR = 40. In the absence of any next to leading order (NLO) QCD corrections to the pair production cross-sections of strongly interacting n = 1 KK-excitations in mUED, we have used only the LO signal cross-sections in our analysis. It is also worth noting that the NLO corrections to the lowest order QCD dijet cross-section is also not known. If the K-factor arising from the NLO corrections to the signal cross-section is approximately the same as that for the overall background, S/ √ B will increase by √ K. Since K is expected to be ≥ 1, the NLO cross-section is likely to give a better significance. On the other hand using a typical value of K = 1.5 for the signal, we find that even if the over all K-factor of the background is 3, the significance computed from the LO cross section will reduce by 0.9. Thus the estimates based on the LO cross sections are likely to be fairly conservative.
Signal cross-sections are estimated with the Pythia -6.4.20 [32] using the LO CTEQ6L parton distribution functions (PDF) [33], setting both the scales of PDF and α s at √ŝ whereŝ being the partonic CM energy. The dominant SM backgrounds those can give rise to jets + E T energy signature are tt+ jets, W/Z+ jets, QCD production of jets. The sub-dominant contributions come from W W + jets, W Z+ jets and ZZ+ jets productions. tt production and QCD production of jets have been estimated using Pythia, while cross-sections for the W/Z productions have been calculated using ALPGEN [34] in conjunction with Pythia 2 . The cross-section for QCD events have been computed by Pythia in two bins: (a) 25 GeV < √ŝ < 400 GeV (denoted by QCD1 in Table.1) and (b) 400 GeV < √ŝ < 1000 GeV (denoted by QCD2 in Table.1) . The contributions from other bins being negligible will not be shown any further. In our simulation using Pythia we have taken into account the effects of initial and final state radiation as well as fragmentation and hadronization. A simple toy calorimeter simulation has been implemented with the following criteria: • The calorimeter coverage is |η| < 4.5 with segmentation of ∆η ×∆φ = 0.09×0.09 which resembles a generic LHC detector.
• Jets are ordered in E T with E jet T,min = 20 GeV.
Here, η and φ are the pseudo-rapidity and azimuthal angle of the respective visible objects.
The total background cross-section overwhelms the signal by several orders of magnitude. So one needs to choose some judicious set of cuts to enhance the signal to background ratio. Dominant, SM backgrounds do not have real source of missing energy (i.e. neutrinos). Apparent p T imbalance arises from the finite detector resolution and mis-measurement of jet energies in the detector. Thus one may think that using a rather hard cut on E T could tame the SM backgrounds for the jets + E T signature.
However, due an highly compressed mUED mass spectrum, jets (in general any visible SM particle) coming from the decay of KK-quarks and gluons in case of the signal are quite soft, producing a rather soft visible p T spectra, which in turn gives rise to a soft E T spectrum. To demonstrate this, we have Consequently, one cannot require events with high p T (typically p j T > 100) [26,27]. Rejection of hard leptons in the final state would further restrict our control in reducing the SM background.
In such a situation (events with low missing energy and no lepton), event-shape variables, namely R T [35] and α T [36], are known to be very useful. The CMS collaboration has used the variable α T for controlling the background while looking for the signature of SUSY from the jets + E T data at the 7 TeV run of LHC. It has also been shown recently in [35], that the SM backgrounds to SUSY signals can be brought down to a negligible size by using R T at the LHC.
The event-shape variable, R T , is defined by: where H T is defined to be the scalar sum of p T of all jets. Here, n min j denotes the required minimum number of jets satisfying the criteria : p T > 40 GeV and |η j | ≤ 3.
In fact, R T gives us a control over the number and hardness of the reconstructed jets simultaneously.
In our case, signal events are mainly comprised of 2/3/4 partonic jets, which justifies our choice of (n min j =) 3 leading jets in defining (the numerator of ) R T .
The variable α T is defined as the ratio of the p T of the second hardest jet to the invariant mass of the two highest p T jets [36] and is well known to be very potent in reducing the QCD di-jet events in particular.
To demonstrate the usefulness of R T and α T , we will plot the distributions of these variables for signal and backgrounds in Fig. 2. It is evident from R T and α T distributions in Fig.2, that a judicious choice of these variables can isolate the signal events from the backgrounds.
We have implemented following cuts in succession to enhance the signal to background ratio.
• C2: Events with E T > 50 GeV are selected.
• C3: Events with R T ≤ 0.8 only are selected.
• C5: b-jet identification has been performed in our analysis according to the following procedure.
A reconstructed jet with |η| < 2.5 corresponding to the coverage of tracking detectors matching with a B-hadron of decay length > 0.9 mm has been marked tagged. This criteria ensures that single b-jet tagging efficiency (i.e., the ratio of tagged b-jets and the number of taggable b-jets) ǫ b ≈ 0.5 in tt events. Finally in our signal we have required the signal to be free from tagged b-jet events.
We note in passing that a trigger H T > 250 GeV like the one employed by the CMS collaboration in their α T analysis [37] of jets + E T signal can be quite efficient for our signal. However, it should be stressed that for a model where the particle spectrum is not compressed α T is one of the many variables which can distinguish the signal and the background. In fact both CMS and ATLAS collaborations have analysed LHC data without using the eventshape varibles and, in the context of mSUGRA for example, have obtained stronger constraints. In contrast for models with compressed spectra the options are rather limited and α T and/or other event shape variables may be invaluable for establishing the signal.
Let us discuss the effects of the above cuts on the signal and background. More than 90% (70 %) of QCD1 (QCD2) jets + E T events are removed by C2. Remaining events are taken care by application of C3 and C4. There is no real source of missing energy in QCD processes. The missing energy in these events arise mainly from the jet energy mis-measurements. As a result a cut of 50 GeV could kill a substantial part of this background. C3 and C4 play the pivotal role to reduce the tt, W/Z + jets events to a negligible level.In addition the veto against tagged b-jets further reduce the tt events.
We have summarised the effects of the cuts in Table. 1 .
We present the main results of our analysis in Table 2. The number of events after all cuts for 1 fb −1 luminosity, are presented in Table 2    At this point it is worthwhile to compare our results with two other similar analyses [23,30], involving signals containg one or more leptons, on exploring mUED at the LHC running at 7 TeV.
Analysis presented in [23], has used the conventional weapons of visible p T and E T distributions to fight with the SM backgrounds. However, authors in ref. [23], used the multi-lepton (2-and 3-leptons) final states in association with jets (using 2 fb −1 data at 7 TeV run of LHC) , to look for the mUED signal. Assuming 5 events to be the benchmark for discovery for a background free signal, the R −1 reach in this paper, is in the ballpark of 700 GeV, with 2 fb −1 of data. According to Ref. [23], the best reach is obtained in the tri-lepton (+ jets) channel. This is somehow expected, as the SM background rate in this channel is practically vanishing. Mass reach obtained in Ref. [23] is also very similar to what has been obtained in our analysis. In another recent work [30], authors have used a somewhat new strategy to explore the mUED parameter space again at 7 TeV run of LHC. Here kinematic varible M T 2 has been used to dig out the 1 lepton + jets signal arising from mUED, from the SM background.

Conclusion
To summarise, we have explored the possibility of discovering the mUED model at the LHC using the jets + E T channel, which among various signatures of mUED has the largest cross section. It is well known that the mass splittings among different n = 1 KK-excitations of the SM particles are generically small as they are generated by loop driven effects. As a result, typical signatures of mUED would involve relatively low p T leptons and/or jets accompanied by a soft E T spectrum (see Fig. 1).
In contrast, in nSUGRA motivated SUSY models the corresponding signals consist of jets, leptons and E T which are considerably harder. Thus the traditional strong cuts on visible or E T which are often useful in isolating SUSY and other new physics signals from the SM backgrounds, may not be very efficient while searching for n = 1 KK excitations in mUED.
For final states involving multiple leptons of moderately large p T signals of mUED may still be viable both at the LHC at 7 TeV [23,30] and 14 TeV [13,22] runs. However, the jets + E T signal with the largest cross-sections did not receive the due attention because of the apprehension that in the absence of the coventional strong cuts, this signal will be swamped by a large QCD background.
We, however, feel that this signature having the largest cross-sections, should be looked for at the LHC for a complete understanding of the mUED model. To this end we have proposed a new search strategy. In view of our generator level simulations it appears that even in the absence of the standard cuts usually employed for establishing new physics signals, a healthy signal in the above channel can be established by a judicious use of the event shape variables α T and R T .
We have generated the jets + E T signal in mUED using PYTHIA. The SM backgrounds have been estimated using ALPGEN and PYTHIA. As expected attempts to remove the SM background by applying strong cuts on p T of the jets and E T , turned out to be futile (see Figs. 1). On the other hand demanding α T to be greater than 0.56 has eventually removed all the QCD and W/Z + jets backgrounds. Additionally, demanding R T to be less than 0.85 completely killed the tt and residual W/Z + jets events (see Table 1). Requiring 10 signal events after all cuts is then sufficient to claim a discovery for this background free signal. We find that in mUED, R −1 upto 850 GeV (700 GeV) can be probed at the ongoing LHC experiments with 7 TeV center of mass energy with an integrated luminosity of 12 fb −1 (5 fb −1 ) ( Table 2). Looking at the present performance of the LHC experiments, it may be expected that this amount of data will be available by the end of 7 TeV run.
Though, we have demonstrated the utility of the event shape variables in the context of mUED, these variables can as well be used for searching a large class of new physics scenarios with compressed mass spectra.
A case in point is the unconstrained minimal supersymmetric standard model (MSSM) with a mass difference of a few hundred GeV seperating the heaviest strongly interacting superparticle and the lightest supersymmetric particle (LSP). It can be readily checked that the p T distributions and the E T distribution in a typical SUSY signal in such a scenario will be relatively soft. Consequently the signal will be rather insensetive to the SUSY searches by the ATLAS and the CMS collaborations even if the squark-gluino masses are relatively small, and cannot be constrained by the present LHC data. It will be interesting to develop an alternative search strategy based on the event shape variables for these models.
It may be recalled that it was pointed out long ago [4] that the signatures of mUED and R-parity conserving mSUGRA could be similar. However, in most versions of the MSSM like mSUGRA, the sparticle spectra are well spread out and standard hard cuts can separate the MSSM signal from the signatures of mUED. However, the compressed version of the MSSM will indeed give rise to signals very similar to the signals of mUED. It would then especially challenging to differentiate between this compressed SUSY with mUED in the jets + E T channel . Event shape variables may play a crucial role to this end.
Several authors have discussed [28,29] the possibility of partially compressed spectra in the framework of supersymmetry for various theoretical reasons. Characteristic signals at the LHC of such compressed spectra in mSUGRA type scenarios have also been discussed [28]. However, it should be noted that in neither of the models discussed above the mass spectrum is as compressed as in the mUED model. Consequently, exploration/exclusion of such models at the LHC, can still be possible using large visible/missing energy cuts. However, it would be interesting to see whether the event shape variables can extend the mass reach at the LHC in these cases. In the fiigures, P7 denotes signal with R −1 = 700 GeV and ΛR = 10.