Scalar Neutrinos at the LHC

We study a softly-broken supersymmetric model whose gauge symmetry is that of the standard model (SM) gauge group times an extra Abelian symmetry U(1)'. We call this gauge-extended model U(1)' model, and we study a U(1)' model with a secluded sector such that neutrinos acquire Dirac masses via higher-dimensional terms allowed by the U(1)' invariance. In this model the mu term of the minimal supersymmetric model (MSSM) is dynamically induced by the vacuum expectation value of a singlet scalar. In addition, the model contains exotic particles necessary for anomaly cancellation, and extra singlet bosons for achieving correct Z'/Z mass hierarchy. The neutrinos are charged under U(1)', and thus, their production and decay channels differ from those in the MSSM in strength and topology. We implement the model into standard packages and perform a detailed analysis of sneutrino production and decay at the Large Hadron Collider, for various mass scenarios, concentrating on three types of signals: (1) 0lep+ MET,(2) 2lep+MET, and (3) 4lep + MET. We compare the results with those of the MSSM whenever possible, and analyze the SM background for each signal. The sneutrino production and decays provide clear signatures enabling distinction of the U(1)' model from the MSSM at the LHC.


I. INTRODUCTION AND MOTIVATION
The MSSM is arguably the most popular 'new physics' scenario referring to a perturbative completion of the SM beyond Fermi energies. Motivated by the resolution of such long standing problems of the SM as the gauge hierarchy problem, the existence of dark matter and the added attraction of gauge unification, nevertheless, it still has some outstanding problems. One of these is the so-called µ problem [1]. Supersymmetric models which extend the MSSM via an extra gauge group generally intend to solve µ problem and incorporate an extra singlet field, whose coupling to the Higgs fields and VEV generate dynamically the µ term. These models extend the SU(2) L ⊗ U(1) Y MSSM electroweak symmetry by an extra U(1) gauge symmetry. Such an extension is minimal, and it is well motivated in superstring theories [2], grand unified theories [3] and in dynamical electroweak breaking theories [4].
The simplest versions contain a singlet field and an extra neutral gauge boson. Other versions also allow right-handed neutrinos into the spectrum. In a non-minimal version of the U(1) extended MSSM, which includes several singlet (S) fields, the tension between the electroweak scale and developing a large enough Z ′ mass is resolved. We call this version of the model secluded sector U(1) ′ , a shorthand notation for SU(3) c ⊗ SU(2) L ⊗ U(1) Y ⊗ U(1) ′ , the gauge symmetry underlying the model, and describe it in the next section. In the MSSM, as in the SM, neutrinos are massless. The fact that neutrino oscillation imply non-vanishing neutrino masses is a strong motivation to consider an extended form of the MSSM. Small neutrino masses consistent with neutrino oscillation phenomenology are usually explained by the see-saw mechanism [5]. In the see-saw mechanism, large Majorana masses for righthanded neutrinos induce small Majorana masses for left-handed neutrinos. In the scalar sector, right-handed sneutrinos mix with the left handed sneutrinos and give potentially new signals for extended symmetry. The choice of U(1) symmetry would determine the magnitude and type of neutrino masses. In this paper, we consider a U(1) ′ extended form of the MSSM that contains Dirac-type neutrino masses.
Direct or indirect detection of the superpartners of the Standard Model particles, the definitive signal for supersymmetry, is one of the major aims of the LHC experiments. Except for the LSP in the R−parity conserving supersymmetry, the superpartners are expected to decay instantaneously into SM particles, plus the LSP, detected as missing energy. The common methodology for detection is to analyze the production and cascade decays of the supersymmetric particles. As the right sneutrinos, which can mix with the left sneutrinos are a feature of the U(1) ′ model that distinguishes it from MSSM, studying sneutrino signals would be an important test for this model.
Systematic analyses of sneutrino decays in the MSSM have been performed in [6]. The aim of this article is to perform a comparative study of LHC signals of sneutrino production and decays in the MSSM and in a supersymmetric model with a secluded U(1) ′ breaking sector [7] via their decay chain topologies. Differences between MSSM and the secluded sector U(1) ′ model likely reveal themselves via decay modes of the sneutrino. We analyze the signals, and, for completeness, we also include possible Standard Model backgrounds.
In most variants of the MSSM consistent with relic density calculations, the LSP is the lightest neutralino, typically a mixed state of bino (fermionic partner of the U(1) Y gauge boson) and the higgsino. In a previous work [8], we showed that a minimal U(1) ′ model (one extra singlet boson) could be consistent with the excess positron observed in satellite experiments, choosing on of the right-handed sneutrinos as the LSP. However, for the purpose of this work (dependent on parameter space chosen to compare our results with those of MSSM), the secluded sector U(1) ′ lightest neutralino appears consistently to be the lightest supersymmetric particle (LSP) and therefore is a potentially viable dark matter (DM) candidate, although its composition is likely to differ from the lightest neutralino in MSSM.
Here we perform a thorough analysis of sneutrino production and decay in the secluded sector U(1) ′ model. In order to compare with previous signals, we establish a set of three mSUGRA-inspired benchmarks for our model. Similar to the mSUGRA benchmark points analyzed in MSSM (LM1, LM2, LM6) [9][10][11], we analyze the corresponding scenarios in secluded sector U(1) ′ model (LM1 ′ , LM2 ′ , LM6 ′ ). Here LM stands for Low Mass, a choice likely to yield visible signals at the LHC.
Our paper is organized as follows. We briefly introduce the model in Section II, then define the parameters and physical masses of supersymmetric particles in the secluded sector U(1) ′ model in Section III. For each benchmark point, we insure that DM candidate of the U(1) ′ model yields relic densities consistent with the WMAP range of cold dark matter density [12]. We then perform a comparative analysis of the production, decays and detectability of sneutrinos within these benchmark supersymmetric scenarios. During this analysis we focus on the multilepton plus missing energy signatures of the supersymmetric scenarios.
We present the results of our simulation analysis for the LHC. In Section IV we conclude the work. We leave the extensive details of the model for the Appendices. The MSSM suffers from a naturalness problem due to the presence of µ parameter, responsible for giving masses to the Higgs bosons and Higgsino in the superpotential. From a purely theoretical point of view, the value of this parameter is expected to be either of the order of the GUT, Planck scale or zero. For phenomenological aspects, however, it must be of the order of the scale of electroweak symmetry breaking (EWSB) and it has to be non-zero to agree with the experimental data. Seen from the low energy point of view, adding an extra U(1) is needed in order to solve the µ problem [1] of the MSSM. Basically the problem is remedied by extending the matter and gauge structure of the MSSM, e.g. within unified and/or string models by introducing an additional singlet filed S, whose VEV generates the µ term dynamically. Theories with an extra U(1) ′ broken at the electroweak-to-TeV scale by SM singlets are known to be able to generate an appropriately sized µ parameter (see The other success of the U(1) ′ symmetry is being able to generate pertinent neutrino masses by introducing right-handed neutrinos into the superpotential. The right-handed neutrino sector and the µ parameter can be correlated for both Majorana [13] and Dirac masses [14]. We assume here that lepton number is an accidental symmetry that is conserved at the perturbative level. Hence, the neutrinos are Dirac fermions, requiring Yukawa couplings of O (10 −13 ). These couplings are technically natural, but an explanation for such a strong suppression is clearly desirable. One way this can occur is if the U(1) ′ invariance suppresses leading order contributions to Dirac neutrino masses and allows higher-dimensional operators [14].
In this work, we extend the MSSM in the following ways. First, the gauge structure of the MSSM, SU(3) C ⊗SU(2) L ⊗U(1) Y , is enriched to include an extra Abelian group factor U(1) ′ .
Second, we promote the µ parameter into dynamical field, S, which is charged under the U(1) ′ . Third, exotics with Yukawa couplings to S are included to make the theory anomalyfree. Fourth, Z ′ /Z mass hierarchy in the model is ensured by three additional SU(2) singlet fields which are coming from secluded sector of the model. The model also includes a term that provides suppressed Dirac neutrino masses in accordance with observations. We present the main relevant points in this section, leaving the details for the appendices.
In the minimal version of the model which contains only one singlet S, there is some tension between the electroweak scale and the need to generate a large enough M ′ Z . These two problems can be decoupled without fine tuning when several additional fields are incorporated into the model. An example of this kind of non-minimal model is secluded sector model. The secluded sector model involves an ordinary sector of symmetry breaking fields, which includes two Higgs doublets, and an SU(2) L singlet S. After acquiring a VEV, S generates an effective µ parameter µ = h s S . The secluded sector of the model includes  three SU(2) L singlet fields S i , i = 1, 2, 3 which acquire large VEVs. All four VEVs of the singlet fields S, S 1,2,3 contribute to Z ′ mass. Thus, in this model, Z ′ /Z mass hierarchy is implemented mainly through the secluded sector of the model.
The superpotential of the model is given by where the fields entering the equation, together with their quantum numbers are listed in Table I. Here, M R is a large mass scale and h ν is the Yukawa coupling responsible for generating neutrino masses.
The U(1) ′ charges of the fields satisfy a number of conditions arising from phenomenological constraints, as well as from gauge invariance of the model and from the requirement of cancellation of gauge and gravitational anomalies. They are as follows.
The U(1) ′ charges satisfy Q ′ Hu + Q ′ H d = 0 to forbid the bare µ term, Q ′ L + Q ′ Hu + Q ′ N = 0 to induce neutrino masses correctly, and Q ′ S 1 + Q ′ S 2 + Q ′ S 3 = 0 to correctly generate the Z − Z ′ mass hierarchy. Gauge invariance of the superpotential implies For the model to be anomaly-free the U(1) ′ charges of fields must satisfy respectively. All these anomaly cancellation conditions are satisfied for a particular pattern of charges and parameters. It is found that the solution to the mixed anomaly constraints requires n Q = 3 color triplet pairs with hypercharge Y Q = −1/3, and n L = 5 singlet pairs with Y L = − 2/5. With these parameter values one obtains the U(1) ′ model displayed in Table II. The U(1) ′ charges for Higgs fields in the model are chosen as Under the conditions above, the supersymmetry breaking soft terms for the secluded sector model are where V I sof t are the allowed U(1) ′ dimension-2 operators and V o sof t term is defined as We set m 2 S 1 S 2 = 0 as only two of the S i fields are needed to break the global U(1) symmetries. To insure that the potential is not bounded from below, we require In the model, the charge of the quark doublet Q is kept as a free parameter after the In this model the left and right sneutrinos mix, and the mixing matrix can in general be expressed as where i, j are the flavor indices and the matrix elements are given by Here M 2 L i and M 2 N i are soft mass terms and A ν i are trilinear couplings (assumed flavordiagonal). Dirac neutrino masses m ν , the µ parameter and ρ s in the equations above are expressed as In this model, neutrino masses are chosen to be Dirac-type. The effective neutrino Yukawa coupling Y ν leads to neutrino masses in agreement with the experiment. Numerically, we Ref. [15] where there is difficulty with inducing a small µ ef f while satisfying the Z ′ mass bound, which is around 1 TeV. This is because both µ ef f and m Z ′ are proportional to the vacuum expectation value of the additional scalar field S. One needs three additional scalars to ameliorate the picture the VEVs of the new scalars are kept large large. This is one motivation for the secluded U(1) ′ model. For further details of the model, see [7]. The Feynman diagrams contributing to the hard production of scalar neutrinos are given in Fig 1. For simplicity we neglect the mixing between Z ( the Z boson of the SM) and Z ′ in the numerical analysis so that Z 1 ≡ Z and Z 2 ≡ Z ′ . In addition to Z ′ exchange (left-handed diagram), all CP-even Higgs bosons contribute to the process in the s-channel (right-handed diagram).
Once the scalar neutrinos are produced, they will decay. The decay pattern strictly depends on scenario chosen for the free parameters. Since we are interested in rather light scalar neutrinos (assuming low-energy SUSY exits), we prefer to choose MSSM-like Low Mass (LM) scenarios [9]. Battaglia et. al have proposed updated post-WMAP benchmark points for the constrained MSSM [10] modifying earlier proposal [11], and we include these points in Table III.
To compare our results with MSSM predictions, we choose three low-mass MSSM scenarios (benchmark points), namely LM1, LM2 and LM6, from the low mass scenarios of MSUGRA and use Softsusy package [16] to generate the MSSM spectrum. In the secluded U(1) ′ we choose LM-like scenarios, denoted as LM1 ′ , LM2 ′ and LM6 ′ by keeping the overlapping parameters the same and fixing the additional parameters to agree with phenomenological constraints on masses. The input parameters for LM1, LM2 and LM6 for MSSM as well as their corresponding prime versions for the secluded U(1) ′ are given in Table III. As seen from Table III,  showing the same pattern as in the neutrino sector. With these chosen masses we can foresee that the production cross section for the left-handed sneutrinos will dominate the one for the right-handed ones.
The validity of the MSSM scenarios LM1, LM2 and LM6 has been confronted with both the LEP and Tevatron data. There will be no contributions to the LEP observables from our LMX ′ , X = 1, 2, 6 scenarios since the lightest Higgs boson mass in the model is 218 GeV, which is already above the LEP energy. For the Tevatron case, however, one needs do a more careful analysis. Nevertheless, as the LMX ′ scenarios aim to be consistent with   the corresponding MSSM scenarios, in the limit where the extra U(1) ′ particles decouple, we expect consistency with the Tevatron data. To verify this point, we used the package HiggsBounds [17], which yields results for any arbitrary Higgs sector. The production cross sections for the scattering pp →ν ℓ L,Rν * ℓ L,R processes are listed in Table V,  In Table V, we also included the relic density of the dark matter for all six scenarios. This calculation is straightforward using the Micromegas package [21], once we include the model files from CalcHEP. All the numbers are within the 1σ range of the WMAP result [22] which can be given with those from the Sloan Digital Sky Survey [12] We note that the relic density of the dark matter Ω DM h 2 is very sensitive to the free parameter R Y ′ listed in Table III which varies between 42 to 50. It's defined (see also Appendix C) as the ratio between bare U(1) gaugino masses where M Y and M Y ′ are the Bino and Bino ′ mass parameters appearing in the 9 × 9 neutralino mixing matrix. More details are given in Appendix C. In Table IV the Lightest Supersymmetric Particle (LSP) is the lightest neutralino χ 0 1 with masses 96 GeV, 63 GeV and 79 GeV for the LM1 ′ , LM2 ′ and LM6 ′ scenarios, respectively. The next-to-lightest supersymmetric particle is χ 0 2 with masses 99 GeV, 138 GeV and 158 GeV, respectively. For such a spectrum, there will be no kinematically available two-body decays for the χ 0 2 , so that three-body channels need to be considered. The three-body decay modes relevant to 14 the analysis here are given in Fig. 2. These decay modes will be considered in the LHC simulation but not the relic density calculation, as they give negligible contributions. The sizable contributions to the relic density are for the LM1 ′ scenario In the LM2 ′ (LM6 ′ ) only χ 0 1 χ 0 1 annihilation contributes to the relic density of the dark matter as follows • χ 0 1 χ 0 1 → ν lνl , l = e, µ (0% (3%)) • χ 0 1 χ 0 1 → dd/ss (1% (0%)) Contributions from the χ 0 2 χ 0 2 or χ 0 1 χ 0 2 annihilations for the χ 0 1 scenario are due to the fact that χ 0 1 and χ 0 2 are almost degenerate in mass and since the two-body decay channel limit is used in Micromegas, χ 0 2 acts very similar to χ 0 1 . There is no sizable contributions from χ 0 2 in the other two scenario since χ 0 2 is much heavier. The bino, wino, higgsino and singlino compositions of the neutralinos for the scenarios LM1 ′ , LM2 ′ and LM6 ′ are given in Table VI in Appendix D. The LSP χ 0 1 is mainly bino for LM1 ′ but mostly singlino ( S) for LM2 ′ and LM6 ′ (94.2% and 93.6%, respectively, for the two scenarios). The situation is reversed for the next-to-LSP, χ 0 2 .

B. The LHC Signals
After discussing the chosen scenarios and the details of the relic density calculation of the dark matter, we proceed to discuss the signals at LHC from scalar neutrino production processes. To determine and classify all possible signals for the scenarios LM1 ′ , LM2 ′ and LM6 ′ , we need to look at the decay topology of the scalar neutrinos.
Since we include MSSM scenarios LM1, LM2 and LM6 for comparison purposes, we first outline the main decay modes governing the decay channels. The left-handed scalar neutrinos ν ℓ L decay to ν ℓ χ 0 1 with about 100% branching ratio for the LM1 and LM6, since all the other neutralinos are heavier than the scalar neutrinos. The picture is a bit more complicated for the LM2 where ν ℓ L , ℓ = e, µ decay to ν ℓ χ 0 1 (71%), ℓ χ ± 1 (20%) and ν ℓ χ 0 2 (8.8%). For the ν τ L , the branching decay ratios are W τ 1 (61.5%), ν τ χ 0 1 (34.2%), τ χ ± 1 (3%) and ν τ χ 0 2 (1.3%). Further in the decay chain χ 0 2 decays mainly to τ τ 1 /τ τ * 1 (48% for each channel), and the chargino χ ± 1 toν τ τ 1 (with 95.4% branching ratio) and W χ 0 1 (4.6% branching ratio). In the secluded U(1) ′ model, the decay modes of the scalar neutrinos with more than 1% branching ratio are, for the scenarios There will be further decays of χ 0 2 and χ 0 4 in the chain. It is better to consider χ 0 4 first. Again in the same notation (LM1 ′ /LM2 ′ /LM6 ′ ) it decays as • χ 0 4 → τ τ * 1 (τ τ * 2 ) , 6.5% (4.9%) / 9.1% (3.7%) / 8.6% (3.9%) • χ 0 4 → ℓ ℓ * L (ℓ ℓ * R ) , 6.0% (5.3%) / 5.2% (5.0%) / 4.0% (8.3%) where ℓ = e, µ and the conjugated decay modes are not listed. Then the decay modes of the scalar leptons for ℓ = e, µ * are • ℓ L → ℓ χ 0 1 (ℓ χ 0 2 ) , 6.7% (93.3%) / 90.1% (9.9%) / 92.6% (7.4%) • ℓ R → ℓ χ 0 1 (ℓ χ 0 2 ) , 20% (80%) / 71.6% (28.4%) / 89.7% (10.3%) As can be seen from the above decay patterns, each decay ends up with either an LSP χ 0 1 or next-to-LSP particle χ 0 2 . As mentioned earlier, χ 0 2 cannot decay into two-body but instead must undergo the one of the three-body decays given in Fig. 2. The relative ratios are † given in the (LM1 ′ /LM2 ′ /LM6 ′ ) order as In the light of these decay patterns, there are mainly three types of signal: (1) 0ℓ+ E T , (2) 2ℓ+ E T and (3) 4ℓ+ E T . It is in fact also possible to produce signals with six or eight leptons but the probability is very suppressed thus we ignore such signals. Therefore, in the rest of this section we discuss these three signals at LHC. Predictions from MSSM will be included as well. In MSSM there is no the 4ℓ+ E T type of signal in MSSM for the LM1 and LM2 and LM2 scenarios. The 2ℓ+ E T signal is possible through chargino χ ± 1 decay. The usual concern is the possible background for the signals from the SM. For the 0ℓ+ E T mode, the background will come from the Drell-Yan (D-Y), pp → ν ℓνℓ , and pp → ZZ where each of Z decays invisibly. Since the D-Y has a huge cross section, some cuts need to be implemented. In the 2ℓ+ E T case, in addition to the D-Y and ZZ production (where one of the Z decays leptonicaly), there is W + W − production. In principle there could be contributions from the tt with jet veto, but we ignore such possibility since the b-jets are going to be quite energetic and can be tagged. The process pp → ZZ → 4ℓ can be the * We discard ℓ = τ case since such a pattern ends up with a τ lepton in the final state. We concentrate only on the first two generations of the charged leptons. † Note that the τ − τ − channel is not kinematically open for the LM1 ′ scenario.
background for the 4ℓ+ E T decay mode. However, a simple E T cut would eliminate events from the SM process pp → ZZ → 4ℓ. We confirmed this with our event simulation.
At the first stage, the following basic cuts are applied to suppress the SM background.
It is required that, whenever relevant, • Each isolated charged lepton (electron or muon) has a transverse momentum p T (ℓ) > 15 GeV.
• The missing transverse energy satisfies E T > 100 GeV.
• The leptons are constrained to be in the central barrel region of the detector by forcing the pseudorapidity |η| < 2.
As mention above, a missing transverse energy cut E T > 100 GeV practically gets rid of the SM background for the 4ℓ+ E T signal, which is now considered background free. For the 4ℓ+ E T signal, in order to get enough statistics after the cuts (as much less number of events pass the cuts as compared of the other two signals), we relaxed the some of the above cuts. We use p T (ℓ) > 5 GeV and ∆R ℓℓ > 0.2 for the analysis of this signal.
With the above cuts, the SM background is still larger than the signals 0ℓ+ E T and 2ℓ+ E T . The D-Y and W + W − dominate the ZZ cross section and they are all well above the signal for E T < 500 GeV. Such background domination happens in various other distributions in most part of the region. There is no point to present these figures. Instead we need to find a better way to handle the background. After examining the results at the first stage, we decided to use E sum T , also known as the effective mass m eff in literature. This variable could be helpful in reducing the backgrounds while keeping most of the signal events especially if we use a suitable value for the cuts. E sum T is defined as the scalar sum of the lepton transverse momenta and the missing transverse energy where the missing transverse energy E T is the sum of the total x and y components of the momenta in quadratures. Since it has been observed that the signal processes lead to mostly high m eff (or E sum T ) distributions, a cut on m eff would substantially reduce the background.
where E is the total calorimeter energy, P is the total visible momentum and M invisible is the total mass of all invisible particles produced in each event, which is the only unknown. All the others variables can be measured at the detector. Henceŝ The events are generated at the partonic level with CalcHEP [18] and passed to Pythia [24] with the use of CalcHEP-Pythia interface for hadronization and cuts. We simulated 4 × 10 6 events for the 0ℓ+ E T , 2ℓ+ E T and 4ℓ+ E T signals. Since the relative number of events in each signal turns out to be proportional to the relevant branching ratio combination, the number of events can be simply weighed by w = σ(pp →ν ℓν * ℓ ) × L/N tot where L is the integrated luminosity and N tot is the total number of event generated. We set L = 100 fb −1 , the ultimate goal that is expected at the LHC. Even though the current reach of LHC center of mass energy is 7 TeV, we use 14 TeV in the numerical study, which maximizes the reach in the parameter space.

The Missing Energy Signal: 0ℓ+ E T
The distributions of E T , E sum T , andŝ 1/2 min (0) are depicted in Fig. 3 for the three scenarios LM1 ′ , LM2 ′ and LM6 ′ as well as the three benchmarks for the MSSM. In general the LM6 ′ scenario has the largest event pass the cuts, with similar results for the LM2 ′ , while the LM1 ′ has the lowest. In fact about 80% of the events pass the cuts in LM2 ′ and LM6 ′ 20 but only 60% do so for the LM1 ′ . In all three scenarios, 100% of the events pass the E T cut so that we are only losing 20% to 40% of them by employing the m ef f cut. This is because the direct LSP decay modes of the scalar neutrinos (both the left handed and right handed one) are either not available or suppressed for the LM1 ′ , so that the 0ℓ+ E T signal would emerge from indirect decay channels through χ 0 2 or χ 0 4 decays, with smaller branching ratio combinations. This can be understood from details provided earlier. The distributions for the secluded U(1) ′ model dominate the ones for the MSSM since basically the total production cross section in the secluded U(1) ′ model is much bigger.
The background distributions for the D-Y and ZZ processes are also included in the E T and E sum T graphs. The rate of success for the D-Y events passing both of the cuts are only about eight in 10 6 . To give an idea how effective the m eff cut is, the success rate of events was about a bit more than 3% before implementing the m eff cut. The situation is even more drastic for the ZZ case. While the almost 100% of them passed the E T cut, this number goes down to 0.3% with the m eff cut.
We included theŝ 1/2 min (0) graphs in the second row of Fig. 3 to estimate the mass scale of the parent particles, i.e., the left handed and right handed scalar neutrinos. The graph on the bottom right panel is nothing but the zoom-in version of the one left handed side for the secluded U(1) ′ model. We cannot say anything about the MSSM case since the sum of the parent particle masses are varying in the 300 GeV to 600 GeV range, so that theŝ 1/2 min (0) peak is washed out due to the m eff cut at 750 GeV. Indeed, for the secluded model we should expect two different peaks, one for the production of the left handed scalar neutrinos and the other one for the right handed ones. The peak for the left-handed sneutrinos which are much lighter are also washed out. We will see the picture clearer for the 4ℓ+ E T signal.
In the right panel, we also indicated the positions of the peaks, which are correlated to the masses of the right handed scalar neutrinos. Of course, in reality to determine the peak position by fitting the data, a better job is needed . We just want to prove a point here.
The peak position is related to the mass of ν ℓ R (since we produce them in pair) From the peak positions in the graph we can estimate the average right handed sneutrino masses m ν ℓ R ∼ (530, 565, 600) GeV for the (LM1 ′ , LM2 ′ , LM6 ′ ), respectively, while the real average values should read (460, 563, 654) GeV from Table IV. One source of error is not knowing the mass of the LSP (though we find out that this is not significant here since the LSP mass is rather light and around 100 GeV) and the other is lack of a real fitting to the data to pin down the location of the peaks. The estimated values are still fairly good. We should also note that the method works better for signals with more visible particles.

The Dilepton Signal: 2ℓ+ E T
We analyze the 2ℓ+ E T signal in a similar fashion to the 0ℓ+ E T one in the previous subsection. The results are shown in Fig. 4 and Fig. 5. The main background is from W W and ZZ. The D-Y does not contribute due to the transverse missing energy cut. After all the cuts, about 0.2% and 0.4% of the events pass for the W W and ZZ backgrounds, respectively. The rates were about 7% and 19%, respectively, before the m eff cut. The situation for the (LM1 ′ , LM2 ′ , LM6 ′ ) scenarios after all the cuts signal is (0.9%, 50%, 50%) survival, but 100% in each cases before the m eff cut. For the MSSM, only the LM2 gives 2ℓ+ E T signal since, for the other two scenarios, the ν ℓ L χ 0 1 are the only final staes. The number of events past the cuts for the LM2 decreases to 15% from 100% after inclusion of the m eff cut. We depicted the p T spectra of both leptons ordered with respect to their hardness in Fig. 5. As expected the MSSM leptons are softer, and the distribution for ones from the LM2 ′ and LM6 ′ are very similar. The LM1 ′ scenario is somewhere in between. In the invariant mass of the leptons, the LM2 ′ and LM6 ′ curves peak at around 60 GeV and from the mass spectra in Table IV, the mass difference m χ 0 2 − m χ 0 1 is between 75 GeV to 80 GeV.

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The 2ℓ+ E T signal mainly goes through χ 0 2 . For the LM1 ′ the mass difference is 3 GeV and not visible. The ZZ peaks at around Z boson mass as expected.
In Fig. 5, we also include the ∆R ℓ + ℓ − and ∆η ℓ + ℓ − distributions. It is seen that for both the MSSM and the secluded U(1) ′ model more leptons emerge with smaller separation, unlike the W W case the peak is at the point where the others have minimum. The background can be reduced further by adjusting the M eff cut value. The leptons peak when they have the same pseudorapidity.

The Tetralepton Signal: 4ℓ+ E T
As we mentioned earlier, the 4ℓ+ E T signal is practically background-free. The ZZ background disappears after the E T cut. Taking into account having relatively few 4ℓ+ E T events, we relaxed the p T and ∆R cut values. It is also true that MSSM scenarios LM1, LM2 and LM6 do not yield a 4ℓ+ E T type of signal. For the LM1 ′ , only 2% of the events pass the cuts and among them 1% of these are 2e2µ, while the rest of the events are shared between 4e and 4µ. The situation is different for the LM2 ′ and LM6 ′ . The events which pass the cuts are around 68% for both cases and again half of them are the 2e2µ type and the rest is shared equally between 4e and 4µ. In fact, there are more 4ℓ+ E T events in the LM1 ′ scenario as compared to the other two scenarios (about 7.5% of N tot = 4 × 10 6 for LM1 ′ but only 0.1% and 0.4% for LM2 ′ and LM6 ′ , respectively). The reason is that the signal goes through χ 0 2 which is the dominant mode for the LM1 ′ but not for the LM2 ′ or LM6 ′ . However, the cuts reduce the LM1 ′ events very significantly. Again the reason is the fact that χ 0 2 and χ 0 1 are almost degenerate for LM1 ′ , which leads to very soft leptons. In Fig. 6, E T , E sum T , andŝ 1/2 min (0) distributions of the 4ℓ+ E T signal at 14 TeV with integrated luminosity L = 100 fb −1 are shown for the three scenarios in the secluded U(1) ′ model. As promised, we include aŝ 1/2 min (0) graph with the peak correlated with the ν ℓ L ν * ℓ L production as well as the ν ℓ R ν * ℓ R production (no m eff cut). We can roughly tell the positions of the peak without doing a serious fitting. For the LM1 ′ , the first peak is around 250 GeV and the second one is around 950 GeV. For the LM2 ′ , they are at (470 GeV, 1070 GeV) for the first and the second peaks, respectively. For the LM6 ′ , the peak positions are close to the LM2 ′ case, i.e., they are at (490 GeV, 1110 GeV). Then we can estimate the masses for We suspect that the deviations are mainly responsible for not determining the peak position after fitting the data to a curve. Also, simple averaging is not quite right. One should At this point, it is convenient to give a couple of remarks on the scenarios adopted here. As we mentioned earlier, a U(1) ′ model with one singlet and right handed sneutrinos [8] can explain the excess positron flux observed by various satellite experiments. However, this requires a rather special mass spectrum. Indeed, it turns out that the LSP must one of the right handed scalar neutrinos with a mass around 100 GeV, and the next-to-LSP must also be a right handed scalar neutrino weighing at the TeV scale. All the other SUSY particles have to be heavier. One might ask why we did not consider such a scenario here. There are a couple of reasons. First of all, excess positron flux observation doesn't need to have an explanation coming from particle physics, only. Secondly, the signal for such a scenario would be mainly just missing transverse energy since all the SUSY particles other than the LSP are above the TeV scale so that the cross section for left-handed sneutrino production would be much smaller. Practically, missing energy signal with no visible particle is not useful experimentally. Finally, in this work, we focused on only low-scale SUSY scenarios which would be discovered with the early LHC data at 14 TeV.
After producing and decaying the sneutrinos, we identify three final-state signals: 0ℓ+ E T , 2ℓ+ E T and 4ℓ+ E T and proceed to analyze them at LHC, for 14 TeV center-of-mass energy and with integrated luminosity L = 100 fb −1 . We compare these signals with the 0ℓ+ E T and 2ℓ+ E T signals in MSSM, and discuss the SM background (coming from Drell Yan, ZZ and W W production) for each. While 0ℓ+ E T is the strongest, it has to compete with MSSM and suffers from considerable background suppression, while the 4ℓ+ E T signal has no MSSM equivalent, is practically background free, but has few events.
We analyze the signals and suggest cuts to distinguish it from the background. In particular E sum T ≡ m eff , the scalar sum of the lepton transverse momenta and the missing energy is found to be high for the signal, thus a cut on m eff will likely reduce the background.
Additionally a new parameterŝ 1/2 min is found to be useful for estimating the mass of parent particles in hard scattering. (The peak inŝ 1/2 min gives the mass threshold of left and right handed sneutrinos in the decay process). Using these considerations, we can estimate the production cross section, the products of decay and estimate the sneutrino masses. The MSSM production differs both in the number of events expected, cross section, E sum T ,ŝ 1/2 min , in the 0ℓ+ E T case; and additionally in the p T spectra of leptons (for 2ℓ+ E T case). The 4ℓ+ E T case has no MSSM equivalent and little, if any, background, so the U(1) ′ is clear there; however the number of events, especially after passing detector cuts, is small.
In conclusion, our extensive analysis shows significant enhancement of U(1) ′ signal over the MSSM signal in sneutrino production and decays, and indicates how the two models can be distinguished from each other and the background. This provides a distinct collider signal for the secluded U(1) ′ model at the LHC. In this Appendix, we present the complete Lagrangian of the U(1) ′ model and highlight the differences between this and the MSSM Lagrangian. Although parts of this formulation have appeared elsewhere [7,15,25], we include the complete model information for consistency, and to help future studies. The total Lagrangian incorporates kinetic terms and various interaction terms among the fields. We discuss below the distinct pieces separately.
The kinetic terms of the Lagrangian are given by where j = 1, 2, 3. The interactions of the gauge fields with the rest (fermions, sfermions, gauginos, Higgs and Higgsino fields) are contained in the piece where X runs over the fields charged under U(1) ′ . In (A1), Z ′ µν is the field strength tensor of Z ′ µ , and D µ S j = (∂ µ + ig Y ′ Q ′ S j Z ′ µ )S j for j = 1, 2, 3. The part of the U(1) ′ Lagrangian spanned by the F -terms is given by where φ i is the scalar component of the i-the chiral superfield in the superpotential.
The D-term contributions to the Lagrangian are given by The soft-breaking sector of the U(1) ′ Lagrangian is where M Z ′ is U(1) ′ gaugino mass defined below in (C2), and A s is the extra trilinear soft coupling.
Finally, the part of the Lagrangian describing the fermion-sfermion-ino interactions, as well as the Higgs-Higgsino-Higgsino interactions, is given by All parts of the the U(1) ′ model Lagrangian listed above are described in the current basis. Eventually, the fields must be transformed into the physical basis where each field obtains a definite mass. The neutral gauginos and Higgsinos form the neutralino sector whose physical states are expressed as in (C1), after diagonalizing the mass matrix (C2). for the scenarios LM1 ′ , LM2 ′ and LM6 ′ .