Longlived triplinos and displaced lepton signals at the LHC
Abstract
We explore the possibility of having superpartners of triplet Higgs bosons, named as ‘triplinos’. They form a part of light neutralinos and charginos in a \(Y=0\) extended supersymmetric Standard Model. For this model such electroweakinos do not have direct couplings to the Standard Model fermions. On top of that, due to very compressed spectrum for lighter neutralinos and charginos, their decay products coming from three body decays are very soft and thus can evade the current collider bounds. These decays are particularly interesting since they give rise to displaced leptonic signatures. We categorise the parameter space, while exploring different displaced decay possibilities. A PYTHIA based simulation has been performed to find out the displaced charged lepton, jet and bjet final states at the LHC with center of mass energy of 14 TeV.
1 Introduction
The discovery of the Higgs boson [1, 2] was the last piece in the Standard Model (SM), opening a new era in the particle physics. However, the LHC experiments have not ruled out the possibility of other scalars in the electroweak symmetry breaking (EWSB). The extension of the scalar sector in the context of supersymmetry is motivated by various reasons. Introduction of supersymmetry can solve the hierarchy problem, and along with conserved Rparity, it can give rise to a stable dark matter candidate. The discovery of a \(\sim 125\) GeV Higgs boson in the minimal supersymmetric extension of the Standard Model (MSSM), demands the supersymmetric (SUSY) mass scale either to be very heavy or it requires large mass splitting between the superpartners of the top quarks [3, 4]. This brings back the finetuning problem. An extension of the Higgs sector provides a solution to the problem with extra treelevel and looplevel contributions to the Higgs bosons mass. Thus SUSY mass scale around TeV is still allowed [5]. Various such extensions include MSSM with a singlet [6], \(Y=0\) triplet [5, 7, 8, 9, 10], \(Y=\pm 1\) triplets [11], and the supersymmetric version [12] of the GeorgiMachacek model [13]. Also supersymmetric extensions with both singlets and triplets have been studied extensively [11, 14, 15, 16, 17]. In this article we focus on the extension of MSSM with \(Y=0\) triplets [5, 7, 8, 9, 10].
In particular, our focus is on the phenomenology of the electroweak gaugino and Higgsino sectors of the model. More precisely, the superpartners of the additional triplet scalars will mix with the standard MSSM neutralinos and charginos in the spectrum. In the gauge basis we call them ’triplinos’. One basic difference is that unlike gauginos and Higgsinos, they do not directly couple to the SM fermions and consequently to their superpartners. This feature affects the indirect bounds on the parameter space [9]. In this article we explore the production and decays of such triplinos at the LHC. For the neutral parts, the coupling to fermions and Z boson comes via mixing to the SU(2) doublets and hypercharged particles, which makes the phenomenology very interesting as we expect displaced decays of such triplinos (charginos and neutralinos). Occasionally the decay products of triplinos are so soft that they will be missed at the detectors and will give rise to disappearing charged tracks for tripletlike charginos. Such disappearing charged tracks have been investigated for some SUSY models at 8 and 13 TeV at the LHC experiments [18, 19] as well as in the phenomenological studies [20, 21]. Here we investigate such scenarios for this model by choosing parameter regions on the basis of the gauge structure of the lightest supersymmetric particle (LSP) and next to LSP (NLSP).
The article is organised as follows. In Sect. 2 we give a brief introduction to the model along with the electroweak gaugino sectors. In Sect. 3 we find out the parameter spaces in the model consistent with the Higgs data and the different kinds of NLSPLSP scenarios. The collider simulation and related phenomenology are discussed in Sect. 4. Finally we conclude in Sect. 5.
2 Model
Superpartners of the SU(2) doublet and triplet Higgs bosons and of W and B bosons constitute the neutralinos and chargino sectors. At EWSB their same charge gauge eigenstates mix also with each other. The production and decay phenomenology of neutralinos and charginos depend strongly on the mixing angles. For triplinos (superpartners of triplets), couplings with fermions are proportional to the doublettriplet mixing angle, since directly triplinos do not couple to the fermions (or sfermions). In the subsections below we discuss the neutralino and chargino sectors separately, as well as the mixings among different gauge states.
2.1 Neutralino sector
2.2 Chargino sector
3 Parameter space scan
In this study we consider phenomenological low energy TESSM model. However, we respect the perturbativity limits of the dimensionless couplings of the model in the scan. In particular, the reason why we scanned the parameter space for \(\lambda \) \(\le 1.2\) is to respect its perturbativity limit as it was previously shown in [9] that \(\lambda (M_Z)\sim 1\) stays perturbative up to cut off scale \(\Lambda _{UV}=10^4\) TeV.
During the general parameter scan we collected the data points respecting the constraints given in Eq. (3.2) including the chargino LEP bound. The scan was performed for the free parameters whose regions in the parameter space are given in Eq. (3.1). All chosen benchmark points are below \(2\sigma \) upper bound of \(B \rightarrow X_s \gamma \) [5, 9].
We created sample points by scanning over 14 parameters (economical) which are responsible for our phenomenological studies as given in Eq. (3.1). Out of the points we have generated, we took 10 points spread over three different kind of scenarios for our analysis.
3.1 Sc 1: Triplino LSP
3.2 Sc 2: Triplino NLSP
In Sc 2 we focus on the phenomenology of the triplino like second lightest neutralino \(\tilde{\chi }_{2}^{0}\) chosen as NLSP. We have performed a scan respecting the constraints given in Eq. (3.2) and ask for the points where triplino component of NLSP is more than \(90\%\). This scenario is quite interesting, since for the triplinolike NLSP the current LSP mass bound from the lepton mode \(\tilde{\chi }_{2}^{0}\rightarrow \ell \tilde{ \ell } \rightarrow \ell \ell \tilde{\chi }_{1}^{0}\) is less tight [27, 28, 29, 30, 31] because NLSP does not couple to leptons due to its triplino nature. The mass hierarchy among neutralinos and charginos for the data points is given in Fig. 4. Here the red colour corresponds to the tripletlike chargino and neutralinos, the binolike LSP is denoted by green colour. The heavier charginos and neutralinos arrange themselves also in Sc 2 as either degenerate wino or Higgsino states, and are denoted by blue and black colour. Again one of the neutralinos is not degenerate with other particles, and is shown with cyan colour. The most striking feature of this scenario is that requiring a triplet like neutralino NLSP leads to binolike LSP in all data sets. This is because the charged and neutral states with same nature are almost mass degenerate, and thus requirement of a triplinolike neutralino NLSP leads to a chargino with mass always slightly greater than the corresponding neutralino in the same gauge representation. Demanding either wino or triplinolike neutralino NLSP leaves no choice but bino to be LSP, since bino does not have any charged partner. The triplinolike neutralino NLSP leads to the lightest chargino with mass very close to NLSP making it next to NLSP (NNLSP).
3.3 Sc 3: Higgsino LSP
In the search of long lived neutralinos and charginos we also dwell on the possibility of having Higgsinolike LSP and triplinolike NLSP, whose interaction vertex is proportional to trilinear coupling \(\lambda \). For small values of \(\lambda \), strongly triplinolike NLSP can be quite long lived before decaying to Higgsino dominated LSP and SM particles. To investigate this possibility we demand that the LSP is at least 50 \(\%\) Higgsinolike and the NLSP is at least 50 \(\%\) triplinolike during the parameter scan of scenario Sc 3. In Fig. 6 we observe that the NLSP turns out to be the lightest chargino which is almost mass degenerate and has the same Higgsinolike nature with the LSP. In this respect this scenario is similar with Sc 1 and one needs to calculate the oneloop masses for neutralinos and charginos to see if quantum corrections can change the mass hierarchy [33, 34].^{1}
Benchmark points from Sc1 for collider study consistent with the \(\sim 125\) GeV Higgs mass where the lifetime of NLSP is given as \(\tau _{NLSP}\) and the proper decay length of NLSP is given as \(c\,\tau _{NLSP}\)
Benchmark  LSP mass  NLSP mass  NNLSP mass  \(\tau _{NLSP}\)  \(c\, \tau _{NLSP}\) 

points  (GeV)  (GeV)  (GeV)  (ns)  (cm) 
BP1  542.30  542.50  864.70  0.79  23.61 
BP2  561.12  561.54  651.82  0.022  0.646 
BP3  530.75  530.94  771.40  1.21  36.15 
BP4  498.38  498.53  722.40  3.27  97.76 
4 LHC phenomenology
In this section we look for the displaced tracks for the scenarios discussed above by selecting few benchmark points from each scenario. Before going into detailed analysis we first introduce our set up for the simulation at the LHC with 14 TeV of center of mass energy. After the set up we discuss the phenomenology of the different scenarios separately.

the calorimeter coverage is \(\mathrm \eta  < 4.5\)

the minimum transverse momentum of the jet \( p_{T,min}^{jet} = 10\) GeV and jets are ordered in \(p_{T}\)

leptons (\(\mathrm \ell =e,~\mu \)) are selected with \(p_T \ge 5\) GeV and \(\mathrm \eta  \le 2.5\)

no jet should be accompanied by a hard lepton in the event

\(\Delta R_{lj}\ge 0.4\) and \(\Delta R_{ll}\ge 0.2\)

Since an efficient identification of the leptons is crucial for our study, we additionally require a hadronic activity within a cone of \(\Delta R = 0.3\) between two isolated leptons to be \(\le 0.15\, p^{\ell }_T\) GeV, with \(p^{\ell }_T\) the transverse momentum of the lepton, in the specified cone.
4.1 Sc 1: Triplino LSP
For the LHC simulation we first consider Sc 1, where we have a triplinolike LSP and a triplinolike chargino NLSP. For the collider study we select four benchmark points from this scenario as given in Table 1, where the mass spectra for NNLSP, NLSP and LSP are listed and we can see that NLSP and LSP are nearly degenerate. For all four points NLSP is triplinolike chargino and it can be seen that the decay length for the chargino NLSP is \({\mathcal {O}}\) (1–100) cm. However, loop corrections can alter the mass hierarchy in which case we can have an electromagnetically charged LSP, i.e. a dark matter candidate, which is not physical [33, 34, 43]. For this purpose we have checked the mass hierarchy via SPheno [36] considering contributions from all particles at oneloop level and the hierarchy remains the same for all benchmark points under consideration. From Table 1 we see that the treelevel mass difference between the NLSP and LSP is around \({\mathcal {O}}(200)\) MeV, sufficient to have \(\tilde{\chi }^\pm _1 \rightarrow \pi ^\pm \tilde{\chi }^0_1\) decay.
Pair and associated production cross sections for \(\tilde{\chi }_{1,2}^{\pm }\) and \(\tilde{\chi }_{1,2}^{0}\) at 14 TeV for the benchmark points for Sc I
Benchmark  \(\tilde{\chi }_1^{\pm }\tilde{\chi }_1^{\mp }\)  \(\tilde{\chi }_1^{\pm }\tilde{\chi }_1^{0}\)  \(\tilde{\chi }_1^{\pm }\tilde{\chi }_2^{0}\)  \(\tilde{\chi }_1^{\pm }\tilde{\chi }_2^{\mp }\)  \(\tilde{\chi }_2^{0}\tilde{\chi }_2^{0}\)  \(\tilde{\chi }_2^{0}\tilde{\chi }_1^{0}\)  \(\tilde{\chi }_2^{0}\tilde{\chi }_2^{\pm }\) 

points  (fb)  (fb)  (fb)  (fb)  (fb)  (fb)  (fb) 
BP1  14.33  30.17  4.71\(\times 10^{2}\)  0.204  1.6\(\times 10^{2}\)  3.8\(\times 10^{2}\)  0.82 
BP2  11.50  20.03  0.12  0.352  1.4\(\times 10^{6}\)  6.3\(\times 10^{2}\)  0.89 
BP3  15.79  31.97  0.56  6.0\(\times 10^{2}\)  8.5\(\times 10^{5}\)  4.7\(\times 10^{4}\)  1.17 
BP4  20.84  43.71  8.37\(\times 10^{2}\)  7.2\(\times 10^{2}\)  5.5\(\times 10^{5}\)  3.74\(\times 10^{4}\)  2.21 
Number of displaced events with disappearing charged track in the ranges of 1–10 cm, 0.1–1 m and 1–10 m for the benchmark points of scenario Sc 1 at the LHC with 14 TeV center of mass energy and at an integrated luminosity of 100 fb\(^{1}\)
Benchmark  Process  BP1  BP2  BP3  BP4 

points  
0.1–1 cm  \(\tilde{\chi }_1^{\pm }\tilde{\chi }_1^{\mp }\)  119.5  960.3  89.5  46.4 
\(\tilde{\chi }_1^{\pm }\tilde{\chi }_1^{0}\)  291.1  1715.4  204.7  108.9  
1–10 cm  \(\tilde{\chi }_1^{\pm }\tilde{\chi }_1^{\mp }\)  599.1  111.8  518.8  329.2 
\(\tilde{\chi }_1^{\pm }\tilde{\chi }_1^{0}\)  1374.2  209.6  1141.1  779.2  
10 cm–1 m  \(\tilde{\chi }_1^{\pm }\tilde{\chi }_1^{\mp }\)  685.5  0.3  889.8  1194.7 
\(\tilde{\chi }_1^{\pm }\tilde{\chi }_1^{0}\)  1314.4  0.4  1734.5  2598.1  
1–10 m  \(\tilde{\chi }_1^{\pm }\tilde{\chi }_1^{\mp }\)  27.4  0.0  79.9  510.5 
\(\tilde{\chi }_1^{\pm }\tilde{\chi }_1^{0}\)  34.6  0.0  114.3  881.1 
Number of events with multiple charged leptons with at least one of them displaced with displacement 0.1 mm to 10 m at 14 TeV for the benchmark points in scenario Sc 1. Here the leptons are rather soft \(p^{\ell }_T \ge 5\) GeV and at least one of them is displaced
Benchmark  \(n_{\ell }\ge 1\)  \(n_{\ell }\ge 2\)  

points  \(\tilde{\chi }^\pm _1\tilde{\chi }^\mp _1\)  \(\tilde{\chi }^\pm _1\tilde{\chi }^0_1\)  \(\tilde{\chi }^\pm _1\tilde{\chi }^\mp _1\)  \(\tilde{\chi }^\pm _1\tilde{\chi }^0_1\) 
BP1  2.1 \({\left\{ \begin{array}{ll} 0.0\\ 0.3\\ 0.9\\ 0.9 \end{array}\right. }\)  3.2\({\left\{ \begin{array}{ll} 0.2\\ 0.2\\ 1.6\\ 1.2 \end{array}\right. }\)  0.1  0.0 
BP2  1.0\({\left\{ \begin{array}{ll} 0.3\\ 0.6\\ 0.1\\ 0.0 \end{array}\right. }\)  55.0\({\left\{ \begin{array}{ll} 42.2\\ 12.7\\ 0.1\\ 0.0 \end{array}\right. }\)  0.2  0.0 
BP3  0.3\({\left\{ \begin{array}{ll} 0.0\\ 0.0\\ 0.1\\ 0.2 \end{array}\right. }\)  0.0  0.0  0.1 
BP4  7.7\({\left\{ \begin{array}{ll} 0.0\\ 0.3\\ 2.2\\ 5.2 \end{array}\right. }\)  0.2\({\left\{ \begin{array}{ll} 0.0\\ 0.0\\ 0.1\\ 0.1 \end{array}\right. }\)  0.0  0.0 
In this scenario the NLSP is a chargino, which has large momentum before decaying into charged leptons and LSP. In Table 3 we show numbers of events which may give rise to disappearing charged tracks at the LHC. Such displacement can be as large as 10 m for some benchmark points. It can be seen that the main contribution comes from the lightest chargino pair production (\(\tilde{\chi }^\pm _1\tilde{\chi }^\mp _1\)) and the lightest chargino production in association with LSP (\(\tilde{\chi }^\pm _1\tilde{\chi }^0_1\)). Due to degeneracy of the spectrum it is most likely that majority of the charged leptons and jets from the decay remain undetected as they will fall below the initial trigger cuts.Nevertheless, in this Section we try to see such soft charged leptons and jets.
Table 4 presents in Sc 1 the number of charged leptons (\(e,\, \mu \)) with \(p^{\ell }_T \ge 5\) GeV at the LHC with center of mass energy of 14 TeV at an integrated luminosity of 100 fb\(^{1}\) with one of them being produced with a displacement. The displacements can be from 0.1 mm to 10 m as listed in Table 4. It can be seen that the corresponding leptonic events are only few due to the small branching fraction of \(\tilde{\chi }^\pm _1\) to leptons for the benchmark points. However, for BP2 the \(\tilde{\chi }^\pm _1\tilde{\chi }^0_1\) contribution have sufficiently many leptonic events due to the relatively large leptonic branching fraction, \( \tilde{\chi }^\pm _1 \rightarrow \ell ^\pm \nu \tilde{\chi }^0_1 \simeq 37\%\). Otherwise probing such leptonic final states one has to go for high luminosity LHC \({\mathcal {O}}(3000)\) fb\(^{1}\).
In Table 5 we show the displaced jets that come from the decays of charginotype NLSP for the benchmark points at the LHC with center of mass energy of 14 TeV at an integrated luminosity of 100 fb\(^{1}\). Here we demand that at least one of the jets should be displaced and the jet momenta can be rather small \(p^j_T \ge 10\) GeV. Due to the isolation criteria (for jetjet, jetlepton and leptonlepton), as given before, the contribution is much more from \(\tilde{\chi }^\pm _1\tilde{\chi }^0_1\) than from \(\tilde{\chi }^\pm _1\tilde{\chi }^\mp _1\). Of course the latter has larger crosssection that also adds to the contribution.
4.2 Sc 2: Triplino NLSP
Number of events with multiple jets with at least one of them displaced with displacement 0.1 mm to 10 m at 14 TeV for the benchmark points in scenario Sc 1. Here the leptons are rather soft \(p^{\ell }_T \ge 5\) GeV and at least one of them is displaced
Benchmark  \(n_{j}\ge 1\)  \(n_{j}\ge 2\)  

points  \(\tilde{\chi }^\pm _1\tilde{\chi }^\mp _1\)  \(\tilde{\chi }^\pm _1\tilde{\chi }^0_1\)  \(\tilde{\chi }^\pm _1\tilde{\chi }^\mp _1\)  \(\tilde{\chi }^\pm _1\tilde{\chi }^0_1\) 
BP1  593.9\({\left\{ \begin{array}{ll} 50.6\\ 249.4\\ 283.9\\ 10.0 \end{array}\right. }\)  2455.8\({\left\{ \begin{array}{ll} 235.3\\ 1120.4\\ 1073.1\\ 27.0 \end{array}\right. }\)  399.9\({\left\{ \begin{array}{ll} 34.0\\ 168.9\\ 190.0\\ 7.0 \end{array}\right. }\)  1819.9\({\left\{ \begin{array}{ll} 172.1\\ 826.3\\ 801.5\\ 20.0 \end{array}\right. }\) 
BP2  878.6\({\left\{ \begin{array}{ll} 785.7\\ 92.8\\ 0.1\\ 0.0 \end{array}\right. }\)  1589.8\({\left\{ \begin{array}{ll} 1413.6\\ 175.9\\ 0.3\\ 0.0 \end{array}\right. }\)  653.8\({\left\{ \begin{array}{ll} 585.4\\ 68.3\\ 0.1\\ 0.0 \end{array}\right. }\)  1155.6\({\left\{ \begin{array}{ll} 1030.9\\ 124.5\\ 0.2\\ 0.0 \end{array}\right. }\) 
BP3  655.2\({\left\{ \begin{array}{ll} 37.0\\ 217.2\\ 369.1\\ 31.9 \end{array}\right. }\)  2615.5\({\left\{ \begin{array}{ll} 167.2\\ 928.8\\ 1424.1\\ 95.4 \end{array}\right. }\)  445.4\({\left\{ \begin{array}{ll} 26.0\\ 147.8\\ 249.3\\ 22.3 \end{array}\right. }\)  1938.4\({\left\{ \begin{array}{ll} 125.6\\ 686.9\\ 1054.6\\ 71.3 \end{array}\right. }\) 
BP4  860.9\({\left\{ \begin{array}{ll} 19.5\\ 138.5\\ 493.7\\ 209.2 \end{array}\right. }\)  3562.0\({\left\{ \begin{array}{ll} 87.5\\ 634.1\\ 2118.3\\ 722.1 \end{array}\right. }\)  577.6\({\left\{ \begin{array}{ll} 13.3\\ 89.9\\ 333.7\\ 140.7 \end{array}\right. }\)  2631.9\({\left\{ \begin{array}{ll} 61.8\\ 468.1\\ 1565.7\\ 536.3 \end{array}\right. }\) 
Benchmark points selected from scenario Sc 2 for collider study consistent with the \(\sim 125\) GeV Higgs mass where the lifetime of NLSP is given as \(\tau _{NLSP}\) and the proper decay length of NLSP is given as \(c\,\tau _{NLSP}\). This scenario has a triplino like NLSP \(\tilde{ \chi }^0_2\) and nearly degenerate charginolike NNLSP \(\tilde{ \chi }^{\pm }_1\)
Benchmark  LSP mass  NLSP  NNLSP  \(\tau _{NLSP}\)  \(c\, \tau _{NLSP}\) 

points  (GeV)  (GeV)  (GeV)  (ns)  (cm) 
BP5  153.10  174.825  174.830  0.092  2.75 
BP6  484.05  499.947  499.952  1.23  36.70 
BP7  330.80  348.56  348.57  4.482  134.18 
Pair and associated production cross sections for \(\tilde{\chi }_{1,2}^{\pm }\) and \(\tilde{\chi }_{1,2}^{0}\) at 14 TeV for each benchmark point in scenario Sc 2
Benchmark  \(\sigma _{\tilde{\chi }_1^{\pm }\tilde{\chi }_1^{\mp }}\)  \(\sigma _{\tilde{\chi }_1^{\pm }\tilde{\chi }_1^{0}}\)  \(\sigma _{\tilde{\chi }_1^{\pm }\tilde{\chi }_2^{0}}\)  \(\sigma _{\tilde{\chi }_1^{\pm }\tilde{\chi }_2^{\mp }}\)  \(\sigma _{\tilde{\chi }_2^{0}\tilde{\chi }_2^{0}} \)  \(\sigma _{\tilde{\chi }_2^{0}\tilde{\chi }_1^{0}}\)  \(\sigma _{\tilde{\chi }_2^{0}\tilde{\chi }_2^{\pm }}\) 

points  (fb)  (fb)  (fb)  (fb)  (fb)  (fb)  (fb) 
BP5  1289  8.29\(\times 10^{2}\)  2565.7  2.6\(\times 10^{6}\)  \(<10^{8}\)  \(<10^{7}\)  1.23\(\times 10^{5}\) 
BP6  20.95  2.68\(\times 10^{3}\)  44.01  \(<10^{7}\)  \(<10^{10}\)  \(<10^{9}\)  7.83 \(\times 10^{6}\) 
BP7  94.13  1.16\(\times 10^{3}\)  192.8  \(<10^{7}\)  \(<10^{11}\)  \(<10^{9}\)  3.5\(\times 10^{5}\) 
Table 8 presents the decay branching fractions of \(\tilde{\chi }^0_2\) and \(\tilde{\chi }^\pm _1\) for the benchmark points in scenario Sc 2. It can be seen that in BP5, the \(\tilde{\chi }^0_2\) decays to charged lepton pairs by 24% and for other BPs, the branching fraction is \(\sim 10^{4}\). For all the benchmark points \(\tilde{\chi }^0_2\) dominantly decays into \(b\bar{b}\tilde{\chi }^0_1\) with branching fractions 53%, 99% and 99% for BP5, BP6 and BP7, respectively, giving rise to displaced jets.
The multilepton plus missing energy bounds in [30, 31] do not exclude our parameter space due to the following reasons. First, the charged leptons coming from \(\tilde{\chi }^\pm _1\) or \(\tilde{\chi }^0_2\) are coming from threebody decays due to the lack of phase space. Thus they are very soft and will not appear after the basic cuts demanded in [30, 31] for the electron and muon, which are \(\ge 20\) and 30 GeV, respectively. Second, the decay branching fraction of the leptonic modes is much smaller in our case. We see from Table 8 that the most dominant mode is the hadronic one. We also should not forget that for some benchmark points the production crosssections are less compared to the MSSM case, where either wino or Higgsinolike NLSPs are considered. \(\tilde{\chi }^\pm _1\) which is NNLSP in this only gives rise to prompt leptons and has no contribution towards displaced charged leptonic signature as discussed earlier.
Branching fraction of \(\tilde{\chi }^0_2\) and \(\tilde{\chi }^\pm _1\) for the benchmark points in scenario Sc 2
Decay  Benchmark points  

modes  BP5  BP6  BP7 
\(\tilde{\chi }^0_2 \rightarrow \nu \bar{\nu } \tilde{\chi }^0_1\)  0.11  \(2.7\times 10^{4}\)  \(2.0\times 10^{4}\) 
\(\tilde{\chi }^0_2 \rightarrow \ell \bar{\ell } \tilde{\chi }^0_1\)  0.02  \(1.4\times 10^{4}\)  \(9.8\times 10^{4}\) 
\(\tilde{\chi }^0_2 \rightarrow \tau \bar{\tau } \tilde{\chi }^0_1\)  0.04  \(4.7\times 10^{3}\)  \(3.7\times 10^{4}\) 
\(\tilde{\chi }^0_2 \rightarrow q \bar{q} \tilde{\chi }^0_1\)  0.82  0.99  0.99 
\(\tilde{\chi }^\pm _1 \rightarrow \ell \bar{\nu } \tilde{\chi }^0_1\)  0.11  0.11  0.11 
\(\tilde{\chi }^\pm _1 \rightarrow \tau \bar{\nu } \tilde{\chi }^0_1\)  0.11  0.11  0.11 
\(\tilde{\chi }^\pm _1 \rightarrow q q' \tilde{\chi }^0_1\)  0.67  0.67  0.67 
We choose events where we have at least one displaced charged lepton with different displaced decay lengths for the multilepton final states for the benchmark points. Such events at the LHC with 14 TeV center of mass energy at 100 fb\(^{1}\) integrated luminosity are collected in Table 9. For single displaced lepton events we again decompose the displaced length \(\ell _d\) in four different ranges: \(0.1 \,\text {mm}\, <\ell _d \le 1\) cm, \(1 \,\text {cm}\, <\ell _d \le 10\) cm, \(10 \,\text {cm}\, <\ell _d \le 1\) m and \(1 \,\text {m}\, <\ell _d \le 10\) m, respectively. The presence of one displaced lepton makes the final states completely background free. We see that only BP5 has promising number of events at 100 fb\(^{1}\) of integrated luminosity, for other benchmark points one has to wait for highluminosity (HL), i.e., \({\mathcal {O}}(3000)\) fb\(^{1}\) at the LHC. Only BP5 gives rise to sufficient number of trilepton events at 100 fb\(^{1}\) of integrated luminosity.
Number of events with multiple charged leptons with at least one of them is displaced with displacement 0.1mm to 10 m at 14 TeV for the benchmark points in scenario 2
Benchmark points  \(n_{\ell }\ge 1\)  \(n_{\ell }\ge 2\)  \(n_{\ell }\ge 3\) 

BP5  7799.7\({\left\{ \begin{array}{ll} 3586.8\\ 3940.9\\ 272.0 \\ 0.0 \end{array}\right. }\)  4038.4  543.9 
BP6  2.4\({\left\{ \begin{array}{ll} 0.1\\ 1.0\\ 1.1\\ 0.2 \end{array}\right. }\)  1.0  0.0 
BP7  3.8\({\left\{ \begin{array}{ll} 0.4\\ 1.5\\ 1.9\\ 0.0 \end{array}\right. }\)  1.2  0.0 
Number of events with multiple jets with at least one of them is displaced with displacement 0.1mm to 10 m at 14 TeV for the benchmark points in scenario Sc 2
Benchmark  \(n_{j}\ge 1\)  \(n_{j}\ge 2\)  \(n_{b}\ge 1\) 

points  
BP5  16,1818.7\({\left\{ \begin{array}{ll} 67098.2\\ 88285.7\\ 6414.3\\ 20.5 \end{array}\right. }\)  82,595.1\({\left\{ \begin{array}{ll} 31178.4\\ 46895.9\\ 4505.4\\ 15.4 \end{array}\right. }\)  389.9\({\left\{ \begin{array}{ll}118.0\\ 236.0\\ 35.9\\ 0.0\end{array}\right. }\) 
BP6  2783.0\({\left\{ \begin{array}{ll} 163.7\\ 924.7\\ 1570.1\\ 124.5 \end{array}\right. }\)  1448.7\({\left\{ \begin{array}{ll} 81.3\\ 460.0\\ 829.3\\ 78.1 \end{array}\right. }\)  5.3\({\left\{ \begin{array}{ll} 0.0\\ 1.5\\ 3.0\\ 0.8 \end{array}\right. }\) 
BP7  12251.6.1\({\left\{ \begin{array}{ll} 197.0\\ 1458.7\\ 6471.9\\ 4124.0 \end{array}\right. }\)  6412.8\({\left\{ \begin{array}{ll} 92.9 \\ 706.4\\ 3271.8\\ 2341.7\end{array}\right. }\)  24.3\({\left\{ \begin{array}{ll}0.0\\ 1.9\\ 10.4\\ 12.0\end{array}\right. }\) 
Benchmark points for a collider study consistent with the \(\sim 125\) GeV Higgs mass where the lifetime of NLSP is given as \( \tau _{NLSP}\) and the proper decay length of NLSP is given as \(c\,\tau _{NLSP}\)
Benchmark  NLSP  LSP mass  NLSP mass  NNLSP mass  \(\tau _{NLSP}\)  \(c\, \tau _{NLSP}\) 

points  (GeV)  (GeV)  (GeV)  (ns)  (cm)  
BP8  \(\tilde{\chi }_1^{\pm }\)  113.648  114.476  195.124  0.0038  0.113 
BP9  \(\tilde{\chi }_1^{\pm }\)  367.33  368.161  439.22  0.0028  0.082 
BP10  \(\tilde{\chi }_1^{\pm }\)  177.38  177.73  211.401  0.274  8.16 
4.3 Sc 3: Higgsino LSP
Pair and associated production cross sections for \(\tilde{\chi }_{1,2}^{\pm }\) and \(\tilde{\chi }_{1,2}^{0}\) at 14 TeV for each benchmark point in scenario 3
Benchmark  \(\sigma _{\tilde{\chi }_1^{\pm }\tilde{\chi }_1^{\mp }}\)  \(\sigma _{\tilde{\chi }_1^{\pm }\tilde{\chi }_1^{0}}\)  \(\sigma _{\tilde{\chi }_1^{\pm }\tilde{\chi }_2^{0}}\)  \(\sigma _{\tilde{\chi }_1^{\pm }\tilde{\chi }_2^{\mp }}\)  \(\sigma _{\tilde{\chi }_2^{0}\tilde{\chi }_2^{0}} \)  \(\sigma _{\tilde{\chi }_2^{0}\tilde{\chi }_1^{0}}\)  \(\sigma _{\tilde{\chi }_2^{0}\tilde{\chi }_2^{\pm }}\) 

points  (fb)  (fb)  (fb)  (fb)  (fb)  (fb)  (fb) 
BP8  3495.03  275.86  547.89  62.30  1.11  86.12  99.48 
BP9  44.52  3.70  13.40  4.31  1.4\(\times 10^{3}\)  2.14  6.93 
BP10  693.80  53.08  219.04  78.70  0.289  41.43  115.1 
Number of displaced NLSP decays which can have charged track in the ranges of 0.1–1 cm, 1–10 cm, 0.1–1 m and 1–10 m for the benchmark points of scenario Sc 3 at the LHC with 14 TeV center of mass energy and at an integrated luminosity of 100 fb\(^{1}\).
Benchmark points  Process  BP8  BP9  BP10 

0.1–1 cm  \(\tilde{\chi }_1^{\pm }\tilde{\chi }_1^{\mp }\)  29,0786.5  3441.6  14816.8 
\(\tilde{\chi }_1^{\pm }\tilde{\chi }_1^{0}\)  23,810.6  304.7  883.1  
\(\tilde{\chi }_1^{\pm }\tilde{\chi }_2^{0}\)  47,382.5  1057.3  4340.5  
1–10 cm  \(\chi _1^{\pm }\tilde{\chi }_1^{\mp }\)  1481.9  2.6  41,067.4 
\(\tilde{\chi }_1^{\pm }\tilde{\chi }_1^{0}\)  163.3  0.3  3054.9  
\(\tilde{\chi }_1^{\pm }\tilde{\chi }_2^{0}\)  373.6  1.3  12,902.8  
10 cm–1 m  \(\tilde{\chi }_1^{\pm }\tilde{\chi }_1^{\mp }\)  69.9  0.0  13,221.1 
\(\tilde{\chi }_1^{\pm }\tilde{\chi }_1^{0}\)  0.6  0.0  1418.4  
\(\tilde{\chi }_1^{\pm }\tilde{\chi }_2^{0}\)  2.2  0.0  4576.2  
1–10 m  \(\tilde{\chi }_1^{\pm }\tilde{\chi }_1^{\mp }\)  0.0  0.0  63.8 
\(\tilde{\chi }_1^{\pm }\tilde{\chi }_1^{0}\)  0.0  0.0  11.0  
\(\tilde{\chi }_1^{\pm }\tilde{\chi }_2^{0}\)  0.0  0.0  30.2 
Table 13 gives numbers of events with displaced lightest chargino NLSP decay for the range of 0.1 mm to 10 m for the benchmark points. As anticipated only BP10 has events with \({\mathcal {O}}(10)\) meter of displacements. Here we have considered the dominant contributions from \(\tilde{\chi }^\pm _1\tilde{\chi }^\mp _1,\, \tilde{\chi }^\pm _1\tilde{\chi }^0_1,\, \tilde{\chi }^\pm _1\tilde{\chi }^0_2\) production processes. \(\tilde{\chi }^0_2\) is the NNLSP and has a prompt decay for all three benchmark points. However, it can decay to \( \tilde{\chi }^\pm _1\) which can give rise to additional displaced decays. Out of these events most of the events will end up giving disappearing charged track as the decay products will be below the initial trigger cuts. Nevertheless, we will bank on the possibility of the boosted decay events where the NLSP with higher momentum forward some momentum to the decay products i.e., the charged leptons and jets. The other possibility is that the final state gets high momentum recoil due to some ISR jets. Both these effects are incorporated in our PYTHIA based analysis.
Number of events with multiple charged leptons with at least one of them displaced with displacement 0.1 mm to 10 m at 14 TeV for the benchmark points in scenario Sc 3. Here the leptons are rather soft \(p^{\ell }_T \ge 5\) GeV and at least one of them is displaced
Benchmark  \(n_{\ell }\ge 1\)  \(n_{\ell }\ge 2\)  

points  \(\tilde{\chi }^\pm _1\tilde{\chi }^\mp _1\)  \(\tilde{\chi }^\pm _1\tilde{\chi }^0_1\)  \(\tilde{\chi }^\pm _1\tilde{\chi }^0_2\)  \(\tilde{\chi }^\pm _1\tilde{\chi }^\mp _1\)  \(\tilde{\chi }^\pm _1\tilde{\chi }^0_1\)  \(\tilde{\chi }^\pm _1\tilde{\chi }^0_2\) 
BP8  636.1\({\left\{ \begin{array}{ll} 223.7\\ 349.5\\ 62.9\\ 0.0 \end{array}\right. }\)  18.3 \({\left\{ \begin{array}{ll} 10.4\\ 8.3\\ 0.6\\ 0.0 \end{array}\right. }\)  29.9\({\left\{ \begin{array}{ll} 17.4\\ 12.5\\ 0.0\\ 0.0 \end{array}\right. }\)  118.8  0.0  5.0 
BP9  3.3\({\left\{ \begin{array}{ll} 2.3\\ 1.0\\ 0.0\\ 0.0 \end{array}\right. }\)  0.1\({\left\{ \begin{array}{ll} 0.1\\ 0.0\\ 0.0\\ 0.0 \end{array}\right. }\)  0.4\({\left\{ \begin{array}{ll} 0.3\\ 0.1\\ 0.0\\ 0.0 \end{array}\right. }\)  0.0  0.0  0.1 
BP10  29.2\({\left\{ \begin{array}{ll} 0.0\\ 2.8\\ 9.7\\ 16.7 \end{array}\right. }\)  1.4\({\left\{ \begin{array}{ll} 0.0\\ 0.0\\ 0.7\\ 0.7 \end{array}\right. }\)  4.8\({\left\{ \begin{array}{ll} 0.0\\ 0.0\\ 2.2\\ 2.6 \end{array}\right. }\)  2.8  0.0  0.9 
Number of events with multiple jets with at least one of them displaced with displacement 0.1 mm to 10 m at 14 TeV for the benchmark points in scenario Sc 3
Benchmark  \(n_{j}\ge 1\)  

points  \(\tilde{\chi }^\pm _1\tilde{\chi }^\mp _1\)  \(\tilde{\chi }^\pm _1\tilde{\chi }^0_1\)  \(\tilde{\chi }^\pm _1\tilde{\chi }^0_2\) 
BP8  21,7237.1\({\left\{ \begin{array}{ll} 215943.9\\ 1286.2\\ 7.0\\ 0.0 \end{array}\right. }\)  18,028.6\({\left\{ \begin{array}{ll} 17898.9\\ 129.7\\ 0.0\\ 0.0 \end{array}\right. }\)  44,478.7\({\left\{ \begin{array}{ll} 44117.6\\ 361.1\\ 0.0\\ 0.0 \end{array}\right. }\) 
BP9  2791.7\({\left\{ \begin{array}{ll} 2789.7\\ 2.0\\ 0.0\\ 0.0 \end{array}\right. }\)  248.0\({\left\{ \begin{array}{ll} 247.8\\ 0.2\\ 0.0\\ 0.0 \end{array}\right. }\)  1010.1\({\left\{ \begin{array}{ll} 1009.1\\ 1.0\\ 0.0\\ 0.0 \end{array}\right. }\) 
BP10  53,128.3\({\left\{ \begin{array}{ll} 11229.8\\ 31501.3\\ 10357.0\\ 40.2 \end{array}\right. }\)  4183.7\({\left\{ \begin{array}{ll} 683.5\\ 2372.6\\ 1119.8\\ 7.8 \end{array}\right. }\)  18,826.9\({\left\{ \begin{array}{ll} 3691.7\\ 11089.6\\ 4023.3\\ 22.3 \end{array}\right. }\) 
Number of events with dijet with at least one of them displaced with displacement 0.1 mm to 10 m at 14 TeV for the benchmark points in scenario Sc 3. The last column shows if at least one of them is a displaced bjet
Benchmark  \(n_{j}\ge 2\)  \(n_{b}\ge 1\)  

points  \(\tilde{\chi }^\pm _1\tilde{\chi }^\mp _1\)  \(\tilde{\chi }^\pm _1\tilde{\chi }^0_1\)  \(\tilde{\chi }^\pm _1\tilde{\chi }^0_2\)  \(\tilde{\chi }^\pm _1\tilde{\chi }^0_2\) 
BP8  15,516.9\({\left\{ \begin{array}{ll} 149692.1\\ 817.8\\ 7.0\\ 0.0 \end{array}\right. }\)  12,670.2\({\left\{ \begin{array}{ll} 12580.3\\ 89.9\\ 0.0\\ 0.0 \end{array}\right. }\)  38,549.1\({\left\{ \begin{array}{ll} 38260.2\\ 288.9\\ 0.0\\ 0.0 \end{array}\right. }\)  580.3\({\left\{ \begin{array}{ll} 575.3\\ 5.0\\ 0.0\\ 0.0\end{array}\right. }\) 
BP9  2046.0\({\left\{ \begin{array}{ll} 2045.1\\ 0.9\\ 0.0\\ 0.0 \end{array}\right. }\)  182.6\({\left\{ \begin{array}{ll} 182.4\\ 0.2\\ 0.0\\ 0.0 \end{array}\right. }\)  889.9\({\left\{ \begin{array}{ll} 888.9\\ 1.0\\ 0.0\\ 0.0 \end{array}\right. }\)  29.6\({\left\{ \begin{array}{ll} 29.6 \\ 0.0\\ 0.0\\ 0.0 \end{array}\right. }\) 
BP10  37,861.9\({\left\{ \begin{array}{ll} 7906.5\\ 22363.9\\ 7570.7\\ 20.8 \end{array}\right. }\)  3022.3\({\left\{ \begin{array}{ll} 493.7\\ 1706.2\\ 818.0\\ 4.4 \end{array}\right. }\)  14,462.3\({\left\{ \begin{array}{ll} 2791.0\\ 8524.2\\ 3128.3\\ 18.8 \end{array}\right. }\)  47.3\({\left\{ \begin{array}{ll} 7.9\\ 25.0\\ 14.0\\ 0.4\end{array}\right. }\) 
Table 16 shows the number of events for the dijet final states for the benchmark points at the LHC with 14 TeV of center of mass energy at an integrated luminosity of 100 fb\(^{1}\), where we demand to have at least one of the jets to be produced via displaced decay of the NLSP. The dominant contributions are from \(\tilde{\chi }^\pm _1\tilde{\chi }^\mp _1, \, \tilde{\chi }^\pm _1\tilde{\chi }^0_1,\, \tilde{\chi }^\pm _1\tilde{\chi }^0_2\), respectively. The requirement of soft jets are again motivated from the compressed mass spectrum for NLSPLSP and a demand of \(p^j_T \ge 20\) GeV will reduce the number of events by 5865%. In that we need to go for higher luminosity LHC in order of have sufficient number of events.
Finally in the last column of Table 16 we present the number of events where we have a least one displaced bjet in the final state. Such bjets produced via the displaced decay of NLSP can be really promising. Along with the displaced charged leptons it can give additional handle for the system.
5 Discussion and conclusion
In this article we have considered the phenomenology of the electroweak gaugino sector for the \(Y=0\) triplet extended supersymmetric SM. The triplet extension is motivated due to reducing the demand for large SUSY mass scale for a desired \(\sim 125\) GeV Higgs boson. Such extensions specially with \(Y=0\) do not couple to fermions and give rise to interesting phenomenology in the neutral and charged Higgs sectors [5, 9, 10, 14, 15, 16, 17].
Similar to Higgs sectors the phenomenology of electroweak chargino and neutralino sectors differ from MSSM and is thus worth exploring. We noticed that tripletlike charginos and neutralinos are almost mass degenerate. In scenario Sc 1, such triplinolike low lying states give rise to displaced phenomenology. In scenario Sc 2, both the NLSP and NNLSP are of triplinotype and they are also nearly degenerate as mass eigenstates tend to follow the same gauge structure. Similar feature for Higgs mass eigenstates following the gauge structure in a supersymmetric extended Higgs scenario has already been observed [14, 15, 16, 17]. The triplinolike chargino and triplet charged Higgs boson do not couple to the fermions, so in principle pure tripletstate will not contribute to the rare processes like \(B \rightarrow X_s \gamma \). Thus, in TESSM the triplet contribution to the \(B \rightarrow X_s \gamma \) process happens via the mixing with the doublet Higgs bosons. Due to mixing the allowed parameter regions by \(B \rightarrow X_s \gamma \) constraint differ from MSSM for chosen values of \(\mu _D, A_{t,b}, \tan {\beta }\) [9].
Unlike scalar component of the \(Y=0\) fermionic triplet in supersymmetric TypeIII seesaw [34, 43], these triplinos are fermions, do not carry any lepton numbers and couple to Higgs boson via TypeIII Yukawa coupling. The scalar triplino decay in this model can give rise to displaced Higgs production [43]. Such features can be explored in order to distinguish the \(Y=0\) SU(2) triplets with different spins. Generically seesaw models predict displaced decays due to very small Yukawa couplings [54, 55].
Displaced jets can come from various other models including Rparity violating decays and recent LHC searches have put some bounds on models [56]. Rparity violating Higgs decays can also lead to displaced multilepton final states [57]. In a supersymmetric U(1) extended scenario, superpartners of righthanded neutrinos can have displaced decays due to a very suppressed coupling occurring because of the cancellation among the parameters in the superpotential and the soft parameters [58, 59, 60]. However, in these cases the corresponding decay products have relatively large momentum, enough to be detected. In this study we have used rather soft triggers, i.e., \(p^{\ell }_T \ge 5\) GeV and \(p^{j}_T \ge 10\) GeV. Application of larger momentum cuts i.e., \(p^{\ell }_T \ge 20\) GeV and \(p^{j}_T \ge 20\) GeV reduce the leptonic and jet final state events by \(\sim 41\%\) and \(\sim 43\%\), respectively. For such large momentum cuts, the high luminosity version of LHC is essential.
Footnotes
 1.
For all the chosen benchmark points oneloop corrections to the chargino and neutralino sectors are also checked with SPheno 3.3.7 [36] by using model files obtained from SARAH 4.1.0 [37]. After the corrections are taken into account the LSP at treelevel for all benchmark points stays as LSP at 1loop level and 1loop mass contributions to neutralinos and charginos are \(\le 4\%\) of their tree level masses. From the phenomenological point of view such contributions do not change the collider signatures since the mass differences among LSP, NLSP and NNSLP are not altered drastically. This is why we use their treelevel masses for the phenomenological discussions.
Notes
Acknowledgements
PB acknowledges University of Helsinki for the visit during initial part of the project. PB also thanks Prof. Rahul Sinha for arranging the visit at Institute of Mathematical Sciences, Chennai for the final part of the project. ASK acknowledges Namık Kemal University, Physics Department for the hospitality during the initial part of the project. KH acknowledges H2020MSCARICE2014 grant no. 645722 (NonMinimalHiggs).
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