Same-sign Multilepton Signatures of an $SU(2)_R$ Quintuplet at the LHC

We study in detail the collider signatures of an $SU(2)_R$ fermionic quintuplet in the framework of left-right symmetric model in the context of the 13 TeV LHC. Apart from giving a viable dark matter candidate ($\chi^0$), this model provides unique collider imprints in the form of same-sign multileptons through the decays of multi-charged components of the quintuplet. In particular, we consider the scenario where the quintuplet carries $(B - L) = 4$ charge, allowing for the presence of high charge-multiplicity particles with relatively larger mass differences among them compared to $(B - L)$ = 0 or 2. In this paper, we mainly focus on the same-sign n-lepton signatures (nSSL). We show that with an integrated luminosity of 500 $fb^{-1}$, the mass of the neutral component, $M_{\chi^0} \leq 480~(800)$ GeV can be excluded at 95\% CL in the 2SSL (3SSL) channel after imposing several selection criteria. We also show that a $5\sigma$ discovery is also achievable if $M_{\chi^0} \leq 390~(750)$ GeV in the 2SSL (3SSL) channel with 1000 $fb^{-1}$ integrated luminosity.


Introduction
The Standard model (SM) of particle physics is the most successful description of the fundamental particles and interactions. Almost all the predictions of the SM have been verified by different experiments. Yet a number of terrestrial and extra-terrestrial observations compel us to think of the SM as a low energy theory requiring new physics at the high scale. The observation of neutrino oscillation, existence of dark matter (DM) and dark energy, baryon asymmetry of the universe are a few among the many anomalies that have been observed so far. Some of these anomalies, including the generation of light neutrino masses and the existence of a suitable DM candidate can be addressed in the Quintuplet Dark Matter model [1][2][3] in a left-right (LR) symmetric framework that has been considered in the present work. This model is inspired by Minimal Dark Matter [4][5][6][7] scenario and can also give rise to very interesting collider signatures, which we have studied in detail in this paper.
Minimal Dark Matter models are minimal extensions of the SM with a bosonic or fermionic multiplet which include a stable (over the lifetime of the universe), colored and electrically neutral particle candidate for DM. These new multiplets are chosen to be an n-tuplet of the SU (2) group with no strong interactions. The stability of the n-tuplet is either accidental or is ensured by some discrete symmetry. A quintuplet fermionic multiplet is unique in the sense that it is the smallest multiplet which does not require any discrete symmetries to ascertain the stability of its neutral component. For example, the SM fermions and scalars being doublets or singlets under SU (2), the neutral component of a SU (2) quintuplet fermion can only decay into SM particles through operators with mass dimension 6 or higher. Thus its decay width is suppressed at least by a factor of 1/Λ 2 , where Λ is the scale of new physics. In this scenario, one can ensure the stability of a TeV scale DM for Λ 10 14 GeV. An SU (2) L quintuplet on the other hand has severe constraints from observed DM relic density and limits on DM-nucleon scattering cross-section from direct DM detection experiments. Also, due to small radiative corrections from the SM gauge bosons (W ± , Z and photon), the particles in an SU (2) L quintuplet are nearly degenerate (only a few hundred MeV splitting). Therefore, the decay of a component of the quintuplet to another component gives rise to soft leptons/jets making it difficult to detect at the collider experiments. However, one can exploit these small mass splittings to search for the SU (2) L quintuplet fermion particles using disappearing track signature [8]. SU (2) L quintuplet fermions with additional quadruplet scalars [9,10] can also give rise to interesting signatures at the collider experiments. But, in this case, the neutral component of the quintuplet fermion is stable only over a very finely tuned region of the parameter space.
An alternate solution is to instead introduce a left-right symmetric (LRS) framework [11,12] with a quintuplet being charged under SU (2) R . LRS models with the gauge group extended to SU (3) C ×SU (2) L ×SU (2) R ×U (1) B−L are one of the most well motivated extensions of the SM for a number of reasons. Firstly, they can explain the origin of parity violation observed in the SM as a symmetry broken spontaneously at some high scale. The conservation of parity (P) symmetry at high scale forbids P-violating terms in the QCD Lagrangian [13][14][15][16][17][18][19][20][21] and hence, can naturally solve the strong-CP problem without introducing a global Peccei-Quinn symmetry [22]. Moreover, the presence of a right-handed neutrino in the particle spectrum is essentially governed by the gauge structure and hence, naturally explaining the origin of light neutrino masses.
In this work, we consider SU (3) C × SU (2) L × SU (2) R × U (1) B−L gauge symmetry and introduce a vector-like fermion multiplet which is a quintuplet under SU (2) R and singlet under SU (2) L . We also introduce a scalar multiplet which is doublet under SU (2) R to break SU (2) R × U (1) B−L → U (1) Y and a scalar bidoublet to break the electroweak symmetry, SU (2) L × U (1) Y → U (1) EW . In this scenario, the hypercharge quantum number is a derived quantity and allows for many different combinations of charge assignment for the quintuplet including the possibilities of having a neutral component which could be good candidate for dark matter. The dark matter phenomenology of this particular scenario was studied in details in Ref. [1,3]. It was shown in Ref. [3] that in the presence of a singlet scalar, an SU (2) R quintuplet fermion with neutral state mass even as low as 100 GeV can explain the observed relic density (RD) data and is also consistent with DM direct detection experiments.
The tree-level masses of the quintuplet particles are still degenerate. However, the mass degeneracy among the quintuplet fermions of different charges are now lifted at the righthanded symmetry breaking scale (heavy right-handed gauge bosons are running in the loops) resulting in much larger mass splitting among them. In particular, the mass splitting maximizes for (B − L) = 4 (see Ref. [3]) resulting into relatively harder leptons and jets at the collider experiments. In this work, we study the production and subsequent decay of the high charge-multiplicity components of the quintuplet for (B − L) = 4 at the LHC experiment. We focus our study in the same-sign lepton (SSL) channels at the 13 TeV LHC. The main advantage of SSL channels at LHC is that these channels are less background prone. The SSL channels carry distinct features of Supersymmetry and many other models as referred in several studies [23][24][25][26]. ATLAS and CMS have so far looked in SSL channels in different context, see for example Ref. [27,28]. We have seen that when the neutral component's mass is small, the leptons are soft due to the small mass difference among the components of the quintuplets. Soft leptons also appear in different supersymmetric searches [29][30][31]. Also, soft leptons in 2-opposite sign same flavor channel has been studied in Ref. [32], where the leading and subleading electrons and muons are required to satisfy p T ≥ 5 GeV.
Rest of this paper is organized as follows. In Section 2, we briefly introduce the model. Production and subsequent decays of the charged components of the quintuplet fermions are discussed in Section 3. In Section 4, we discuss the two, three, and four same-sign multilepton signatures (2SSL, 3SSL, and 4SSL) and the corresponding SM backgrounds at the LHC. We also present the exclusion limit and discovery reach at the 13 TeV LHC for SSL channels in detail. Finally, we conclude in Section 5 with discussions.

Quintuplet Dark Matter Model
The gauge group in left-right symmetric models is extended to The matter fermion sector is given as: where, the numbers in the bracket corresponds to SU (3) C , SU (2) L , SU (2) R and U (1) B−L quantum numbers respectively. Here we see that all the quarks and leptons are a part of either left-handed or right-handed doublets. For any particle in this model, the electric charge Q is given as: represents the third component of the isospin for SU (2) L/R . An additional singlet fermion N (1,1,1,0) is also introduced to generate the light neutrino mass through inverse seesaw mechanism [33][34][35][36][37][38].
To break the right-handed symmetry, electroweak (EW) symmetry and to generate the quark and lepton masses and mixing, a minimal scalar Higgs sector is required and given by, The non-zero vacuum expectation values (VEV) of the scalar fields are H 0 The VEV of the doublet v R is responsible for breaking the right-handed symmetry while bidoublet VEVs v 1 and v 2 break the EW symmetry.
One can thus obtain the charged gauge boson mass-squared matrix (M 2 W ) in the basis (W ± R , W ± L ) and the neutral gauge boson mass-squared matrix (M 2 Z ) in the basis (W 3 R , W 3 L , V ) as: where, v 2 = v 2 1 +v 2 2 is the EW VEV ∼ 174 GeV while g L , g R and g B−L are the SU (2) L , SU (2) R and U (1) B−L gauge couplings respectively. Our model corresponds to a LRS scenario where the parity and right-handed symmetry breaking scales are decoupled [39]. This is evident from the fact that our scalar spectrum does not contain a left-handed doublet, and hence the left and right-handed gauge couplings may not be the same. Thus, neglecting the left-right mixing, the new right-handed heavy gauge bosons masses are : (2.4) The left-handed W and Z boson masses are given by their usual expression in the SM with the identification of the effective hypercharge gauge coupling as, . (2.5) The right-handed VEV needs to be quite high so as to get a large enough Z R mass in order to avoid direct detection constraints for dark matter. As can be seen from Fig. 5 of Ref. [3], the mass of the Z R boson should be at least 7 TeV to circumvent the direct detection constraints for a dark matter mass of 150 GeV. Since we have considered a parameter space with the lowest value of quintuplet dark matter mass of 150 GeV for our collider analysis, this limit needs to be satisfied. For this reason, we choose v R = 13 TeV, which gives M W R = 6.0 TeV and M Z R = 7.14 TeV.
Motivated by Minimal Dark Matter models, we consider an SU (2) R vector-like fermion quintuplet, which can accommodate the dark matter. We represent the quintuplet as, where X = 0, 2, 4 are its possible (B − L) quantum numbers. The neutral component of χ can be a viable dark matter while its charged components can be produced at the colliders. The couplings of the gauge bosons (Z, Z R , W R and photon) with the quintuplet fields are, Here and χ i represents the component of the quintuplet χ with electric charge Q χ i = i.
The fermion masses are generated as the bidoublet fields get non-zero VEV and the corresponding Yukawa Lagrangian is given as: where Y and f are the Yukawa couplings and Φ = τ 2 Φ * τ 2 , H R = iτ 2 H * R . Hence, the quark and charged lepton masses are: (2.10) We choose a large tan β (= v 1 /v 2 ) limit so that Y q 33 ∼ 1 for the top quark mass while Y q 33 < 10 −2 . A smaller value of tan β would require a larger value of Y 33 in general, leading to the top Yukawa becoming non-perturbative at relatively lower mass scales. The neutrinos get masses through the inverse seesaw mechanism with the 3 × 3 mass matrix in the basis (ν L , ν R , N ) given as: where m D = Y l v 1 + Y l v 2 is the neutrino Dirac mass term. Assuming f R v R >> m D , µ N , the approximate expressions for the neutrino mass eigenvalues (for one generation) are, (2.12) So in this framework, light neutrino masses can be easily generated by appropriate choice of parameters.
The quintuplet fermion in this model can have a few different values of (B − L) quantum numbers (0, 2, and 4) but for our study we will only consider the case with (B − L) = 4. This scenario will have highest charge multiplicity particles, hence gives rise to interesting collider signatures. Component fields of the SU (2) R quintuplet for (B − L) = 4 can be expressed as, For brevity, we will denote χ ±±±± as χ 4± , χ ±±± as χ 3± , and χ ±± as χ 2± from here onwards.
It is evident from Eq. 2.9, that all components (χ i ) of the quintuplet are degenerate in mass at the tree level. Their masses are all equal to M χ as given in Eq. 2.9. The mass splitting between the various charged states are generated by the radiative corrections given as: where To calculate the mass splittings, we have chosen the value of g R = 0.653 at the scale of Z R boson mass. This is merely a choice in our parameter region. In the limit of small leftright mixing, the value of g L = 0.653 at the electroweak scale is determined by the measured values of α EM and weak mixing angle θ W . The mass splitting between the various charged states of the quintuplet as a function of the neutral quintuplet mass has been shown in Fig. 1 for the case with (B −L) = 4. The mass difference between the components of the quintuplets increase with their mass. In order to satisfy the correct RD, one needs to introduce a singlet scalar as shown in Ref. [3]. The same paper also has in-depth discussion of the model, dark matter phenomenology and collider phenomenology of the singlet scalar. In this work, we are interested in the collider signatures of the quintuplet fermions at the LHC which will be discussed in the following sections. Quintuplet Mass differences with B-L=4

Production and Decay of Multi-charged Quintuplet Fermions
The quintuplet, being charged under SU (2) R and U (1) B−L , has gauge interaction with photon, SM Z boson, Z R and W ± R (see Eq. 2.7) 1 . Therefore, the quintuplet fermions can be pair-produced at the LHC via quark-antiquark initiated Drell-Yan (DY) process with a photon/Z/Z R in the s-channel as shown in the left panel of Fig. 2. The electrically charged components of the quintuplet (χ) can also be produced from photon-photon fusion in the initial state (γγ → χ i χ i ), where i = 4, 3, 2, and 1. The right panel of Fig. 2 shows a representative diagram of the photon-photon fusion process for the pair-production of χ i χ i . Photo production of χ i± χ i∓ pairs takes place via a t or a u channel exchange of a χ i± and hence, is not suppressed by the parton center of mass energy. Moreover, the coupling of photon with a pair of χ i± being proportional to its charge (i), the matrix element squared of photo productions are enhanced by a factor of i 4 . However, the photo-production of charged fermions at the LHC is suppressed by the small parton density of photon inside a proton. To denote the charge multiplicity of the quintuplet in the following, we adopt the notation χ n± , where n runs from 0 to 4. In fact, the parton density of the photon is so small that most of the older versions of PDF's do not include photon as a parton. However, if we want to include QED correction to the PDF, inclusion of the photon as a parton with an associated parton distribution function is necessary. In the era of precision physics at the LHC when PDF's are determined upto NNLO in QCD, NLO QED corrections are important (since α 2 s is of the same order of magnitude as α) for the consistency of calculations. Moreover, as discussed previously, photon-initiated processes could become significant at high energies for some processes. In view of these facts, NNPDF [40,41], MRST [42] and CTEQ [43] have already included photon PDF into their PDF sets.
In order to compute the cross-sections and generate events at the LHC, we incorporate the model Lagrangian of Eq. 2.7 in FeynRules (v2.3.13) [44,45]. We implement the couplings for each component of the quintuplet (i =0, 1, 2, 3, 4) with the gauge bosons, derived from Eq. 2.7. Using FeynRules we generate the model file for MadGraph5 aMC@NLO (v2.2.1) [46]. For the cross-sections, we use the NNPDF23LO1 parton distributions [47] with the factorization and renormalization scales kept fixed at the central m 2 T scale after k T -clustering of the event. The quark-antiquark initiated DY production cross-section for the χ 4+ χ 4− pairs are presented in Fig. 3 (right panel) at the LHC with 13 TeV center of mass energy. Being s-channel, DY pairproduction cross-sections are significantly suppressed for larger χ 4± masses. In Fig. 3 (right panel), we also present the photo-production cross-section of χ 4± χ 4∓ pairs as a function of χ 4± mass (M χ 4± ) at the 13 TeV LHC. It shows that photon-photon fusion contributes significantly for M χ 4± < 800 GeV and for M χ 4± > 800, photo-production dominates over the DY contribution. In the left panel of Fig. 3 we present the total (DY+photo-production) pair-production cross-sections for χ 4± χ 4∓ , χ 3± χ 3∓ , and χ 2± χ 2∓ as a function of M χ 0 at the LHC with √ s = 13 TeV. The total pair-production cross-sections varies between a few pb to a few fb as we vary the χ 0 mass between 200 GeV to 1 TeV. Quintuplet fermions can also be produced in association with another quintuplet fermion from quark-antiquark initial state via a W ± R exchange in the s-channel. However, associated production cross-sections are suppressed by the mass of the W ± R in the s-channel. In Table 1, we present the numerical values of pair and associated production cross-sections for a particular benchmark point. Cross-section (pb) After being produced at the LHC, the quintuplet fermions undergo a tree-level 3-body decay into a lighter component and a pair of SM quarks or leptons. χ 0 being stable remains invisible in the detector. Therefore, the pair/associated production of the quintuplet fermions gives rise to multiple-jets and/or leptons (including the same-sign multileptons) and missing Process Cross-section (pb) Process transverse energy signature at the LHC. However, the 3-body decay of the quintuplet fermions proceed through an off-shell W ± R boson with a mass of few TeV. Therefore, before going into the details of signal and background analysis, it is important to compute the decay width of the quintuplet fermions to ensure that they decay inside the detector. For a particle having a decay width less than 10 −16 GeV, it will escape the detector before it can decay. We can see from Fig. 4 that the decay widths of all the charged fermions in the (B − L) = 4 quintuplet are always larger than 10 −16 GeV, which ensures that they will decay inside the detector. If the decay width of the charged fermions fall in the range around 10 −13 to 10 −16 GeV, then there may be a possibility to see the displaced vertex signature as well. For a major part of the parameter space considered in this paper, the decay widths of χ 2± , χ 3± , and χ 4± are always above 10 −13 GeV (see Fig. 4). Therefore, we do not explore the possibility of displaced vertex signature in this work.  case, assuming MW R = 6 TeV and MZ R = 7.14 TeV. If the decay width is less than 10 −16 GeV, the particle decays outside the detector.
If a charged (n = 1, 2, 3, 4) component of the quintuplet (χ n± ) is produced, it will form a cascade of decay via the process discussed above. For example, the main contribution in the 4 same-sign lepton channel (4SSL) will come from the production pp → χ 4+ χ 4− , and the decays of χ 4+ and χ 4− , as shown in Fig. 5. Other components of the quintuplet can also decay in the same manner and depending on the decay pattern there can be interesting collider signatures in the same-sign lepton (SSL) and other multilepton channels. In this study, we focus mainly on 2, 3, and 4 same-sign multilepton signals (2SSL, 3SSL, and 4SSL). Figure 5: Cascade decay of χ 4± into leptons (l = e, µ) and jets, contributing to the 4SSL channel.

Collider Signature of Quintuplets
As discussed in the previous section, the production and decay of the quintuplet fermions give rise to multiple leptons/jets in association with missing transverse energy signatures at the LHC. For example, the production of χ 4± χ 4∓ pairs could result into 0 to 8 leptons (including same-sign 2, 3, and 4 leptons) in the final state depending on the decay cascade of χ 4± . Fully leptonic/hadronic decay cascade of both χ 4± results into 8/0 leptons signature. Whereas, leptonic decay cascade (fully or partially) for one χ 4± and hadronic decay cascade of the other χ 4∓ give rise to four same-sign leptons in the final state. The pair and associated production of all combinations of χ 4± , χ 3± , and χ 2± contribute in the 2SSL channel. For the 3SSL channel, χ 4+ χ 4− , χ 3+ χ 3− , χ 4+ χ 3− , and χ 3+ χ 2− contribute, but for the 4SSL channel the signal stems only from χ 4+ χ 4− and χ 4+ χ 3− . The cross-section (σ) × effective Branching Ratio (BR) in different SSL channels are listed in Table 2 for a few selected masses of the quintuplet. The simulation of production and decay of the quintuplet fermion pairs at the LHC are discussed in the following section.

Event Generation and Simulation
The signal events for the production of the quintuplets are simulated using MadGraph [46,48] and showered with PYTHIA [49]. After that, the events are passed through DELPHES 3 [50] for detector simulation. In DELPHES, we choose the isolation cut for leptons to be ∆R max = 0.5 while reconstructing the events. This requirement ensures no hadronic activity  inside this isolation cone. The isolation cut reduces the SM background of the leptons coming from the decays of B-mesons. The probability of a jet to be misidentified as a lepton is taken as a modulo inside DELPHES [51]. In our model, leptons get produced from the decay of a heavier component of the quintuplet to a lighter component. As discussed earlier, small mass splitting between different components of the quintuplet results in soft leptons. For such soft leptons the charge misidentification probability is small and hence neglected. The leading SM backgrounds for 2SSL are tt, ZZ, W Z, W W , ttW , ttZ, tth, and hZ. Semileptonic decay of tt contributes to the 2SSL when the b-quark generated from decay of top quark further decays leptonically. On the other hand, di-boson production contributes to the 2SSL channel if one or more leptons from the leptonic decay of the SM bosons fall outside the detector coverage (leptons are too soft or they fall in the high rapidity region). Here, bbW could also contribute when one lepton results from the W ± decay and the other lepton with same electric charge arises from leptonic B-meson decays. Among the above mentioned backgrounds, the dominant contribution in 2SSL channel comes from W Z, ZZ, and ttW . In the 3SSL channel, following SM backgrounds are considered: ttW, ttZ, tth , W W Z, W ZZ, ZZZ, tttt, and ttbb. Out of all these possibilities, major contributions come from ttW and W ZZ. All background events are generated using MadGraph and the cross-sections are taken upto NLO (see Refs. [52][53][54][55][56][57][58][59]).

Event Selection
Following are the generator level acceptance cuts that we impose while simulating the signal and backgrounds.
• ∆R l,l > 0.2 (l, l = e, µ), ∆R j,j > 0.5, and ∆R ,j > 0.4. transverse momentum of the leptons and jets, and the effective mass which are defined as: The distributions of the E miss T , H T (l), and m eff are shown in Fig. 7 for the 2SSL (left panel) and 3SSL (right panel) channel. We find that an upper limit on H T (l) and H T (j) help to reduce the backgrounds significantly. In Fig. 8, we plot distribution of the E miss T /m eff for both the channels. In the next section, we find that a cut on the lower values of the E miss T /m eff turns out to be quite effective to reduce the QCD-jet backgrounds. The backgrounds from ttW and ttZ can be reduced by applying a b-jet veto. Another effective way to reduce the same-sign multilepton backgrounds is to consider only small values of the transverse mass (m T ). We imposed further selection criteria on these kinematic variables to enhance the signal to background ratios in the 2SSL, 3SSL, and 4SSL channels. The final event selection criteria are listed in Table 3 and the effects are discussed in the next section.

Exclusion Limits and Discovery Reach in the Same-sign Multilepton Channels
As discussed in Table 3, the same-sign lepton (l = e, µ) final states are required to pass the selections S1, S2, and S3 in the 2SSL channel. For 3SSL, and 4SSL channels we only impose S1 and S2. While analyzing the same-sign multilepton channels, we find that the remaining background is small after passing through several selections. If the background is small then the standard formula (s/ √ b) overestimates the discovery significance. Also, in real experiments, the background (b) is never known with 100% accuracy. Therefore, Selection Cuts Table 3: Selection criteria (S1, S2, and S3) that we consider for the 2SSL, 3SSL, and 4SSL channels. In selection S1, we only consider the events with exactly 2, 3 or 4 leptons with same sign. Other events containing opposite sign leptons are vetoed. Here l = e, µ. Also, note that for the 3SSL and 4SSL channels, we do not impose selection criteria S3.
while calculating the discovery significance and exclusion, we include an uncertainty in the background (∆ b ) [60]. This analysis is helpful to deal with small backgrounds, implemented before in Ref. [61]. The significance for discovery is defined as, In the above equation, if b is large, then we obtain the well known expression It is evident from the above discussion that if b is small, s/ √ b overestimates the significance. Therefore, we use the expression given in Eq. 4.2 to estimate the discovery reach by assuming Z dis ≥ 5 which corresponds to 5σ discovery (p < 2.86 × 10 −7 ). To set the exclusion limit at a given confidence level (CL), we use the following expression In the above equation, if ∆ b = 0, For a median expected 95% CL exclusion (p = 0.05), we use Z exc ≥ 1.645 for different ∆ b . With increasing amount of LHC data, and hence for a better understanding of the detector response, the experimental uncertainties in the estimation of the SM backgrounds are expected to be reduced significantly. Therefore, we assume that the systematic uncertainty in background estimation falls as 1/ √ L and we also incorporate this effect in ∆ b . We choose different values of the systematic uncertainties at 10%, 25% and 50% at 10 f b −1 integrated luminosity and scale the uncertainty appropriately for higher luminosities.  Table 4: Signal cross-sections after passing the various selection criteria in the 2SSL channel at the 13 TeV LHC for different masses of the quintuplet. Here n runs from 0 to 4 in a given quintuplet. We assume BR(χ Q+1 → lνχ Q ) = 0.22 where l = e, µ and BR(χ Q+1 → qqχ Q ) = 0.67.

Process
Cross-section (fb) S1 (fb)  For the two same-sign lepton channel (2SSL), we require exactly 2 leptons (ee or µµ or eµ). The selection criteria in 2SSL channel are listed in Table 3. The signal cross-section after passing various selections (S1, S2, and S3) are given in Table 4 for 2SSL channel at the 13 TeV LHC. The signal events suffer from a very low missing transverse energy (E miss T ), which comes mainly from the neutral state of the quintuplet (χ 0 ). So, enforcing a cut on E miss T will yield smaller signal cross-section, as can be seen in Table 4. On the other hand, a cut on the lower limit of the missing energy effectively reduces the probability of jet faking leptons in the final state [62]. So, here we choose three different E miss T cuts, S3 x , S3 y , and S3 z . The background cross-section to pass the same selections are given in Table 5 for 2SSL channel. We find that the selection S3 is very effective in reducing the backgrounds. In Fig. 9 and Fig. 10, projections of the required luminosity for 95% confidence level exclusion (Z exc ≥ 1.645) and 5σ discovery (Z dic ≥ 5) are shown as a function of the neutral state mass (M χ 0 ), for two different selections S3 x and S3 z . To make the predictions we use Eq. 4.2 and Eq. 4.5 and vary the uncertainty in the backgrounds between 0−50%. As a larger E miss T cut further reduces the signal cross-section, more luminosity is expected to be required to set an exclusion in S3 z compared to S3 x . But from Fig. 9, it is clear that the cut on E miss T is not that sensitive since a strong E miss T cut also reduces the background cross-section at a comparable rate, as reflected in Table 4 and Table 5. With 3000 f b −1 integrated luminosity, one can exclude up to 610 GeV of the neutral state mass (M χ 0 ) if selection S3 x is applied. Also from Fig. 10, we can say that after selection S3 x , even with 3000 f b −1 integrated luminosity, the discovery prospects will be challenging if the neutral state mass is greater than 475 GeV.
In the 3SSL channel, exactly three same-sign leptons (eee or µµµ or eµµ or eeµ ) are required to pass the selections S1 and S2 (see Table 3). These two selections are sufficient to suppress the backgrounds. Moreover, as the signal cross-section is small, implementing the S3 selection criterion reduces the signal cross-section significantly. Table 6 and Table 7 gives the signal and background cross-section respectively after the selections (S1 and S2) for 3SSL channel at the 13 TeV LHC. It is clear from the table that selection S2 is sufficient to make prediction for exclusion and discovery as the total background becomes sufficiently small with ttW being the dominant background. The results for the exclusion and discovery are calculated as before and shown in Fig. 11. A quintuplet with neutral state mass (M χ 0 ) up to 800 GeV can be excluded with only 500 f b −1 luminosity. As the signal cross-section is small in 3SSL channel, we also plot the required luminosity to observe 10 signal events (red line in Fig. 11). A quintuplet with neutral state mass M χ 0 ≤ 800 GeV can be excluded with 800 f b −1 luminosity if at least 10 signal events are required. It might be also possible to discover a M χ 0 up to 750 GeV with 1000 f b −1 luminosity.
The 4SSL channel can provide a very clean signature as the background is almost nonexistent. The events are required to pass both S1 and S2, but the signal cross-section becomes quite small if we impose S2. For example, if the mass of the neutral state of the quintuplet is 300 GeV, the signal cross-section after passing S2 is only 0.003 fb. If the same selection criteria is applied, this channel has practically zero background, smaller by a factor of α compared to 3SSL channel. Hence, in Fig. 12, we only plot the required luminosity to observe 5 and 10 signal events as a function of the neutral state mass (M χ 0 ) at 13 TeV if selection S2 is imposed. We find that for 300 GeV neutral state mass, the required luminosity will be greater than 3000 f b −1 in order to see 10 signal events.   Table 7: Background cross-sections in the 3SSL channel after passing the selection criteria S1 (third column) and S2 (fourth column) at the 13 TeV LHC.

Concluding Remarks
In this paper, we consider the left-right symmetric model with a SU (2) R quintuplet fermion. The neutral state of this quintuplet, which is also the lightest, can be a viable dark matter candidate, while its charged fields can give rich collider signatures in the form of the multilepton final states. We study in detail the collider imprints of the same-sign multilepton final states in the context of the 13 TeV LHC. We consider the scenario where the quintuplet fermion possesses (B − L) = 4 charge, since it gives the most interesting collider signatures due to the presence of high charge-multiplicity particles producing lepton-rich final states. These high charge-multiplicity particles can be pair produced through quark-antiquark initiated Drell-Yan processes or through photo production by photon-photon fusion process. Here, we show that the photon-photon fusion process contributes significantly in the total cross-section of the quintuplet fermions at the 13 TeV LHC. They can also have associated production into two quintuplet fermions of different charges through a W R boson. But, the production cross-section of this channel would be negligibly small. Once produced, the  quintuplet fermions decay into the next lightest member of that quintuplet and two leptons or two quarks through an off-shell W R boson. This ultimately gives rise to final states comprising of a number of leptons, jets, and missing energy. Here, we study the same-sign multilepton signatures such as 2SSL, 3SSL, and 4SSL final states in the context of the LHC experiment at 13 TeV. For our analysis, we consider several benchmark points with the neutral state mass (M χ 0 ) of the quintuplet ranging from 200 GeV to 800 GeV. For the 2SSL case M χ 0 ≤ 610 GeV can be we can excluded at 95% confidence level for 3000 f b −1 luminosity. The discovery prospect at 5σ level, being much more challenging, has an upper limit of M χ 0 ≤ 475 GeV. As far as the 3SSL channel is concerned, it has a much lower background as compared to the 2SSL channel. This enhances both the exclusion and discovery potential in the 3SSL channel. The LHC at 13 TeV would be able to exclude a M χ 0 ≤ 800 GeV at 95% CL with an integrated luminosity of 500 f b −1 . Discovery at 5σ is achievable upto M χ 0 ≤ 750 GeV with 1000 f b −1 luminosity. The 4SSL is the cleanest channel with almost zero background, but at the same time it will have a very small signal cross-section which makes it extremely difficult to place a limit for exclusion or predict any discovery potential.
Overall, our study reflects that with the 13 TeV LHC, a 5σ discovery reach or a 95% CL exclusion limit on the SU (2) R quintuplet mass can be achieved by observing the same-sign multilepton signatures. We hope that the study performed in this paper will add to the long standing quest to search for new physics at LHC through the same-sign multilepton final states.