1 Introduction
###### Abstract

If new leptons exist close to the electroweak scale, they can be produced in pairs at LHC through standard or new interactions. We study the production of heavy lepton pairs in SM extensions with: (i) a Majorana or Dirac lepton triplet, as those appearing in type-III seesaw; (ii) a lepton isodoublet ; (iii) a charged isosinglet ; (iv) a Majorana or Dirac neutrino singlet and an additional gauge boson. It is shown that the trilepton final state , which has a small SM background, constitutes the golden channel for heavy neutrino searches, being very sensitive to Majorana or Dirac neutrinos in triplet, doublet or singlet representations. For higher luminosities, signals in this final state can also distinguish lepton triplets from doublets and singlets. The Majorana or Dirac nature of the heavy neutrinos is revealed by the presence or not of like-sign dilepton signals without significant missing energy. Notably, large signals but with large missing energy are characteristic of Dirac triplets, distinguishing them from the other two models with a heavy Dirac neutrino. Further discrimination is achieved with the analysis of the clean final state.

Heavy lepton pair production at LHC:

[2mm] model discrimination with multi-lepton signals

J. A. Aguilar–Saavedra

[0.2cm] Departamento de Física Teórica y del Cosmos and CAFPE,

[0.1cm]

## 1 Introduction

Being a discovery machine, the Large Hadron Collider (LHC) will hopefully uncover any new physics close to the electroweak scale. In particular, the several variants of the seesaw mechanism proposed to explain light neutrino masses can be tested [1, 2]. In case that one of these mechanisms is responsible for the light neutrino mass generation and seesaw messengers exist around the TeV scale or below, positive signals could be observed at LHC.

There are three types of tree-level seesaw which can originate light neutrino Majorana masses. The original seesaw [3, 4, 5, 6], also known as seesaw I, introduces right-handed neutrino singlets . Seesaw II [7, 8, 9, 10, 11] enlarges the SM with a complex scalar triplet with hypercharge , which contains three scalars , , . Seesaw III [12, 13] introduces lepton triplets with , each containing a charged lepton and a neutral one . In these three seesaw mechanisms, the lepton number violating (LNV) operator [14]

 (O5)ij=CijΛ¯¯¯¯¯¯¯¯LciL~ϕ∗~ϕ†LjL, (1)

is generated after integration of the heavy degrees of freedom, where are the SM lepton doublets with a flavour index, and is the SM Higgs. Subsequently, when electroweak symmetry is spontaneously broken, this operator gives light neutrino Majorana masses. The scale at which this operator is generated (i.e. the mass scale of the seesaw messengers) is not necessarily very high but it might happen that it is around the TeV. In this case, the new leptons predicted in models of type-I and type-III seesaw might be produced at LHC.111In seesaw II the scalars predicted can also be produced and observed in this mass range [1] (see also Refs. [15, 16, 17, 18, 19, 20]). For seesaw III, if the new heavy states , have masses up to several hundreds of GeV, they can be produced and observed at LHC already at the low luminosity phase [1]. For seesaw I, the production of heavy neutrino singlets through SM interactions is very suppressed because of the small heavy neutrino mixing with SM particles, and signals are unobservable except for relatively “light” masses around 150 GeV [21]. However, if new interactions exist, either bosons [22, 23, 24, 25, 26], bosons [27, 28, 29, 30] or new scalars [31, 32], heavy neutrino singlets can be copiously produced, either singly or in pairs depending on the model.

The observability of the seesaw I–III signals and the discrimination among these models has been investigated in Ref. [1]. There, an exhaustive analysis of all final states was carried out with a complete signal and background calculation, and the characteristic features of each seesaw model were highlighted. In this paper we will perform a complementary analysis. Our main objective here is to identify the relevant signals whose observation or non-observation would discriminate among different models with new heavy leptons. In particular, we want to design a strategy to determine if new leptons eventually observed at LHC could mediate a type-I or type-III seesaw mechanism. We will study heavy lepton pair production

 pp→E+E−, pp→E±N, pp→NN, (2)

where generically denotes a heavy charged lepton and a neutral one, in several SM extensions with new leptons in different representations. We consider the following additions to the SM particle content:

• A Majorana lepton triplet , containing a charged lepton and a Majorana neutrino . Generically, three such triplets appear in minimal seesaw III realisations, but as in previous studies [1] we restrict our calculations to the lightest one.

• A Dirac lepton triplet . This is an alternative to the minimal seesaw III in which two (quasi-)degenerate Majorana triplets , with opposite CP parities form a (quasi-)Dirac triplet  [2], in analogy with the sometimes called “inverse” type-I seesaw with heavy Dirac neutrinos [33, 34, 35, 36]. In this case the heavy states are two charged leptons , and a Dirac neutrino .

• A lepton isodoublet , in which the heavy neutrino is likely to have (quasi-)Dirac character. A lepton isodoublet cannot generate the operator in Eq. (1) but this does not exclude the possibility that they exist, independently of the neutrino mass generation mechanism.

• A charged lepton isosinglet , which can also exist independently of the neutrino mass generation.

• A Majorana singlet and an extra gauge boson . For definiteness we work with an model with a leptophobic boson and heavy Majorana neutrinos [27], assuming that only one of them, with mass , can be produced in decays. But the results obtained here are general because the relative rate of the multi-lepton signals produced in is only determined by the heavy Majorana neutrino decay channels, and the particular type of boson considered only affects the total production cross section. Therefore, the results shown here can be applied to other models [28, 29] with a trivial rescaling.

• A Dirac singlet , formed by two Majorana singlets, and an extra boson. We work with the same model in Ref. [27] but assuming that two Majorana neutrinos form a (quasi-)Dirac neutrino.

In all the models enumerated above, one or more heavy lepton pairs , , can be produced in hadron collisions. Moreover, in the case of lepton doublets and triplets the two states , are almost degenerate in mass. But because the production processes and especially the heavy lepton decay channels are different in each model, the final state signatures are characteristic and the models can be distinguished already at LHC, without the need of precise measurements at a future collider like ILC. The model discrimination relies on the simultaneous analysis of different final states with two, three and four leptons, and the reconstruction of peaks in invariant mass distributions. We will find that the trilepton signal , with , is common to all models introducing a heavy neutrino,222It can also appear in the case of the singlet but with a very small branching ratio. and has a small SM background. Therefore, it constitutes the golden channel for heavy neutrino searches at LHC, in particular for the search of seesaw messengers. Moreover, the study of this channel can also reveal if a heavy neutrino eventually observed belongs to a triplet or not. Its Dirac or Majorana nature can be determined in the like-sign dilepton final state: the observation of a signal without missing energy clearly indicates its Majorana character whereas the absence of such signal points towards one of the other models. Like-sign dileptons but with large missing energy can distinguish Dirac triplets, which give a large and observable signal, from Dirac doublets and singlets which give much smaller ones. Finally, the model identification is completed with the analysis of four lepton signals and the search of a resonance in the total invariant mass distribution.

We must point out that the models considered in this paper do not exhaust all possibilities for the addition of heavy leptons and/or new interactions to the SM, but rather constitute the cases in which model discrimination seems hardest because the heavy leptons are nearly degenerate, they always decay into a light lepton plus a , or boson and their charge cannot be measured in hadronic decays. Two possibilities not covered here, in which model discrimination is easier, are:

• A fourth SM generation of chiral leptons. In this case, the mass splitting between the mass eigenstates is expected to be large to be consistent with precise electroweak data [37, 38, 39], unlike in the cases examined here. Apart from this distinctive characteristic, the leading decay of the charged lepton would be , so that production would produce events in which the mass resonances have more jets than in the models discussed here. Moreover, anomaly cancellation requires the presence of new quarks with masses of few hundreds of GeV (or new fermions with the same quantum numbers, giving rise to observable resonances [39]), which would be produced in pairs and observed already with a relatively small luminosity [40, 41].

• A Majorana neutrino coupling to a new boson, as for example those appearing in left-right models. In this case the heavy neutrino can be produced in association with a light lepton,

 pp→W′→ℓN. (3)

This process gives signals with up to three charged leptons in some regions of parameter space [26], but they can be clearly distinguished from heavy lepton pair production by the reconstruction of only one heavy resonance which, together with an energetic light lepton, produces a Jacobian peak at the mass.

In this work we do not consider scalar triplet production (seesaw II) either, which gives signals kinematically very different with sharp peaks in like-sign dilepton invariant mass distributions. It is interesting, however, to note that in seesaw II the trilepton signals are the most important as well [1]. Multi-lepton signals can also appear in pair production of new quarks [42] but they can be easily distinguished from the models studied here by mass reconstruction and also by the presence of significant single lepton signals with several -tagged jets.

The structure of this paper is as follows. After this introduction, we briefly summarise in section 2 the relevant Lagrangian terms, the production processes at LHC and the decay channels of the heavy leptons in the models studied. In section 3 we describe how the signals and backgrounds are simulated. The results for the , and final states are presented in sections 46. Section 7 summarises these results and shows explicitly how the six models considered in this work can be distinguished. We draw our conclusions in section 8. In appendix A we give the partial widths for heavy lepton decays in the different models studied.

## 2 Description of the models

Here we present the different models studied in turn, collecting the interactions relevant for our analysis and enumerating the production processes at LHC and the allowed decay channels of the heavy leptons. At the end of this section we summarise the main features and compare among the different models.

### 2.1 A Majorana lepton triplet

The relevant Lagrangian for any number of Majorana triplets has been previously given in Ref. [1], and we follow the notation in that work. For a single triplet , the interactions of the heavy leptons , with SM leptons , is, at first order in the light-heavy mixing ,

 LW =−g(¯EγμNW−μ+¯NγμEW+μ) −g√2(VlN¯lγμPLNW−μ+V∗lN¯NγμPLlW+μ) −g(VlN¯EγμPRνlW−μ+V∗lN¯νlγμPREW+μ), LZ =gcW¯EγμEZμ +g2cW¯νlγμ(VlNPL−V∗lNPR)NZμ +g√2cW(VlN¯lγμPLE+V∗lN¯EγμPLl)Zμ, Lγ =e¯EγμEAμ, LH =gmN2MW¯νl(VlNPR+V∗lNPL)NH +gmE√2MW(VlN¯lPRE+V∗lN¯EPLl)H. (4)

Heavy lepton pairs are produced by the gauge , and interactions,

 q¯q→Z∗/γ∗→E+E−, q¯q′→W∗→E±N, (5)

(note that there are no interactions because the triplet has zero hypercharge, and pairs are not produced). The heavy leptons , decay to SM leptons plus a gauge or Higgs boson:

 E+→νW+,E+→l+Z,E+→l+H, N→l−W+,N→l+W−,N→νZ,N→νH. (6)

The two heavy states are nearly degenerate in mass, with a small splitting due to radiative corrections, and the decays between the heavy states are very suppressed [43].

### 2.2 A Dirac lepton triplet

A (quasi-)Dirac lepton triplet is formed by two (quasi-)degenerate Majorana ones with opposite CP parities. As it was shown in Ref. [2], the heavy fields can be redefined in such a way that the Lagrangian is written in terms of two charged leptons , (the fermion is positively charged in the second case) and a Dirac neutrino , and lepton number is conserved up to effects of the order of light neutrino masses. At first order in we have

 LW =−g(¯E−1γμN−¯NγμE+2)W−μ−g(¯NγμE−1−¯E+2γμN)W+μ −g√2(VlN¯lγμPLNW−μ+V∗lN¯NγμPLlW+μ) +g(VlN¯νlγμPLE+2W−μ+V∗lN¯E+2γμPLνlW+μ), LZ =gcW(¯E−1γμE−1−¯E+2γμE+2)Zμ +g2cW(VlN¯νlγμPLN+V∗lN¯NγμPLνl)Zμ +g√2cW(VlN¯lγμPLE−1+V∗lN¯E−1γμPLl)Zμ, Lγ =e(¯E−1γμE−1−¯E+2γμE+2)Aμ, LH =gmN2MW(VlN¯νlPRN+V∗lN¯NPLνl)H +gmE1√2MW(VlN¯lPRE−1+V∗lN¯E−1PLl)H. (7)

Heavy lepton pairs are produced by the gauge , and interactions,

 q¯q→Z∗/γ∗→E+iE−i, q¯q′→W∗→E±iN, (8)

Since there are two charged fermions instead of only one (and a Dirac neutrino is equivalent to two Majorana ones), the total heavy lepton production cross section is twice larger than for a Majorana triplet. The decays have some differences with respect to a Majorana triplet because does not couple to light neutrinos, does not couple to light charged leptons and decays conserve lepton number. Thus, the allowed ones are

 E−1→l−Z,E−1→l−H,E+2→νW+, N→l−W+,N→νZ,N→νH. (9)

### 2.3 A lepton isodoublet

The Lagrangian for a lepton isodoublet can be found in Ref. [44]. With our notation, the terms involved in heavy lepton production and decay are, at first order in ,

 LW =−g√2(¯EγμNW−μ+¯NγμEW+μ) −g√2(VlN¯lγμPRNW−μ+V∗lN¯NγμPRlW+μ) LZ =−g2cW([−1+2s2W]¯EγμE+¯NγμN)Zμ +g2cW(VlN¯lγμPRE+V∗lN¯EγμPRl)Zμ, Lγ =e¯EγμEAμ, LH =gmE2MW(VlN¯lPLE+V∗lN¯EPRl)H. (10)

Note that the neutrino is likely to be a Dirac fermion because the renormalisable gauge-invariant doublet mass term

 Lmass=−mD¯¯¯¯¯¯¯¯¯L4RL4L+H.c., (11)

with , implies a Dirac mass. Additional Majorana masses may appear from dimension-five operators,

 L5mass=CL44Λ¯¯¯¯¯¯¯¯¯Lc4L~ϕ∗~ϕ†L4L+CR44Λ¯¯¯¯¯¯¯¯¯Lc4R~ϕ∗~ϕ†L4R. (12)

However, if the physics generating these operators is the same as the one yielding the light neutrino mass operator in Eq. (1), one would expect that the Majorana mass terms, of order , are much smaller than . In this case, is a (quasi-)Dirac fermion.

The production processes are the same as for a Majorana triplet but now neutral pairs are also produced because they couple to the boson,

 q¯q→Z∗/γ∗→E+E−, q¯q′→W∗→E±N, q¯q→Z∗→¯NN. (13)

A further difference is in the size of the couplings, e.g the coupling to the boson is reduced by a factor , and so the cross section is a factor of two smaller. In this model the heavy lepton decays are also different, being allowed only

 E+→l+Z,E+→l+H, N→l−W+. (14)

### 2.4 A charged singlet

The Lagrangian for a charged lepton isosinglet can also be found in Ref. [44]. In our notation, and at first order in the light-heavy mixing , the relevant terms are

 LW =−g√2(VEνl¯EγμPLνlW−μ+V∗Eνl¯νlγμPLEW+μ), LZ =−gs2WcW¯EγμEZμ +g2cW(VEνl¯EγμPLℓ+V∗Eνl¯lγμPLE)Zμ, Lγ =e¯EγμEAμ, LH =−gmE2MW(VEνl¯EPLl+V∗Eνl¯lPRE)H (15)

In this model only charged lepton pairs are produced,

 q¯q→Z∗/γ∗→E+E−, (16)

which later decay in the three possible modes

 E+→νW+,E+→l+ZE+→l+H. (17)

### 2.5 A Majorana neutrino and a Z′ boson

A heavy Majorana neutrino which is a singlet under interacts with SM fields via a small mixing with SM fermions (for a detailed derivation of the Lagrangian see for example Ref. [45]). Its interactions are therefore suppressed, being at least of order ( interactions are of order ). However, the interactions with an extra boson are not suppressed if is not a singlet under the gauge group , and are determined by the heavy neutrino charge under this extra . At first order in , the relevant Lagrangian is

 LW = −g√2(VlN¯lγμPLNW−μ+V∗lN¯NγμPLlW+μ), LZ = −g2cW¯νlγμ(VlNPL−V∗lNPR)NZμ, LH = −gmN2MW¯νl(VlNPR+V∗lNPL)NH, LZ′ = −g′Q2¯Nγμγ5NZ′μ. (18)

In the model considered here [27] we have , and we have generically denoted the coupling as . We assume that it equals the SM coupling of , but this may change by renormalisation group evolution effects. Heavy neutrino pairs can be produced with the exchange of an -channel boson,

 q¯q→Z′→NN, (19)

and the heavy neutrinos decay giving a , or boson plus a light lepton,

 N→l−W+,N→l+W−,N→νZ,N→νH. (20)

### 2.6 A Dirac neutrino and a Z′ boson

Finally, in the case of a (quasi-)Dirac neutrino composed by two (quasi-)degenerate Majorana neutrinos with opposite CP parities and equal charges under , the relevant Lagrangian is

 LW = −g√2(VlN¯lγμPLNW−μ+V∗lN¯NγμPLlW+μ), LZ = −g2cW(VlN¯νlγμPLN+V∗lN¯NγμPLνl)Zμ, LH = −gmN2MW(VlN¯νlPRN+V∗lN¯NPLνl)H, LZ′ = −g′Q¯Nγμγ5NZ′μ (21)

Heavy Dirac neutrino pairs can be produced in the same process

 q¯q→Z′→¯NN, (22)

and the cross section is twice larger than for a Majorana because the symmetry factor for identical particles is not present in this case (the width is also a factor of two larger).333Note that the Feynman rule for Majorana fermions contains an extra factor of two to account for the two possible Wick contractions, so that the vertex is as in the Dirac case. Heavy neutrino decays are the same except for the absence of the LNV one,

 N→l−W+,N→νZ,N→νH. (23)

### 2.7 Summary

In each of the preceding subsections we have indicated the heavy lepton pair production processes present in each model. For better comparison of the different models, we summarise in Table 1 the coupling constants appearing in the production vertices involved, coupling two heavy leptons to a gauge boson. From now on we will use the labels , to refer to the models with Majorana and Dirac triplets, respectively, and for the doublet and singlet , and , for the SM extensions with a leptophobic boson and a Majorana or Dirac neutrino. The production cross sections are presented in Fig. 1 as a function of the heavy lepton mass (as well as the mass in the corresponding models).

The decay of the heavy leptons takes place in the channels indicated, with partial widths collected in appendix A for reference. Nevertheless, the important quantities for LHC phenomenology are the relative branching ratios. Summing over light leptons , the branching ratios into , and bosons are independent of the mixing. Their values for , are collected in Table 2. This table illustrates the important differences among the models considered, which make the discrimination based on multi-lepton signals quite effective. Note that for masses GeV as considered in the following sections, the branching ratios are already close to the values presented in this table.

## 3 Multi-lepton signal generation

The analysis pursued in this work, aiming to discriminate among several models all giving various multi-lepton signals in different decay channels, is somewhat demanding from the point of view of the simulation. It requires to generate all the signal contributions because many different heavy lepton decay channels, with the subsequent decay, can lead to the same charged lepton multiplicities. The complete signal generation has been done with the program Triada [1] extended to include the models with an isodoublet , an isosinglet and production with decay to a Majorana or Dirac neutrino. All the signal processes enumerated in the previous section, with all the possible decays of the heavy leptons , and the bosons, are included. The Higgs boson decay, which does not carry any spin information, is left to the parton shower Monte Carlo. Signals have been generated with statistics of 300 fb and rescaled to a reference luminosity of 30 fb, in order to reduce statistical fluctuations. The SM background, consisting of the processes in Table 3, is generated using Alpgen [46] with a Monte Carlo statistics of 30 fb. Additional SM processes which were previously shown to be negligible after selection cuts [1] are ignored in this work. Signals and backgrounds are passed through the parton shower Monte Carlo Pythia 6.4[47] to add initial and final state radiation (ISR, FSR) and pile-up, and perform hadronisation. For the backgrounds we use the MLM prescription [48] for the matching to avoid double counting between the matrix-level generator and the parton shower Monte Carlo. We use the fast simulation AcerDET [49] which is a generic LHC detector simulation, neither of ATLAS nor of CMS, finding good agreement with our previous results [1].

We remark that the use of at least a fast simulation of the detector is essential for this and other similar studies, because some of the most important SM backgrounds have charged leptons resulting from quark decays, and these cannot be estimated in a parton-level analysis. In fact, the most recent analyses for supersymmetry searches performed with a full detector simulation [50] confirm the well-known fact that is probably the largest (and most dangerous) SM source of like-sign dileptons. From the point of view of the signal, the use of a fast detector simulation is also necessary because some of the contributions to the multi-leptonic final states studied arise when more charged leptons are produced but missed by the detector.

In the following sections we will take heavy lepton masses GeV for our simulations. Production cross sections are independent of the mixing and, except for unnaturally small values, the heavy leptons will decay well inside the detector. Note that the heavy lepton widths are larger than the quark width for , and present indirect constraints are of order  [51]. In definite seesaw models, heavy lepton mixing is also related to light neutrino masses. However, we do not assume any particular model-dependent relation between light neutrino masses and heavy lepton mixing. Instead, we assume that heavy leptons only couple to the first generation, bearing in mind that for an arbitrary mixing with the first two generations the results obtained would be approximately the same (the signals are equivalent and at high transverse momenta the SM backgrounds involving electrons and muons have roughly the same size). On the other hand, if , only mix with the tau the signals would be very difficult to observe [1]. For the boson we will conservatively take a mass of 650 GeV, because this is approximately the location of the maximum in the heavy lepton pair invariant mass distribution for GeV when they are produced by off-shell bosons. Hence, for such mass the identification of an -channel resonance would be more difficult. This mass is not excluded by present Tevatron searches for resonances. For the model considered, the cross section into final states (assuming ) is about 0.2 pb, well below the 95% confidence level limit for this mass, which is around 0.6 pb [52]. The Higgs boson mass is taken as GeV, in which case it mainly decays into two jets, and seldom produces leptons, only when with leptonic decay. For a heavier Higgs decaying into , , the multi-lepton signals examined here would still be present but some signals with higher lepton multiplicity, originating from heavy lepton decays involving a Higgs boson and , would also be present and might be of interest. In addition, several SM backgrounds (for example, plus jets) would be enhanced. A dedicated analysis is required to examine the precise discovery potential of each channel in such case.

Finally, it is worth commenting here about the statistical prescriptions used to determine a possible discovery. If the background can be precisely known or directly estimated from data, for instance if the signal shows up as a sharp peak, the statistical significance is , where , are the number of signal and background events, respectively. For small , this estimator is replaced by the -number using Poisson statistics. The discovery criteria used in this work are: (i) statistical significance larger than , and (ii) the presence of at least 10 signal events. In most of our results the luminosity required for discovery does not depend on a very precise background normalisation because the background is tiny, so that the signal significance is well above and the limit is determined by having 10 signal events.

## 4 Final state ℓ±ℓ±ℓ∓

This final state is the most characteristic one of a heavy neutrino, and it can appear both in and production, for example in the decay channels

 E+N→ℓ+Zℓ±W∓, Z→q¯q/ν¯ν,W→ℓν, E+N→ℓ+Hℓ±W∓, H→q¯q,W→ℓν, NN→ℓ+W−ℓ−W+, WW→q¯qℓν, (24)

irrespectively of the Dirac or Majorana character of . For a lepton triplet, it can also be produced in several other decays, for example

 E+N→ℓ+ZνZ, ZZ→ℓ+ℓ−q¯q/ν¯ν, E+N→ℓ+ZνH/ℓ+HνZ, Z→ℓ+ℓ−,H→q¯q. (25)

Note that , do not take place in the case of a lepton doublet, which can be exploited to distinguish them from triplets. With this aim, we perform two complementary analyses for the final state, dividing the sample into two disjoint ones. First, we perform a generic analysis as in Ref.[1], which can detect the presence of a heavy neutrino singlet, doublet or triplet decaying in the channels of Eqs. (24). In this analysis we reject events with a boson candidate, that is, with an opposite-charge lepton pair with an invariant mass consistent with . This sample is labelled as (no ). In second place, we perform a new specific analysis to search for the decays in Eqs. (25) and determine whether the neutrino belongs to a triplet. In this case we only accept events with a boson candidate. This sample is labelled as (). The common event pre-selection criteria for the two analyses are: (i) the presence of two like-sign leptons and with transverse momentum GeV and an additional (and only one) lepton of opposite sign, with GeV; (ii) two hard jets with GeV. The cut on transverse momenta of the like-sign pair greatly reduces the SM background from production. The requirement of two jets is used in the kinematical reconstruction, and also reduces the background. We must point out that this background, as simulated with Alpgen, does not include off-shell photons and uses the narrow width approximation for both bosons. The effect of off-shell photons is important in general [53] but in this case this contribution is reduced by the high- requirement on charged leptons. More important is the effect of the width: the narrow approximation underestimates the background for the ‘no ’ sample and overestimates it in the complementary ‘’ one. With a comparison of the reconstructed distributions for and on-shell after detector simulation, we estimate that for the ‘no ’ trilepton final state the background can be at most two times larger than the values given here. This can be compensated, at the cost of some signal efficiency loss, by a wider interval for rejection of events with a candidate, and the discovery potential would be very similar. Model discrimination, of course, would not be affected.

### 4.1 Final state ℓ±ℓ±ℓ∓ (no Z)

In this analysis we ask for event selection the absence of a boson candidate: neither of the two opposite-sign lepton pairs can have an invariant mass closer to than 10 GeV. This is very useful to remove production but also eliminates several of the signal channels. We collect in Table 4 the number of signal and background events for each process and model after pre-selection and selection cuts.

The event reconstruction is performed in three steps, following this procedure [1]:

1. The momentum of the or boson decaying hadronically is reconstructed as the sum of the momenta of the leading and sub-leading jets.

2. One of the heavy charged leptons ( or , depending on the process) can be reconstructed from this boson and one of the two like-sign leptons, and the heavy neutrino from the two remaining leptons (with opposite charge) and the missing neutrino momentum. The longitudinal component of the neutrino momentum is neglected for the moment, and the transverse component is taken as the missing energy. There are two possibilities for this pairing, and we choose the one giving closest invariant masses for the reconstructed and .

3. The reconstruction can be refined by including the longitudinal neutrino momentum. We select among the two charged leptons the least energetic one , and require that its invariant mass with the neutrino is ,

 (pℓs+pν)2=M2W, (26)

taking the transverse components of as the missing energy. This quadratic equation determines the longitudinal neutrino momentum up to a twofold ambiguity, which is resolved selecting the solution with smaller . In case that no real solution exists, the transverse neutrino momentum used in Eq. (26) is decreased until a real solution is found.

The reconstructed heavy lepton masses after selection criteria are shown in Fig. 2 (left) for the five models which give an observable signal. We point out that one of the resonances, labelled as , can be identified as being a neutral lepton, because the peak appears in the invariant mass distribution of two opposite-charge leptons plus missing energy. The identity of the other resonance, labelled as , cannot be established because the charge of the hadronic jets cannot be measured. In fact, depending on the process and the model, it can be a charged or neutral heavy lepton (see Table 4). In Fig. 2 (right) we show the same distributions for the SM background and the background plus the Majorana triplet signal, which is the smallest one. We define the peaks as the intervals

 240

and show in Table 4 the number of signal and background events after these cuts. The statistical significance for 30 fb of the relevant signals (neglecting the background uncertainty) is collected in Table 5, with the luminosity required to achieve discovery. Due to the smallness of the background, the discovery luminosity is determined in each case by the requirement of having at least 10 signal events. For such small luminosities the SM background is tiny, around one event or less, and a very precise normalisation is not very important. Notice also that the signals (and thus the statistical significance) are larger for a lepton doublet than for the triplets, despite the smaller production cross section. This is mainly due to the larger (100%) branching ratio of the mode , and also to the presence of production.

With the results shown, we observe that this final state is very sensitive to the presence of heavy neutrinos in all the models considered (except the one with the charged singlet, which does not have a neutral lepton).444Note that the sensitivity to Majorana triplets can be improved with a more inclusive analysis without event reconstruction, and the luminosity required for discovery can be reduced to 1.7 fb [1]. We can then ask ourselves whether one could already distinguish some of these models. This is indeed possible, although model discrimination probably requires more luminosity than discovery. By examination of the heavy lepton pair invariant mass, one can determine if these leptons are produced by the exchange of an -channel resonance, as it is the case in the models with an extra boson. We show in Fig. 3 this kinematical distribution for the signals only, separating for clarity the models in which the heavy neutrino has Majorana (up) and Dirac nature (down), which can be distinguished by other means (see section 5.1). On the right we show possible experimental results for 10 fb, obtained by making random fluctuations with a Poisson distribution of the bins in the distributions, and normalising to the total expected number of events. The background is much smaller than the signals and has not been included. It is quite clear that the presence of a resonance can be detected or excluded, possibly with a smaller luminosity, but we do not address this issue quantitatively.

### 4.2 Final state ℓ±ℓ±ℓ∓ (Z)

The trilepton sample with a boson candidate suffers from a large background. Nevertheless, several of the decay channels in Eqs. (25) produce a sharp peak in the trilepton invariant mass distribution, corresponding to the heavy charged lepton mass . This peak can be observed over the large background. As event selection criteria we require: (i) a boson candidate, with two opposite-charge leptons having an invariant mass between GeV and GeV; (ii) missing energy GeV. The number of signal and background events after event pre-selection and selection is given in Table 6.

The heavy mass is simply reconstructed as the three-lepton invariant mass. Its distribution is shown in Fig. 4 (left) for the five non-negligible signals. For the lepton triplet the peaks could be seen over the SM background, as it is shown in the right side of this figure for the Majorana triplet. These results can be understood with the following considerations:

1. The off-peak contributions in the lepton triplet models result, for example, from the decay channels in Eqs. (25) with . In this case the resonance would be seen in the invariant mass of two jets plus the other lepton, all of them being decay products. However, the corresponding peak is very broad due to the worse jet energy resolution, and difficult to see over the large background.

2. As expected, in processes where a charged lepton is not present, as in , the distributions do not display a peak.

3. For a lepton doublet the decay channel , with missed by the detector and , , would also produce a trilepton signal with a peak at . However, this process is removed by the missing energy requirement, and the rest of the decay channels do not have any resonance in the trilepton invariant mass, as it can be seen in Fig. 4. This feature clearly distinguishes a lepton doublet from a (Majorana or Dirac) triplet.

Defining the peak region as

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and performing a kinematical cut on this reconstructed mass, we obtain for each process the number of events listed in Table 6. The statistical significance of the signals and the luminosity required for discovery are presented in Table 7.