1 Introduction

September 20, 2010

RECAPP-HRI-2010-009

Discrimination of low missing energy look-alikes at the LHC

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Regional Centre for Accelerator-based Particle Physics

Harish-Chandra Research Institute

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The problem of discriminating possible scenarios of TeV scale new physics with large missing energy signature at the Large Hadron Collider (LHC) has received some attention in the recent past. We consider the complementary, and yet unexplored, case of theories predicting much softer missing energy spectra. As there is enough scope for such models to fake each other by having similar final states at the LHC, we have outlined a systematic method based on a combination of different kinematic features which can be used to distinguish among different possibilities. These features often trace back to the underlying mass spectrum and the spins of the new particles present in these models. As examples of “low missing energy look-alikes”, we consider Supersymmetry with R-parity violation, Universal Extra Dimensions with both KK-parity conserved and KK-parity violated and the Littlest Higgs model with T-parity violated by the Wess-Zumino-Witten anomaly term. Through detailed Monte Carlo analysis of the four and higher lepton final states predicted by these models, we show that the models in their minimal forms may be distinguished at the LHC, while non-minimal variations can always leave scope for further confusion. We find that, for strongly interacting new particle mass-scale (), the simplest versions of the different theories can be discriminated at the LHC running at within an integrated luminosity of () .

1 Introduction

The Large Hadron Collider (LHC) marks the beginning of an era where physics at the TeV scale can be probed at an unprecedented level. One important goal of such investigations is to see whether the standard model (SM) of elementary particles is embedded within a set of new laws which make their presence felt at the TeV scale. Several proposals of such new physics (NP) have been put forward, with motivations ranging from the naturalness problem of the Higgs mass to solving the dark matter puzzle.

Quite a few of such models systematically predict a host of new particles occurring in correspondence with those present in the SM. In addition, the need to accommodate an invisible, weakly interacting particle qualifying as a dark matter candidate often invites the imposition of a symmetry on the theory, which renders the lightest of the new particles stable. This leads to the prediction of large missing transverse energy (MET) at the LHC, due to the cascades of new particles ending up in the massive stable particle that eludes the detectors. Such MET (together with energetic jets, leptons etc.) goes a long way in making such new physics signals conspicuous. Even then, however, one has to worry about distinguishing among different theoretical scenarios, once some excess over SM backgrounds is noticed. Thus one has the task of using the LHC data to differentiate among models like supersymmetry (SUSY), universal extra dimensions (UED) and littlest Higgs with T-parity (LHT), all of which are relevant at the TeV scale. With the SM particles supplemented with new, more massive ones having the same gauge quantum numbers (with only spins differing in the case of SUSY) in all cases, their signals are largely similar. The consequent problem of finding out the model behind a given set of signatures is often dubbed as the LHC inverse problem. The name was coined when it was shown first in the context of SUSY [1] that different choices of parameters within SUSY lead to quantitatively similar LHC signals. The efforts towards distinction were subsequently extended to the aforementioned different scenarios with large missing energy signature at the LHC [2, 3, 4].

Though the scenarios predicting MET signals are attractive from the viewpoint of explaining the dark matter content of the universe, and they also satisfy the electroweak precision constraints while keeping the new particle spectrum ‘natural’, the discrete symmetry ensuring the stability of the weakly interacting massive particles is almost always introduced in an ad hoc manner. For example, it is well-known that the superpotential of the minimal SUSY standard model (MSSM) can include terms which violate the conventionally imposed R-parity, defined as . If SUSY exists, the violation of R-parity cannot therefore be ruled out. Similarly, boundary terms in UED can violate the Kaluza-Klein parity usually held sacrosanct, and T-parity in LHT can be broken by the so-called Wess-Zumino-Witten anomaly term. While one is denied the simplest way of having a dark matter candidate when the symmetry is broken, these are perfectly viable scenarios phenomenologically, perhaps with some alternative dark matter candidate(s). In SUSY, for example, the axino or the gravitino can serve this purpose even if R-parity is broken. And, most importantly, the different scenarios with broken are as amenable to confusion as their -preserving counterparts, as far as signals at the LHC are concerned. The mostly sought-after final states (such as jets + dileptons) are expected from all of these scenarios, various kinematical features are of similar appearance, and in none of the cases does one have the MET tag for ready recognition, in clear contrast to scenarios with unbroken .

Side by side with the problem of large missing energy look-alike models, the disentanglement of ‘low missing energy look-alikes’ is thus an equally challenging issue, on which not much work has been done yet. Some criteria for distinction among this class of look-alikes are developed in this paper. Specifically, we consider four possible scenarios of NP with low missing energy signature:

1. Supersymmetry with R-parity violation (SUSY-RPV)

2. Minimal universal extra dimensions (mUED) with KK-parity conserved (UED-KKC)

3. Minimal universal extra dimensions with KK-parity violated (UED-KKV)

4. Littlest Higgs model with T-parity violated by the Wess-Zumino-Witten anomaly term (LHT-TPV).

It should be noted that UED-KKC is also included in this study. This is because, as will be seen in the following sections, the peculiar features of the mUED spectrum (namely, a large degree of degeneracy) often leads to the lightest stable particle carrying very low transverse momentum. In addition, one often also has nearly back-to-back emission of the invisible particle pair. Consequently, the MET spectrum is rather soft over a large region of the parameter space, and the signals can be of similar nature as those of -violating scenarios. Hence we would like to emphasize that mUED with KK-parity conserved is a scenario which can be easily distinguished by its much softer MET spectrum from other models predicting a massive stable particle (like SUSY with R-parity), but might actually be confused with the other -violating scenarios.

It is well-known that signals containing leptons have relatively less SM backgrounds compared to events with fully hadronic final states. We therefore focus on possible leptonic channels in the various models under consideration. One has to note, however, that it is difficult to devise model-independent cuts such that the SM backgrounds are reduced while keeping a significant fraction of the signal events intact for all the models. For example, strong cuts on the transverse momenta of the leptons cannot be applied in case of mUED as the leptons there are very soft in general, owing to the almost degenerate spectrum of the Kaluza-Klein excitations. This makes it difficult to reduce the SM backgrounds in the single lepton and opposite-sign dilepton channels (which have rather large irreducible backgrounds from  jets and  jets respectively). Although same-sign dilepton and trilepton channels have relatively lower rates within the SM, they are not very suitable for the purpose of distinguishing between the above models. The main reason for this is that many otherwise conspicuous invariant mass peaks cannot be reconstructed in these channels. These invariant mass peaks, however, are very helpful in classifying the models. In addition, since one is now looking at situations where the NP signals are not accompanied by large MET, rising above the SM backgrounds is a relatively harder task which is accomplished better with a larger multiplicity of leptons. Keeping this mind, here we have tried to develop a procedure of model discrimination, depending on four-and higher-lepton signals as far as possible.

The four-lepton channel is viable in all the four models mentioned above, and such events can be used to extract out several qualitative differences among the models, including the presence or absence of mass peaks. Therefore, our study largely focuses on the four-lepton channel. Furthermore, since most cascades start with the production of strongly interacting heavier particles in these new theories, as we can be seen from the appendix, generically we can obtain at least two hadronic jets in the signal. Apart from the four-lepton channel, we also use the presence (or absence) of signals with even higher lepton multiplicity as a discriminating feature. It is of course true that these methods of discrimination can often be applied only after sufficient luminosity has been accumulated. In this sense, our study differs from that of [2], where the inverse problem was considered not only for models with a very large MET signal, but also at a modest luminosity of only.

The paper is organized as follows. The choice of relevant parameters in the various models considered and our general strategy and methods adopted in event generation at the LHC are summarised in section 2. We use this strategy to show some predictions in section 3 to convince the reader that the different scenarios indeed fake each other considerably at the LHC. Section 4 is devoted to a detailed study of kinematics of four-lepton final states, whereby a significant set of distinction criteria are established. In section 5, we discuss the usefulness of the channel with five or more leptons. Some scenarios over and above those covered here in details are qualitatively commented upon in section 6. We summarise and conclude in section 7. Finally, as a useful reference for the reader, we outline the main features of the low-missing energy look-alike models and the possible cascades through which four and higher-lepton signals can arise in those contexts, in an Appendix.

2 Multilepton final states: signal and background processes

2.1 Event generation and event selection criteria

Before we establish that the models mentioned in the introduction (and described in the Appendix) all qualify as look-alikes with low MET, and suggest strategies for their discrimination through multilepton channels, we need to standardise our computation of event rates in these channels. With this in view, we outline here the methodology adopted in our simulation, and the cuts imposed for reducing the SM backgrounds. The predicted rates of events for some benchmark points, after the cuts are employed, are presented at the end of this section.

As the production cross-section for strongly interacting particles is high at the LHC, we start with the production of these heavier ‘partners’ (having different spins for SUSY-RPV, and same spins in the remaining cases) of quarks and gluons at the initial parton level scattering. Though in principle there are contributions to the multilepton final states from electroweak processes as well, they are subleading, and are left out in our estimate. In this sense, our estimates of the total cross-sections in various channels, are in fact lower bounds. Also, the observations made by us subsequently on final state kinematics are unaltered upon the inclusion of these subleading effects.

For our simulation of signal processes, in case of SUSY-RPV, we have used PYTHIA 6.421 [5] for simulating both the production of strongly interacting particles and their subsequent decays. Since the values of the L-violating couplings that we have taken are very small, they do not affect the renormalisation group running of mass parameters from high to low scale [6]. Therefore, The SUSY spectrum is generated with SuSpect 2.41 [7]. For UED, while the production is once again simulated with the help of PYTHIA, both KK-parity conserving and KK-parity violating decay branching fractions are calculated in CalcHEP 2.5 [8] using the model file written by [9] and then passed on to PYTHIA via the SUSY/BSM Les Houches Accord (SLHA) (v1.13) [10]. For UED-KKV, we have implemented the relevant KK-parity violating decay modes in CalcHEP. Finally, for LHT with T-violation the initial parton level hard-scattering matrix elements were calculated and the events generated with the help of CalcHEP. These events, along with the relevant masses, quantum numbers and decay branching fractions were passed on PYTHIA with the help of the SLHA interface for their subsequent analysis. In all cases, showering, hadronization, initial and final state radiations from QED and QCD and multiple interactions are fully included while using PYTHIA.

To simulate the dominant SM backgrounds, events for the processes and were generated with PYTHIA. Backgrounds from have been simulated with the generator ALPGEN [11], and the unweighted event samples have been passed onto PYTHIA for the subsequent analysis.

We have used the leading order CTEQ6L1 [12] parton distribution functions. Specifically, for PYTHIA, the Les Houches Accord Parton Density Function (LHAPDF) [13] interface has been used. The QCD factorization and renormalization scales are in general kept fixed at the sum of masses of the particles which are produced in the initial parton level hard scattering process. If we decrease the QCD scales by a factor of two, the cross-section can increase by about 30%.

While the signal primarily used in our analysis is (), we have also considered events with five or more number of leptons in section 5. No restriction was made initially on the signs and flavours of the leptons. As we shall see subsequently, the ‘total charge of leptons’ can be used as a useful discriminator at a later stage of the analysis.

The different ways in which multilepton signals can arise in the various models under consideration have been described in the appendix. The principal backgrounds to the channel () are , and . Although in case of (where the two associated jets can come from ISR and FSR), there is no real source of MET if we demand a signal (i.e., both the ’s have to decay leptonically), jet energy mismeasurement can give rise to some amount of fake MET.

The following basic selection cuts were applied for both the signal and the background [14, 15]:

Lepton selection:

• and 2.5, where is the transverse momentum and is the pseudorapidity of the lepton (electron or muon).

• Lepton-lepton separation: 0.2, where is the separation in the pseudorapidity–azimuthal angle plane.

• Lepton-jet separation: for all jets with 20 GeV.

• The total energy deposit from all hadronic activity within a cone of around the lepton axis should be 10 GeV.

Jet selection:

• Jets are formed with the help of PYCELL, the inbuilt cluster routine in PYTHIA. The minimum of a jet is taken to be , and we also require 2.5.

We have approximated the detector resolution effects by smearing the energies (transverse momenta) with Gaussian functions [14, 15]. The different contributions to the resolution error have been added in quadrature.

• Electron energy resolution:

 σ(E)E=a√E⊕b⊕cE, (1)

where

 (2)
• Muon resolution:

 σ(pT)pT=⎧⎨⎩a,pT<100GeV,a+blogpT100GeV,pT>100GeV, (3)

with

 (a,b)={(0.008,0.037),|η|<1.5,(0.020,0.050),1.5<|η|<2.5. (4)
• Jet energy resolution:

 σ(ET)ET=a√ET, (5)

with , the default value used in PYCELL.

Under realistic conditions, one would of course have to deal with aspects of misidentification of leptons and jet energy mismeasurement.

Note that, in addition to the basic cuts discussed above and the further cuts on the lepton ’s described in the next sub-section, we also have used a cut on the invariant mass of the opposite sign (OS) lepton pairs formed out of the four-leptons. We have demanded that for all the OS lepton pairs. This cut helps us in reducing backgrounds coming from produced in association with a Z-boson or top quark pairs. We shall collectively refer to the basic isolation cuts and this cut on dilepton invariant masses as Cut-1.

2.2 Numerical results for four-lepton events

Two benchmark points have been chosen for each of the look-alike models and it is seen that the four and higher lepton signals can rise well above SM backgrounds, thus forming the basis of further kinematic analyses. In order to show that our analysis is independent of the mass-scale of new physics involved, we have chosen two benchmark points with different mass spectra. Also, we should emphasize here that in the subsequent analysis we shall be using kinematic features of the final states predicted by the different models which are largely independent of the choice of parameters. This is precisely why we take two different benchmark points and demonstrate that the essential qualitative distinctions between the models do not change as we go from one point to another. Thus our conclusions reflect distinction among the various low-MET models as a whole, and do not pertain to specific benchmark points. The relevant parameters of these models and their values at the benchmark points are described below. For details about the models, we refer the reader to the Appendix.

For SUSY-RPV, we have worked in the minimal supergravity (mSUGRA) framework. This is done just with an economy of free parameters in view, and it does not affect our general conclusions. In this framework, the MSSM mass spectrum at the weak scale is determined by five free parameters. Among them the universal scalar () and gaugino masses () and the universal soft-breaking trilinear scalar interaction () are specified as boundary conditions at a high scale (in this case the scale of gauge coupling unification), while the ratio of the vacuum expectation values of the two Higgs doublets (tan) and the sign of the Higgsino mass parameter (sgn()) as defined in eqn. A-1 are specified at the electroweak scale. In our analysis the electroweak scale has been fixed at , where and are the two mass eigenstates of the top squarks respectively.

In case of the minimal universal extra dimension (mUED) model with conserved Kalutza-Klein (KK) parity (UED-KKC), the essential parameters determining the mass spectrum are the radius of compactification () and the ultra-violet cut-off scale of the theory (). Although in mUED with KK-parity violated (UED-KKV) we have an additional parameter , for small values of this parameter, and once again primarily determine the mass spectrum.

In the Littlest Higgs model with T-parity violation (LHT-TPV), the new T-odd quark and gauge boson masses are determined by two parameters: and (see Appendix for their precise definitions). Apart from that, an additional parameter appears in the T-odd lepton sector, which we have fixed to be equal to throughout our study.

The choice of parameters for the different models are as follows:

1. Point A:

• SUSY-RPV: , , tan, and sgn(). The RPV coupling taken is . With these choices, we find the sparticle masses relevant to our study as (all in GeV) , , , , , , .

• LHT-TPV: , . With these choices, we find the T-odd particle masses relevant to our study as (all in GeV) , , , .

• UED-KKC: GeV and . With these choices of UED-KKC parameters, the masses of relevant KK-particles are given by (all in GeV), , , , , and .

• UED-KKV: For UED-KKV, the values of and are chosen to be same as in the case of UED-KKC. The value of the KK-parity violating parameter is set to 0.001.

2. Point B:

• SUSY-RPV: , , tan, and sgn(). The RPV coupling taken is . With these choices, we find the sparticle masses relevant to our study as (all in GeV) , , , , , , .

• LHT-TPV: , . With these choices, we find the T-odd particle masses relevant to our study as (all in GeV) , , , .

• UED-KKC: GeV and . With these choices of UED-KKC parameters, the masses of relevant KK-particles are given by (all in GeV), , , , , and .

• UED-KKV: For UED-KKV, the values of and are chosen to be same as in the case of UED-KKC. The value of the KK-parity violating parameter is set to 0.001.

For LHT-TPV, UED-KKC and UED-KKV the Higgs mass has been fixed at . The top quark mass has been taken as in our study. In LHT-TPV, the value of has been kept fixed at . The choices of and have been made in order to match the mass scale of the strongly interacting particles in LHT with those of the other models (these particles are predominantly produced in the initial hard scattering at the LHC). We should note here that this could have also been achieved with other different choices of these parameters, and we have remarked about their implication in section 4.2.

Table 1 shows the signal and SM background cross-sections for the channel at LHC running with after Cut-1 and additional cuts on lepton ’s. The signal cross-sections are shown for the two above different choices of parameters in each model. On the whole, it is evident from the table that our event selection criteria assure us of enough background-free events in each case. The backgrounds look somewhat challenging for LHT-TPV for benchmark point B. However, one still can achieve a significance (defined as , and being respectively the number of signal and background events) of with an integrated luminosity of 30 . For point A, is likely to be sufficient for raising the signal way above the backgrounds, and attempting discrimination among various theoretical scenarios via kinematical analysis.

We also show the sensitivity of the signals of the different scenarios to gradually tightened cuts on the leptons. Clearly, the close degeneracy of the spectrum in UED-KKC makes the leptons softer. Thus the signal events fall with stronger cuts imposed on the relatively softer leptons. Although such cuts applied during the offline analysis can be useful in discriminating the UED-KKC scenario from the rest, one has to use this yardstick with caution. This is because the situation can change with different values of the UED parameters and (as can be seen from point B). While they also change the KK excitation masses together with changing the mass-splitting, the estimate of masses from data for UED is not reliable, for reasons to be discussed in the next section. We therefore suggest some kinematical criteria that bypass this caveat.

3 On what ground are the models look-alikes?

In addition to the fact that all the suggested models have appreciable cross-section in the four lepton channel (and also in various other channels that we are not considering for model-discrimination for reasons described in the introduction), in order to ascertain that these models are indeed look-alikes, we first show that certain kinematic distributions, like MET or effective mass have very similar features in these scenarios of new physics. To begin with, we note that with similar masses of the strongly interacting new particles (squarks and gluinos for SUSY-RPV, and for the two variants of UED, and for LHT-TPV), the MET distributions look similar.

The missing transverse energy in an event is given by

 ET/=√(∑px)2+(∑py)2. (6)

Here the sum goes over all the isolated leptons, the jets, as well as the ‘unclustered’ energy deposits.

The MET distributions for the four scenarios under study are shown in Figure 1. The similarity of the MET distributions is obvious in all the four cases, including UED-KKC. For UED-KKC, as mentioned before, the reason behind this is the close degeneracy of the spectra. As a result, in this model the two ’s produced at the end of the cascades on the two sides have little transverse momentum, and quite often they are also back-to-back in the transverse plane. Consequently, the net MET is considerably reduced, in spite of the being a massive particle. Thus UED-KKC is as much of a look-alike with SUSY-RPV and LHT-TPV as UED-KKV.

The confusion among the look-alikes from MET distributions is expected to be more for similar values of the masses of the strongly interacting new particles. Since the direct measurement of mass at LHC is not easy, a measured quantity that often bears the stamp of these masses is the so-called effective mass. It is defined as the scalar sum of the transverse momenta of the isolated leptons and jets and the missing transverse energy,

 Meff=∑pjetsT+∑pleptonsT+ET/, (7)

Note that although usually carries the information about the mass scale of the particles produced in the initial parton level hard scattering, this is not true in all cases. Specifically, it is well-known that for a mass spectrum which is very closely spaced, largely underestimates the relevant mass-scale, the reason being very similar to that for the MET distribution being low in UED-KKC.

If an excess is seen in the () channel, fingers can be pointed at the several models mentioned before. Figure 1 is an example where the MET distributions show similar behaviour when the strongly interacting heavy particles in all of the four aforementioned models under consideration have similar masses. We thus conclude that all the four models clearly qualify as missing energy look-alikes. The minor differences that exist are difficult to use as discriminators, as these can be masked by features of the detector as well as systematic errors. In Figure 2, we also present the distributions for all these models, for the same ‘mass scale’ of for point A (point B). One finds that all the models except UED-KKC have a peak in the distribution at around twice the mass-scale (i.e., for point A). For point A in UED-KKC, the distribution peaks at around 300 GeV. Similar features are also observed for point B.

This fact, if correlated with the total cross-section, can perhaps be used to single out the UED-KKC model from the remaining three. However, one can still vary the excited quark and gluon masses in UED-KKC to match both the MET distributions for other models with a 600 GeV mass-scale. In order for this to happen, however, has to be as large as about 3 TeV. This would not only lead to very low total cross-section but also imply a scenario that is ruled out due to overclosure of the universe through .

However, while similar MET distribution but much softer distribution can single out UED-KKC, similar distributions in both variables but very low cross-sections can be noticed in special situations in the other models as well. For example, one can have RPV SUSY with both the -and -type interactions, with the later being of larger value, thus suppressing the decay of the lightest neutralino into two leptons. In such a case, with 600 GeV, the MET as well as -distributions will be very similar as earlier, but the cross-section may be down by a large factor.

The above example shows that there is a pitfall in using total rate as a discriminant. Keeping this in view, we choose our benchmark points with similar masses for all the models but look for other kinematical features where the differences show up.

4 Analysis of 4l events

4.1 Four-lepton invariant mass distribution: two classes

In the table containing rates of four-lepton final states, we have allowed all the leptons to be of either charge. While we keep open the option of having all charge combinations, in this and the next two subsections we concentrate on those events where one has two positive and two negatively charged leptons. The issue of ‘total charge of the set of leptons’ and its usefulness in model discrimination is taken up section 5.4.

For the channel (with ), the first distribution that we look into is that of the four-lepton invariant mass (). From Figure 3 we can see that, based on the distribution the models can be classified into two categories, 1) those with a peak in the distribution and 2) those without any such peak.

In SUSY-RPV, there is no single bosonic particle decaying, via cascade, to four leptons. Hence, no invariant mass peak is expected in this model and the distribution has a very broad shape, as we see in Figure 3. As discussed earlier, in the example taken, the four leptons here come from the RPV decays of the neutralino and the RPC decays of the chargino.

Similarly, in UED-KKC the four leptons come from the two cascade decay chains and not from a single particle. In this case, the decay of a gives two leptons of opposite charge and same flavour in each chain. Note that the range in which takes values for UED-KKC is rather restricted, as can be seen in Figure 3. We can understand this in the following manner. Let us denote the four-momenta of the two leptons coming from one chain by and , and those of the other two from the second chain by and . Then, an approximate upper bound on can be obtained as follows:

 M24l = (p1+p2+p3+p4)2 (8) = (p1+p2)2+(p3+p4)2+2(p1+p2).(p3+p4)

Now,

 (p1+p2)2≤(M2Z1−M2L1)(M2L1−M2γ1)M2L1 (9)

A similar bound is also applicable to . Finally, we can approximate

 2p1.p3=2(E1E3−→p1.→p3)≃2E1E3(1−cosθ13)≤4E1E3 (10)

Here is the angle between and . Hence, we can finally approximate the upper bound on for UED-KKC as

 M4l≤ ⎷2(M2Z1−M2L1)(M2L1−M2γ1)M2L1+4[E1E3+E1E4+E2E3+E2E4] (11)

The first term within the square-root has the numerical value of about for point A in UED-KKC. Because of the unknown boost of the partonic centre of mass frame, we cannot put any definite upper bound on the ’s of and , and therefore the maximum possible values of the lepton energies are also undetermined. Still, as very little energy is available at the rest frame of the decaying KK-excitations (once again because of low mass-splittings), cannot be very large. This is the reason we expect for UED-KKC to take values in a somewhat restricted range.

For UED-KKV, we observe a very sharp peak in the distribution around which is the mass of for point A (point B). The four leptons in this case come from the cascade decay of a to a lepton pair and a followed by the KKV decay of the to another pair of leptons. There is of course a long tail in the distribution here coming from the cases where all four of the leptons do not come from the decay of a single . For example, they can come from the leptonic decay of the two ’s via KK-parity violating interactions. We demonstrate this full range in the insets of Figure 3. It is, however, important to note that, in these cases, mostly exceeds when two of the leptons come from decay and the two others come from the cascade. On the other hand, the invariant mass is greater than when the four leptons come from the decay of two ’s. This is why we observe an excess after around for point A (point B) in the insets of Figure 3. As long as we have a LKP with KK-parity violating interactions, this very clear peak, followed by a hump, observable in the distribution is a very important feature of UED-KKV.

Finally in LHT-TPV, we see in Figure 3 a very sharp peak superposed in a broad overall distribution. The reason for this is that in the example taken, most of the four-lepton events are due to the decay of an to followed by the leptonic decays of the ’s. These events will not give rise to any invariant mass peak. But, there is a fraction of events where one decays to a pair which then in turn can decay to four-leptons. This will give rise to a peak in as we see in Figure 3. Note that, the branching fraction of an of mass 230 GeV to a pair of Z-bosons is around 22% while it is 77% to a pair of W’s. Over and above that, the branching fraction of to charged leptons is greater than that of Z. This accounts for the spread of events away from the peak, as seen in Figure 3. One may also note that, in general, fewer 4-lepton events are expected in this model from leptonic cascades of the . This is because, for our choice of parameters, has the largest branching ratio in the channel.

Based on the above considerations, LHT-TPV and UED-KKV fall into category-1 while SUSY-RPV and UED-KKC belong to category-2. Note that, this classification for LHT-TPV is valid only for GeV, so that it has sufficient branching fraction for . We shall discuss the other cases later in subsection 4.2.

Our task now is to distinguish between the look-alike models within each category. We do so in the following subsections.

4.2 Pairwise dilepton invariant mass distribution of the four leptons

One can go a little further in the task of model discrimination by combining the information from plots with distributions in the invariant mass distribution () of the OS lepton pairs. Taking events with two pairs of opposite-sign leptons, we first order the leptons of each sign in the descending order of transverse momentum. In order to be sufficiently general in our analysis, no constraint on the flavour of the leptons is imposed while pairing them up. This is because, in SUSY-RPV, flavours of the leptons coming from neutralino decays are not correlated in general, apart from constraints coming from the antisymmetry in the first two indices of the -type terms in the superpotential. Thus in general we can form four possible pairs of opposite sign (OS) leptons.

For the models belonging to category-2, i.e., SUSY-RPV and UED-KKC, the distributions show no peaking behaviour. But, we see in the insets of Figure 4 that the distributions for UED-KKC show a prominent edge at for point A (point B). We note that in 50% of the cases, the lepton pairs come from the same decay chain starting with a (as described in detail in the context of angular correlation between the lepton-pairs in subsection 4.3). Therefore, an invariant mass edge is expected at the value given by , which comes out to be for point A (point B).

For the SUSY-RPV point under consideration, we also see in Figures 4 and 5 an edge in the invariant mass distributions of two OS leptons near the corresponding neutralino mass. But as the two leptons in the pairs we consider have equal probability of coming from either the same chain or two different chains, the mass-edge in the distributions is smeared by the “wrong combinations”. If one forms OS leptons pairs with a very small opening angle between them, the neutralino mass-edge will become very sharp. As the lightest neutralino mass can be as low as  [16], the position of the invariant mass edge for UED-KKC and SUSY-RPV will not be very different for neutralino masses close to this bound. However, for neutralino masses higher than , the edge positions will be quite different, as in UED-KKC the value obtained cannot be that large in any allowed region of the parameter space.

In case of models belonging to category-1, we can see from Figures 4 and 5 that the distributions for UED-KKV show a clear peak at the same value of for all the four possible cases. The peak is at the mass of which is for point A (point B). The two OS leptons coming from the decay of a are expected to be of high transverse momentum, thereby constituting the majority of (11) pairs. Therefore, the peak height is very large for the distribution. As we gradually consider OS combinations of softer leptons, the peak height reduces . This is because, most of the softer leptons come from intermediate stages of the cascade, and invariant mass distributions involving them will just give rise to a broad overall distribution. Therefore, in UED-KKV, as long as the LKP is the heavy photon, such an invariant mass peak is an unmistakable feature of the model. Here, one should also note that the position of the OS dilepton peak is always different from the position of the four-lepton peak as we obtain in UED-KKV. The difference, although not very large, can be observed at the LHC given the fact that the four-lepton channel is a rather clean one. Looking at Figures 3 and 4 we find that for point A, the peak is roughly at 509 GeV () and the peaks are at 475 GeV (). Hence the difference between the values of these two peak positions, which in this case is around 34 GeV, is large enough to be measurable within the experimental resolutions at the LHC. Moreover, note that, these two peaks appear in two different distributions making the resolution even easier. Similar considerations apply for point B, too.

In the example considered here, the corresponding distributions for LHT-TPV also show a clear peak at the mass of the Z-boson (), as we can see from Figures 4 and 5. The Z-peak is superposed over a broad distribution coming from leptons from W’s. Note that for point A, the branching fraction of is 22% and the corresponding branching fraction is 77%. Therefore, relatively fewer dilepton pairs come from the decay of a Z-boson and hence the fraction of events under the Z-peak is smaller compared to the total distribution. For point B, as the branching fraction increases to 35%, the peak at is even more prominent over the continuum coming from . This, however, is not generic to LHT-TPV. As discussed in detail in Ref. [56, 59], as far as the decays of is concerned, there are essentially three possible cases for this model. For lower masses () the decay of is dominated by the loop-induced two-body modes into fermions (case-1), whereas for higher masses () the two-body modes to gauge boson pairs dominate (case-3). For intermediate masses, both the two-body and three-body modes compete (in the three-body mode we have one off-shell or ) (case-2). The points we have analysed here (point A and B), belong to case-3. For case-1 one would obtain a very clear peak in the OS dilepton invariant mass distribution but no peak in , while in case-2 a peak is expected in both OS dilepton and four-lepton distributions at the same mass-value. Therefore, case-1 will give rise to a situation where LHT-TPV belongs to category-2, but it will be distinguishable from SUSY-RPV and UED-KKC by its dilepton peak. And in case-2, LHT-TPV would belong to category-1, but it can still be distinguishable from UED-KKV by the fact that the OS dilepton and four-lepton peaks will be at the same mass-value for LHT-TPV, but at different values for UED-KKV. Moreover, in case -2, , and no peak is expected in UED-KKV at such a low value of the dilepton invariant mass. For details on the reconstruction of such peaks above SM backgrounds in LHT-TPV, we refer the reader to Ref. [59]. Thus, we note that the features of OS dilepton invariant mass distributions, if used in conjunction with other important kinematic characteristics, can help in discriminating models belonging to different categories.

In addition to the invariant mass distributions of the different possible OS dilepton pairs formed out of the four leptons, it might also be useful to look into pairwise correlation of the different ’s as shown in Figure 6. In this figure, for the purpose of illustration, we show the correlation of () and () for the various models at point A on an event-by-event basis (at after Cut-2). We can see from Figure 6 that for the models where we observe peaks in the distributions, the () correlation plot shows two typical lines parallel to the and axes at the values of the peak-position (around for UED-KKV and for LHT-TPV). On the otherhand, for the models showing an edge in the distributions we see from the scatter plots that the values of are mostly concentrated within the upper-bound given by the position of the edge (around for SUSY-RPV and for UED-KKC).

If both the OS dilepton pairs and come from a in UED-KKV or a -boson in case of LHT-TPV, then and will have the same value (with an error-bar, due to detector effects etc.) in the corresponding event. That’s why we expect a “blob” in the () plane as can be seen from Figure 6 for UED-KKV and LHT-TPV (centered around and respectively). For UED-KKC or SUSY-RPV, the boundedness of ’s is once again reflected by the “box-like” distribution, the spread away from the boxes being significantly lesser than for the () case, as the leptons in the pair are much softer. As we have four possible OS lepton pairings as explained before, one can have six different correlation plots between them. But all the essential features remain the same as in the two correlation plots we show for the various models.

4.3 Pairwise angular correlation of the four leptons

In this subsection, we consider the correlation in the opening angle between the lepton pairs. The pairs have been formed out of the four leptons following the same prescription as used in the previous subsection.

In Figures 7 and 8 we have presented distributions of the cosine of the opening angle between the OS lepton pairs for point A and point B respectively. The opening angle is calculated in the lab frame and is defined by the relation

 cosθij=→pi.→pj|→pi||→pj| ;   i,j=1,2 (12)

where and stand for the momenta of positive and negatively charged leptons respectively.

In order to quantify the difference between the various models in the distribution of , we define the following asymmetry variable:

 Aij=∫0+1dσdcosθijd(cosθij)−∫−10dσdcosθijd(cosθij)∫0+1dσdcosθijd(cosθij)+∫−10dσdcosθijd(cosθij). (13)

As we are considering the normalized distribution of here, the denominator of as defined in Equation 13 will be . In Table 2 we show the values of in the different models under consideration.

Let us first consider the models belonging to category-2. We can see from Figures 7 and 8 that for SUSY-RPV, the distribution of tends to peak towards . This is because the fraction of OS lepton pairs which are coming from the decay of a sufficiently boosted single neutralino tend to be highly collimated. The rest of the combinations (which include two leptons coming from two separate decay chains, or one coming from a chargino and another from a neutralino decay) will have OS leptons which are largely un-correlated. Thus we can see a overall flat distribution of with a very significant peaking towards . For the same reason, the values of in SUSY-RPV in Table 2 are larger than in the other models for all . We should note here that the boost of the neutralino is large, thanks to the substantial mass splitting among the gauginos usual in mSUGRA. In a generic MSSM model, the splittings might become smaller, thereby rendering the neutralinos less boosted and the distributions of less sharply peaked towards .

For UED-KKC, we have two possibilities while forming the OS lepton pairs - the two leptons can either come from the same decay chain or they can come from two separate decay chains. In the former case, we expect the two OS leptons to have a smaller opening angle in general. This is because, they come from the decay chain , where the parent will be carrying the boost of the initially produced . As the leptons themselves have very low ’s in the rest frame of the , this boost of the will make them collimated to an extent. For the second possibility, the leptons are, in many cases, nearly back-to-back as they come from the cascade decay of two ’s which for a significant fraction of events lie in two different hemispheres of the detector. For point A, the mass splittings are quite small between the KK-excitations, whereas for point B, they are relatively larger. Since we have demanded two of the leptons to have greater than , it is very likely from the point of view of UED mass splittings that for point A, in a larger fraction of events, both of the hard leptons will not come out from the same decay chain . Therefore, in a significant number of events, the combinations (12) and (21) are expected to be from the same chain, whereas the (11) and (22) pairs will involve both the decay chains. This leads us to expect the cos and cos distributions to be more peaked towards than towards , while the cos and cos distributions have slight peaking near both and . It can be readily verified that Figure 7 is in conformity with these observations. Similarly, we see from Table 2 that (for point A) the values of and are relatively higher and positive, implying significant asymmetry with more events having cos. We also note that and indicate more symmetric distributions for cos and cos as discussed above. This asymmetry, however, is no longer expected if the mass-splittings become larger, as then the OS lepton pairs can come with equal probability from both the chains. We observe this feature in case of point B in Figure 8 and also in Table 2. Therefore, in UED-KKC, the distribution of cos is in general much less asymmetric towards as compared to SUSY-RPV.

Thus, based upon the above features, one should be able to distinguish between SUSY-RPV and UED-KKC. We shall see in what follows that there are also other features like the total charge of the four leptons, or the ratio of five or higher lepton to four-lepton cross-sections which can act as useful discriminators between the models belonging to category-2.

Next we consider the models belonging to category-1. In case of UED-KKV, the two OS leptons of highest come in most cases from the decay of a which itself has a very low to start with. So, in the rest frame of , the two leptons will almost be back-to-back, leading to the slight peaking of towards as seen from Figures 7 and 8. This interesting feature of UED-KKV is also reflected in the value of for point A (point B). The distributions for cos and cos on the other hand are very flat indicating that these leptons have no angular correlation between them. This is not unexpected, since the combinations (12) and (21) will generally be formed when one of the leptons (the harder one with index 1) comes from the decay of , and the other, softer one, from the intermediate stages of the cascade (mostly from the decay of , or ). Therefore, and are close to zero as can be seen from Table 2. Finally, we see that the distribution for cos shows a peaking behaviour towards both and . This can be understood from the fact that the two softest leptons almost always come from the intermediate stages of the cascade where they emerge from either the decays of and . A large fraction of -initiated events gives rise to collimated leptons (giving rise to the peaking towards , while a significant fraction of events where the leptons come from will have them coming out in opposite directions (responsible for the peaking towards .

Finally, from all the distributions of cos and the values of it is clear that the LHT-TPV model has features similar to SUSY-RPV. In particular, as the leptons come from the decays of a boosted (via intermediate or states), they tend to be collimated. The collimation here is somewhat less than as in SUSY-RPV because of the fact that for the chosen parameters (point A), the squark (gluino)-neutralino mass difference () is much larger than the - mass difference ().

Thus while both UED-KKV and LHT-TPV might give rise to clear peaks in the distribution, they show entirely different behaviour as far as the angular correlation between the OS lepton pairs is concerned. This, therefore, can act as a very good discriminator between these models belonging to category-1. In the following subsections, we shall look into some more variables that can be used to further clarify the distinction between these two models, especially when different types of mass-spectra in LHT-TPV tend to obliterate the mass peaks so spectacular for our chosen benchmark points.

We should note here that there is a dip observable in the cos distributions towards the last bin near for UED-KKC and LHT-TPV. This dip, however, is not seen in the cos distribution. This is stemming from the fact that we have demanded all OS lepton pairs to have an invariant mass greater than 10 GeV. Now, when the lepton ’s are not very high themselves, the invariant mass becomes very small when the angle between the leptons tends to zero. These events, therefore, have been removed by the above cut, giving rise to the observed dip. As for the (11) combination the leptons are much harder, the lepton pairs always pass the invariant mass cut, and this feature does not appear for this case.

4.4 Total charge of the four-leptons

Here we consider the variable total charge (Q) of the four leptons obtained in the general channel . Q can take values in the set {-4,-2,0,2,4}. In Figures 910 we see the distribution of Q for the different models. We observe that UED-KKC clearly stands out as in this case the four leptons come from two cascade decay chains starting with ’s leading to for all the events. For the RPV coupling considered for point A, the lightest neutralino in SUSY-RPV always decays to a pair of leptons and a neutrino. If no other leptons come from the cascade, these four leptons will have a total charge . On the other hand, if some additional leptons come from the decays of charginos or sleptons in the cascade, the lepton multiplicity in those events will be higher than four. It is however possible in a certain fraction of events to have a pair of leptons (coming from the decay of a single boosted neutralino) to be so highly collimated that they do not pass the lepton-lepton separation cut. These events might lead to a total charge . For LHT-TPV different combinations of and decays can lead to four-lepton events. Hence, the expected values of Q are (-2,0,2). For UED-KKV, the leptons coming from the decay of are always oppositely charged. But, it is possible to obtain ’s of either charge from the cascades, giving rise to same-sign lepton pairs, over and above those coming from . This leads to events with . Hence, essentially, from the distribution of Q, the UED-KKC model can be separated from the rest.

5 Five or higher lepton events

For all of the models discussed here, additional leptons, over and above those coming from sources discussed in the previous subsections, can come from various stages in the cascades. In Table 3, the rates for final states with five or more leptons are presented for our chosen benchmark points. The cut has been uniformly maintained at 10 GeV for each lepton. The ratios of the five or higher lepton event rates to those for four-leptons are also presented. The SM backgrounds for channels with lepton multiplicity greater than four are negligible.

The rates for such added profusion of leptons depend on the respective spectra. The deciding factor here is the leptonic branching ratio for -odd particles at intermediate stages of the cascade. In this respect, UED-KKC and LHT-TPV fare worse. For UED-KKC, five-lepton events are not expected from the production and decays of the KK-particles. Hence, the very small number of events with lepton multiplicity higher than four come from the decays of B-mesons, pions or photons. For LHT-TPV, with our choice of parameters, there are few additional leptons coming from the intermediate steps in the cascade. Therefore, in most of the events found, the leptons are entirely coming from the decay of the two ’s produced. One should note that this rate will increase for other choices of parameters, especially when the T-odd gauge bosons and the T-odd leptons are lighter than the T-odd quarks. For the SUSY-RPV examples considered, a proliferation of multilepton events is a well-known fact, and that is reflected in the high value of . For point B, the ratio is higher (0.6) than for point A (0.35). This is because, as can be seen in section 2.2, in the former case, the SUSY mass spectrum is such that the chargino can decay to sleptons/sneutrinos, whereas in the later case such decays are not allowed by phase-space considerations. This leads to a higher branching fraction of obtaining a lepton from the cascade, thereby leading to relatively larger rates for events with higher lepton multiplicity in point B. For, UED-KKV, the ratio does not change significantly as we change the mass-scale. Therefore, we conclude that from this ratio, one can always single out the UED-KKC model. In the other models, there is enough room to change the ratios by adjusting the mass-spectra suitably.

6 Other possibilities

In addition to the kinds of new particle spectrum considered above, other possibilities of low missing energy look-alikes may offer themselves for detection as well as discrimination at the LHC. A few illustrative cases are discussed below.

In L-violating SUSY, we have a host of other possibilities. We considered the case of a neutralino LSP with a -type RPV coupling in our analysis. In the presence of -type couplings instead, a neutralino will decay to two quarks and a charged lepton/ neutrino. Hence, the rate of four-lepton events will decrease. In addition, we shall not see the asymmetric peaking behaviour observed in the distributions, too, since the lepton-pairs in this case will not be coming from the decay of a single boosted particle. Similarly, the edge in the dilepton invariant mass distributions will also not be present. There are, however, two features which distinguish this scenario from the rest. Firstly, the total charge distribution will now show a significant increase for . Secondly, with one lepton coming from each lightest neutralino during the SUSY cascades in two chains, a pair of same-sign dileptons occurs frequently at the end of the decay chains. Since the gluino, too, is of Majorana nature, being thereby able to produce charginos of either sign, there will be a surge in same-sign trilepton events observed [21].

A stau LSP scenario with -type couplings will also have similar implications. Here, stau will decay to a lepton and a neutrino. If we have a stau LSP with -type couplings instead, the 4l-signal will be suppressed, as the stau will decay to two quarks in this case. We also note that in presence of relatively larger values of -type couplings, there is a region of the mSUGRA parameter space where the sneutrino can also become an LSP [6, 17]. However, the sneutrino in this case will decay to a pair of quarks thus reducing the possibility of having four leptons in the final state. Finally, we also remark that in the presence of bilinear R-parity violating terms, if we choose the RPV parameters to be consistent with the observed neutrino mass and mixing patterns, the neutralino LSP can decay to , or  [22]. Hence, four-lepton events will again be viable with a peak at in the OS dilepton invariant mass distributions. But there will not be any peak in the corresponding distribution. This last feature thus seems to be generically true in SUSY-RPV.

In the framework of a minimal UED model with KK-parity conservation, is the LKP and characteristic signatures of this scenario were discussed throughout this article. The mUED model is based on the simplifying assumption that the boundary kinetic terms vanish at the cut-off scale . This assumption restricts the mUED spectrum in such a way that the splittings among different KK excitations are small enough to result in soft final state particles and thus low missing . As discussed in section A.2, the boundary terms receive divergent contributions and thus require counterterms. The finite parts of these counterterms remain undetermined and are therefore free parameters of the theory. This additional freedom could be exploited to end up with an unconstrained UED (UUED) scenario with several different possibilities:

• Particular combinations of the aforementioned free parameters can remove the degeneracy of the mUED mass spectrum. This results in harder leptons and jets in the final state and thus gives rise to a harder missing- distribution. Such a version of the UED model no longer falls in the category of low missing energy look-alikes. The corresponding criteria for large missing- scenarios will have to be applied in this situation  [3].

• The values of the additional parameters could be chosen in such a way that even though the mass spectrum remains degenerate as in the case of mUED, the mass of becomes smaller than . This leads to a scenario with as the LKP and therefore, a possible candidate for cold dark matter. In this case, the ’s produced at the end of decay cascades will further decay into pairs, resulting in similar phenomenology as in the case of mUED explored in this work. However, the four-lepton event rate in this case will be significantly reduced due to the fact that mostly decays to pairs, as this channel will now have enhanced phase-space available as compared to .

• One can also have such a combination of parameters that only the positions of and in the mass spectrum are altered. The first possibility is that and are heavier than the quarks. In such situations, quarks will decay into via tree-level 3-body modes. subsequently decays into and combining the two cascade decay chains, one can then obtain four-lepton signals. However, the opposite-sign dilepton invariant mass distributions will not show any invariant mass edge in this scenario. The other possibility is that and may become lighter than the leptons. Here, the possible decay modes of interest are and . Phenomenologically, this scenario will again be quite similar to the mUED cases we have studied.

In the framework of UED-KKV, the masses of the KK-fermions have a small dependence on the value of the KK-parity violating coupling . As shown in Ref. [35], as we increase the value of , the KK-fermion masses decrease. As the quarks are much heavier than and in mUED with KK-parity conserved, the presence of non-zero KK-violating coupling does not lead to any appreciable change in the excited quark masses vis-a-vis those of the remaining particles. Therefore, the decay patterns of the quarks remain the same. However, for smaller , singlet leptons and the are almost degenerate. Therefore, in addition to having a smaller , if we have a larger value of , singlet leptons may become lighter than . For example, this can happen for and . Here, the only possible decay channel available for these singlet leptons is via the KK-parity violating mode to a SM lepton of the same flavour and a . The phenomenology of this scenario will be significantly different from the one we have considered so far with smaller values of () and a LKP, and is therefore an interesting possibility for further studies.

In LHT-TPV, as we have two free parameters and which determine the masses of the T-odd quarks and leptons, the possibility of obtaining a fermionic LTP exists. In such cases, via the T-parity breaking terms, these fermions might decay to standard model particles. As observed in Ref. [56], there are two possible ways in which these fermionic LTP’s can decay. As the WZW term breaks T-parity only in the gauge sector directly, a T-odd lightest fermion can decay by a three-body mode mediated by a virtual T-odd gauge boson. There is also the possibility of having loop-induced two-body decay modes. Therefore, the major decay channels are , and . In the last case, the off-shell might again decay to four-leptons via , but there will not be any peak in the distribution. On the other hand, if the LTP is a T-odd charged lepton, one can observe a spectacular five-lepton peak. The other possible decay modes will also lead to and events in varied rates, although the quantitative predictions of these will require us to determine the relative importance of the three-body and the loop-induced two body decay modes of . A detailed phenomenology of this fermionic LTP scenario will be studied in a future work.

7 Summary and conclusions

We have considered four characteristic scenarios which can pass off as low missing energy look-alikes at the LHC. After convincing the reader that UED-KKC in its minimal form, in spite of containing a stable invisible particle, often falls in this category, we have studied the contribution of each scenario to events with four or more leptons. Since total rates alone, at the four-lepton level at least, can mislead one in the process of discrimination, we have resorted to kinematic features of final states in the different cases.

The first of these is the four-lepton invariant mass distribution. On this, we have found that the models get divided into two categories, depending on whether the four leptons show an invariant mass peak or not. While LHT-TPV and UED-KKV are in the first category, SUSY-RPV and and UED-KKC belong to the second one, thus offering a clear distinction.

For distinguishing between models within each category, we have used three observable quantities, namely, angular correlation and invariant mass of opposite-charge lepton pairs, and the total charge of the four observed leptons. It is found that angular correlations as well as the total charge causes SUSY-RPV to stand out quite clearly with respect to minimal UED-KKC. UED-KKV, too, stands out distinctly from the others, as far as angular correlations are concerned. This, however, still leaves room for discrimination. This happens, for example, where LHT-TPV has such a spectrum that the heavy photon LTP does not decay dominantly into four leptons. The distinction of this scenario with SUSY-RPV and UED-KKC is still possible using the pairwise invariant mass distribution of oppositely charged dileptons. We have also found that the relative positions of the dilepton vs. four-lepton invariant mass peaks, and the existence of an ‘edge’ in the dilepton invariant mass distribution lead to useful discriminating criteria. In addition, the ratio of five or higher lepton event rates to those for four leptons sets UED-KKC apart from the other scenarios.

As mentioned before, we haven’t paid particular attention so far to the flavour content of the four leptons. In SUSY-RPV, depending upon the L-violating coupling chosen, the flavour content will change. However one can discover a pattern in the fraction of events with , , , or , for specific RPV couplings (here stands for the electron or positron and stands for the muon or anti-muon, and, for example, means a four-lepton event with ’s and ). For the coupling that we chose for our analysis, we obtain, as expected, around events to be of -type, whereas and being each. No events are expected to be of or -type. This is certainly a notable feature, but as observed above, these flavour ratios will change if we change the L-violating coupling. For UED-KKC one will always obtain , or -type events, while for UED-KKV all flavour combinations are possible. For LHT-TPV, depending upon the point of parameter space one is in, all flavour combinations are once again possible with varying fractions. Thus, although flavour content of the leptons can sometimes be useful, they might not be a very robust feature of the models, except for the case of UED-KKC.

We have also made a set of qualitative observations on other related scenarios such as RPV via -type or bilinear terms, situations with stau or sneutrino LSP, UED-KKC with an unconstrained particle spectrum and different LTP (LKP) in LHT-TPV (UED-KKV). The qualitative changes that some of these scenarios entailed have been pointed out. On the whole, while the various theoretical models in their ‘minimal’ forms offer clear methods for distinction, a confusion can always be created in variants of the models with various degrees of complications. The same observation holds also for theories predicting large missing . Thus one may perhaps conclude that, while some striking qualitative differences await one in the approach from ‘data to minimal theories’, there is no alternative to a threadbare analysis of the mass spectrum, possibly linking spin information alongside, if one really has to exhaust all possibilities that nature may have in store. Furthermore, the availability of data with high statistics, enabled by large accumulated luminosity, is of great importance. All this is likely to keep the highly challenging character of the LHC experiment alive till the last day of its run.

Appendix A Description of the various models considered

a.1 SUSY with R-parity violation (SUSY-RPV)

The MSSM superpotential is given by [18]

 WMSSM=ylijLiH1¯Ej+ydijQiH1¯Dj+yuijQiH2¯Uj+μH1H2 (A-1)

where and are the two Higgs superfields, L and Q are the SU(2)-doublet lepton and quark superfields and E, U, and D are the singlet lepton, up-type quark, and down-type quark superfields, respectively. is the Higgsino mass parameter and ’s are the strengths of the Yukawa interactions.

If lepton and baryon number are allowed to be broken, the above superpotential can be augmented by the following terms [19]:

 WRp/=λijkLiLj¯Ek+λ′ijkLiQj¯Dk+λ′′ijk¯Ui¯Dj¯Dk+ϵiLiH2. (A-2)

where i, j, and k are flavour indices. Here the term leads to baryon number (B) violating interactions while the other three terms lead to the violation of lepton number (L). In MSSM, one imposes an additional discrete multiplicative symmetry known as R-parity which prevents any such term in the superpotential. R-parity is defined as , where is the spin of the corresponding particle. This prevents, for example, terms which can lead to fast proton decay (although there are dangerous “R-even” dimension-five operators which can still lead to the decay of proton). However, the purpose is equally well-served if only one between B and L is conserved, R-parity violating (RPV) SUSY models are constructed with this in view. Of these, the versions containing L-violating interactions, trilinear and/or bilinear, have the added motivation of offering explanations of neutrino masses and mixing.

The consequences of RPV interactions have been explored extensively in the literature [19]. Especially, when L-violation takes place, although the conventional large missing signature of SUSY is degraded, the possibility of obtaining multilepton final states is enhanced [20]. Recently, it has also been demonstrated that in presence of these L-violating operators, rather striking same-sign three-and four-lepton final states, which are free from SM backgrounds, are expected in large rates at the LHC  [21].

In presence of the -type couplings, if the neutralino is the lightest supersymmetric particle (LSP), it will decay to a pair of leptons and a neutrino. Thus, starting from the pair production of squarks/gluinos in the initial parton level hard scattering, we can obtain two neutralinos at the end of the decay cascade, which in turn can give rise to a four-lepton final state with unsuppressed rate for every SUSY process. Also, at least two additional jets will always be present from the decay of the squark pair. Thus, one can very easily obtain the (). If in addition to this, another lepton is produced from the cascade decay of a chargino, we can also obtain a five-lepton final state.

The -type interactions, on the other hand, cause a neutralino LSP to decay into a lepton and two parton-level jets, this giving a dilepton final state for every SUSY particle production process. Four-lepton final states can arise through two additional leptons produced in cascade, after the initial process. Understandably, the probability of obtaining a four-lepton final state is suppressed compared to dilepton and trileptons.

The bilinear terms imply mixing between neutrinos and neutralinos as also between charged leptons and charginos [22]. Consequently, the lightest neutralino LSP can decay into a neutrino and the Z or a charged lepton and the W, the latter mode being of larger branching ratio. Thus, modulo the leptonic branching ratios of W-and Z-decay, one can have four-lepton final states, with an additional lepton in the cascade to account for the somewhat suppressed five-lepton final states in such a scenario.

It is clear from the above discussion that four-and five-lepton states are expected to have the highest rates in a situation with R-parity is broken through -type interactions alone, with two indices in being either 1 or 2. We, therefore, use this scenario as the benchmark for distinction from other theories through multilepton events. In situations including the other L-violating terms, the dilution in the branching ratio will affect the total rates of such final states (and, as we shall discuss later, the total rates are not very good guidelines in model distinction anyway). However, the kinematical observables on which our proposed distinction criteria are based are likely to remain mostly quite similar. We will comment on some special cases, including those where the lightest neutralino is not the LSP, in section 6.

a.2 Minimal universal extra dimension with KK-parity conservation (UED-KKC)

A rather exciting development in physics beyond the Standard Model (SM) in the last few years is the formulation of theories with compact spacelike extra dimensions whose phenomenology can be tested at the TeV scale. The idea is based on concepts first introduced by Kaluza and Klein [23] in the 1920’s. Extra-dimensional theories can be divided into two main classes. The first includes those where the Standard Model (SM) fields are confined to a (3 + 1) dimensional subspace (3-brane) of the full manifold. Models with the extra spacelike dimensions being both flat [24] or warped [25] fall in this category, although there have been numerous attempts to put some or all of the fields in the ‘bulk’ even within the ambits of these theories. On the other hand, there is a class of models known as Universal Extra Dimension(s) (UED) [26], where all of the SM fields can access the additional dimensions.

In the minimal version of UED (mUED), there is only one extra dimension compactified on a circle of radius ( symmetry). The need to introduce chiral fermions in the resulting four-dimensional effective theory prompts one to impose additional conditions on the extra dimension. This condition is known as ‘orbifolding’ where two diametrically opposite ends of the compact dimension are connected by an axis about which there is a reflection symmetry.

The symmetry breaks the translational invariance along the fifth dimension (denoted by the co-ordinate y) and generates two fixed points at and . From a four-dimensional viewpoint, every field will then have an infinite tower of Kaluza-Klein (KK) modes, the zero modes being identified as the corresponding SM states. The spectrum is essentially governed by where R is the radius of the extra dimension.

UED scenarios can have a number of interesting phenomenological implications. These include a new mechanism of supersymmetry breaking [28], relaxation of the upper limit of the lightest supersymmetric neutral Higgs [29], addressing the issue of fermion mass hierarchy from a different perspective [30] and lowering the unification scale down to a few TeVs [31, 32, 33].

In the absence of the orbifold fixed points, the component of momentum along the extra direction is conserved. From a four-dimensional perspective, this implies KK number conservation, where KK number is given by the position of an excited state in the tower. However, the presence of the two orbifold fixed points breaks the translational symmetry along the compact dimension, and KK number is consequently violated. In principle, one may have some additional interaction terms localised at these fixed points, causing mixing among different KK states. However, if these interactions are symmetric under the exchange of the fixed points (this is another symmetry, not to be confused with the of ), the conservation of KK number breaks down to the conservation of KK parity111In principle, it is possible to have fixed point localized operators that are asymmetric in nature [26]. This could violate KK-parity, analogous to the R-parity violation in supersymmetry. In absence of KK-parity the phenomenology of UED will be drastically different and will be discussed in brief in the next subsection., given by , where is the KK number. This not only implies that level-one KK-modes, the lightest among the new particles, are always produced in pairs, but also ensures that the KK modes do not affect electroweak processes at the tree level. The multiplicatively conserved nature of KK-parity implies that the lightest among the first excitations of the SM fields is stable, and a potential dark matter candidate [27].

The tree-level mass of a level- KK particle is given by , where is the mass associated with the corresponding SM field. Therefore, the tree level mUED spectrum is extremely degenerate and, to start with, the first excitation of any massless SM particle can be the lightest KK-odd particle (LKP). In practice, radiative corrections [34] play an important role in determining the actual spectrum. The correction term can be finite (bulk correction) or it may depend on , the cut-off scale of the model (boundary correction). Bulk corrections arise due to the winding of the internal lines in a loop around the compactified direction [34], and are nonzero and finite only for the gauge boson KK-excitations. On the other hand, the boundary corrections are not finite, but are logarithmically divergent. They are just the counterterms of the total orbifold correction, with the finite parts being completely unknown. Assuming that the boundary kinetic terms vanish at the cutoff scale the corrections from the boundary terms, for a renormalization scale , are proportional to . The bulk and boundary corrections for level-n doublet quarks and leptons ( and ), singlet quarks and leptons ( and ) and KK gauge bosons (, , and ) are given by,

• Bulk corrections:

 δ(m2Bn) = −39ζ(3)a12π2R2 , δ(m2Wn) = −5ζ(3)a22π2R2 , δ(m2gn) = −3ζ(3)a32π2R2 , (A-3)

where, .

• Boundary corrections:

 ¯δmQn = mn(3a3+2716a2+a116)L0 ,  ¯δmun = mn(3a3+a1)L0 , ¯δmdn = mn(3a3+a14)L0 ,            ¯δmLn = mn(2716a2+916a1)L0 , ¯δmen = 9a14mnL0 ,                     ¯δ(m2Bn) = −a16m2nL0 ¯δ(m2Wn) = 15a22m2nL0 ,                    ¯δ(m2gn) = 23a32m2nL0 , ¯δ(m2Hn) = m2n(32a2+34a1−λH16π2)L0+¯¯¯¯¯m2H , (A-4)

where , being the respective gauge coupling constants and is the boundary term for the Higgs scalar, which has been chosen to be zero in our study.

These radiative corrections partially remove the degeneracy in the spectrum [34] and, over most of the parameter space, , the first excitation of the hypercharge gauge boson (), is the LKP 222The KK Weinberg angle is small so that and . . The can produce the right amount of relic density and turns out to be a good dark matter candidate [27]. The mass of is approximately and hence the overclosure of the universe puts an upper bound on 1400 GeV. The lower limit on comes from the low energy observables and direct search of new particles at the Tevatron. Constraints from of the muon [36], flavour changing neutral currents [37, 38, 39], [40], the parameter [26, 41], other electroweak precision tests [42], etc. imply that GeV. The masses of KK particles are also dependent on , the cut-off of UED as an effective theory, which is essentially a free parameter. One loop corrected , and gauge couplings show power law running in the mUED model and almost meet at the scale = [31]. Thus one often takes as the cut-off of the model. If one does not demand such unification, one can extend the value of to about , above which the coupling becomes nonperturbative.

After incorporating the radiative effects, the typical UED spectrum shows that the coloured KK states are on top of the spectrum. Among them, , the gluon, is the heaviest. It can decay to both singlet () and doublet () quarks with almost the same branching ratio, although there is a slight kinematic preference for the singlet channel. can decay only to and an SM quark. On the other hand, a doublet quark decays mostly to or . Hadronic decay modes of and are closed kinematically, so that they decay to different doublet leptons. Similarly can decay only to or . The KK leptons finally decay to the and SM leptons. Thus, the principal signals of such a scenario are jets + leptons + MET, where can vary from 1 to 4.

a.3 mUED with KK-parity violation (UED-KKV)

Let us now briefly introduce KK-parity violation and its phenomenological consequences. As discussed in the previous subsection, operators localised at the orbifold fixed points give rise to mixing between different KK-states. In presence of such operators that are symmetric under exchange of the fixed points, even and odd KK-parity states mix separately, so that KK-parity is still a conserved quantity. However, it is possible to have fixed point operators which are asymmetric in nature, leading to the violation of KK-parity [26]. The phenomenology of KK-parity violation was studied in some detail in Ref. [35]. KK-parity violating couplings allow the LKP to decay into SM particles.

The asymmetry in the localised operators can be introduced by adding the following extra contribution to the operators localized at the point :

 Lf=λΛ∫[i¯ψΓαDαψ−i(Dα¯ψ)Γαψ]δ(y)dy, (A-5)

where, is the 5-dimensional fermion field, are the gamma matrices and are the covariant derivatives defined in (4+1) dimensions, is the strength of the KK-parity violating coupling, and is the cut-off scale. The above operator has the following consequences:

• Equation A-5 gives rise to KK-parity violating mixing between KK-even and odd states. Of them, the mixing between and states are most relevant from the angle of the LHC phenomenology. The admixture of KK-states with the state is suppressed by the higher masses of the former.

• Equation A-5 leads to the coupling between two KK-fermions ( and ) and a gauge boson ():