Same-sign trileptons at the LHC: a window to lepton-number violating supersymmetry
aa r X i v : . [ h e p - ph ] N ov November 02, 2011RECAPP-HRI-2011-006
Same-sign trileptons at the LHC: a window tolepton-number violating supersymmetry
Satyanarayan Mukhopadhyay ∗ and Biswarup Mukhopadhyaya † , Regional Centre for Accelerator-based Particle PhysicsHarish-Chandra Research InstituteChhatnag Road, JhusiAllahabad - 211 019, India
Abstract
We present a detailed investigation to establish that lepton-number (L) violat-ing supersymmetry (SUSY) can be effectively probed at the LHC in the practicallybackground-free same-sign trilepton (SS3 ℓ ) and same-sign four-lepton (SS4 ℓ ) channels.With this in view, we extend our earlier analysis of SS3 ℓ and SS4 ℓ signals by consid-ering situations based on minimal supergravity as well as a phenomenological SUSYmodel. We find that the R-parity violating scenario predicts large event rates, for boththe 7 and 14 TeV runs. Furthermore, we show that it is extremely unlikely to everachieve similar rates in R-parity conserving SUSY. In addition, we show how SS3 ℓ andSS4 ℓ , in conjunction with the mixed-sign trilepton and four-lepton channels, can beused to extract dynamical information about the underlying SUSY theory, namely, theMajorana character of the decaying lightest neutralino and the nature of L-violatingcouplings. We define suitable variables and relationships between them which canbe verified experimentally and which are largely independent of the SUSY productioncross-sections and the cascade decay branching fractions. These theoretical predictionsare validated by Monte Carlo simulations including detector and background effects. ∗ [email protected] † [email protected] Introduction
Discovering new physics at the Large Hadron Collider (LHC) is a cherished dream. In thiscontext, it is always useful to isolate signals which are distinctive of specific new scenarioson the one hand, and are less background-prone on the other. Final states containing amultitude of leptons undoubtedly satisfy the second criterion. In order to address the firstcriterion through them, it is often necessary to probe additional features of the leptons. Onesuch feature is the sign(s) of the leptonic charge(s). It is well-established now that same-signdilepton (SSD) carries a rather distinct signature of supersymmetry (SUSY) [1], and othernew physics scenarios [2], once we carefully apply the event selection criteria to suppress thetop-antitop background.A curiosity that immediately arises is whether same-sign leptons of higher multiplicitycan tell us something more. Although this idea of same-sign trileptons (SS3 ℓ ) was floatedoriginally in the context of top quark signals [3], its efficacy in new physics search wasunexplored until very recently. This is somewhat unfortunate, because the standard model(SM) backgrounds for them are extremely small. Some studies in the context of heavyneutrino signals were reported, though with rather limited scope [4]. In a more recentwork, we pointed out that SS3 ℓ as well as its four-lepton extension (SS4 ℓ ) had considerablepotential in unearthing scenarios where Z -type discrete symmetries were broken in a limitedmanner [5]. In particular, we showed that various R-parity violating SUSY scenarios [6] (withR = ( − (3 B + L +2 S ) , B, L and S being baryon number, lepton number and spin, respectively)predicted large signal rates for SS3 ℓ and moderate rates for even SS4 ℓ , with hardly anybackgrounds. The SS3 ℓ signal is substantial over a range of the parameter space in the 7TeV run, while the predictions for both SS3 ℓ and SS4 ℓ are copious for 14 TeV. This suggestionhas since been utilized in a number of subsequent studies [7]. In this paper, we present amore extensive study in the same direction, pointing out a number of new possibilities ofthe SS3 ℓ signal.Let us begin with some explanation of why such a study is relevant. First of all, theLHC searches for new physics, particularly SUSY, at the initial stage, are concentratingon signals with large missing transverse energy. So far the results have been negative. Ifthey continue to be so, some possibilities to consider will be (a) SUSY without R-parity,(b) a highly compressed SUSY spectrum, and (c) SUSY with stable visible particles. Whilethe signatures of each of the above scenarios have been proposed and investigated in theliterature, the SS3 ℓ and SS4 ℓ signals are exclusively indicative of SUSY without R-parity,with lepton number violation. Since such signals can arise with large rates even during theearly run, they are worth studying seriously, from the sheer event counting point of view.L-violating SUSY has considerable appeal, because mechanisms of neutrino mass gen-eration are suggested there. It is also being increasingly realised nowadays that one mayend up with a dark matter candidate such as the axino or the gravitino in spite of R-parityviolation. Some search limits for R-parity violating SUSY exist in the literature, based onmultilepton ( ≥ ℓ ) signals. However, SS3 ℓ is a rather more unequivocal indication of R-parity violation, since it is very difficult to produce three leptons of the same sign unless theseed of lepton number violation is there. Moreover, as will be discussed later in this paper,enhanced rates for such signals are very unlikely to be found in R-parity conserving versionsof SUSY, even in a purely phenomenological scan of its parameter space. The background1s also vanishingly small, in contrast with the other channels advocated so far. With thisin view, we also demonstrate regions in the parameter space where one can have five signalevents with zero (in practice, ≤
1) background events for some luminosity.The enhanced signal rates were predicted in our earlier study within the framework of aminimal supergravity (mSUGRA) scenario. It is, however, important to go beyond the mostsimple of ‘top-down’ models and investigate SUSY signals at the LHC in a phenomenological,‘bottom-up’ approach. In the current work, we have taken such an approach and looked atthe SUSY parameter space in a relatively unbiased manner, although some simplificationhas been inevitable in order to keep the number of free parameters manageable. This allowsus to point out features of the SUSY spectrum, for which same-sign multileptons are mostlikely to be observed.We have opened another new direction in the present study. There are a number of waysin which R-parity can be violated via L, since one can have the so-called λ -type, λ ′ -type andthe L-violating bilinear terms in the superpotential. Besides, the lightest neutralino neednot be the lightest SUSY particle (LSP) when R-parity is violated, the stau-LSP scenariobeing the most common possibility. We contend here that the SS3 ℓ and SS4 ℓ signal rates,in conjunction with their mixed-sign counterparts of the same multiplicity, display certainmutual relations which distinguish among at least some of the candidate scenarios. Andthese relations are largely independent of the detailed information of the SUSY cascades.Consequently, one may use these signals to find out in a generic way the distinction among the λ -type, λ ′ -type or bilinear couplings. Although our discussion is largely based on scenarioswith a neutralino LSP, alternative scenarios, for example, with stau LSP, can be broughtwithin its scope, as has been briefly indicated in the paper.It should be noted that same-sign multileptons in general, and SS3 ℓ in particular, can beseen in some other non-standard scenarios as well. In most cases, however, the rates are con-siderably smaller than what one would expect for R-parity violating cases with new particleswith similar masses. The first example of this is minimal SUSY standard model (MSSM)where R-parity is conserved; our scan of its parameter space, with the usual constraints sat-isfied, reveals rather low event rates for SS3 ℓ . One has predictions of some interest for LittleHiggs theories where T-parity is broken by the Wess-Zumino-Witten anomaly terms [8, 9, 10].However, it has been shown in our previous study that the rates are much smaller than thosefor R-parity violating SUSY with a spectrum of similar masses [5]. In addition, models withheavy charged leptons and Majorana neutrinos [4] and triply charged heavy leptons [11] canalso lead to an SS3 ℓ signature.The paper is organized as follows. Section 2 is devoted to the standard model contri-butions to same-sign and mixed-sign multilepton channels, and we suggest event selectioncriteria that suppress such contributions as potential backgrounds to the new physics signals.In section 3, we review the different cases of R-parity violating SUSY, and show the eventrates for different benchmark points for mSUGRA, for both the 14 and 7 TeV runs. Section4 contains a study where the parameters are varied in a more phenomenological manner,and regions where R-parity violating SUSY shows up in the SS3 ℓ channel are pointed out.We also explain in the same section why the SS3 ℓ and SS4 ℓ signals are not expected tooccur with appreciable rates when R-parity is conserved, even in a generic MSSM model.In section 5, we show how we can extract information on the Majorana character of thelightest neutralino and the dynamics of R-parity violation from SS3 ℓ and SS4 ℓ signals. We2ummarise and conclude in section 6. As we have discussed in Ref. [5], the SM backgrounds to SS3 ℓ are vanishingly small. Thoughthe channels t ¯ t , t ¯ tW , t ¯ tb ¯ b and t ¯ tt ¯ t can give rise to such events, the only appreciable con-tribution after various kinematic cuts comes from t ¯ tW . These cuts are designed mainly tosuppress the leptons coming from semi-leptonic bottom and charm decays [12].We select events with three and only three leptons in the signal (for SS3 ℓ ), all of whichhave to be of the same-sign. In addition, we demand the following basic selection criteria:1. p l T >
30 GeV, p l T >
30 GeV, p l T >
20 GeV, where l , l and l are the three leptonsordered according to their p T ’s2. Missing transverse energy, E T / >
30 GeV (in order to reduce events with jets faking asleptons).3. Lepton rapidity | η | < . R ll ≥ .
2, where (∆ R ) = (∆ η ) + (∆ φ ) quantifies theseparation in the pseudorapidity-azimuthal angle plane.5. Lepton-jet separation ∆ R lj ≥ . E T ≥
20 GeV.6. Relative isolation criterion to restrict the hadronic activity around a lepton has beenused, i.e., we demand P p T (hadron) / p T (lepton) ≤ .
2, where the sum is over allhadrons within a cone of ∆ R ≤ . ℓ weregenerated with the code ALPGEN [13], and showering, decays and hadronisation were doneusing PYTHIA 6.421 [14]. The effect of B − ¯ B mixing on lepton signs has been taken intoaccount within PYTHIA. We have approximated the detector resolution effects by smearingthe energies (transverse momenta) of the leptons and jets with Gaussian functions [15, 16].After imposing the above cuts the total SS3 ℓ contribution from the SM at 14 TeV LHCturns out to be 2 . × − fb, of which 2 . × − fb comes from the t ¯ tW process. At7 TeV LHC, the total SM cross-section for SS3 ℓ comes down to 7 . × − fb. We have usedCTEQ6L1 [17] parton distribution functions for all our signal and background calculations.As mentioned before, for further details on these backgrounds we refer the reader to ourprevious study in Ref. [5].Needless to say, the SM backgrounds to the SS4 ℓ channel will be even smaller than SS3 ℓ ,and can be safely neglected. As we shall see later in section 5, we can construct certainobservables which depend only on the Majorana nature of the LSP and the L-violating cou-pling involved and not upon other parameters determining the cascade decays. In additionto the SS3 ℓ and SS4 ℓ cross-sections, these variables shall also depend upon the total trilepton33 ℓ ) and four-lepton (4 ℓ ) cross-sections in a given scenario, with specific kinematic criteria.Thus we need to evaluate and include the SM backgrounds in the 3 ℓ and 4 ℓ channels, andsubject them to the same set of cuts irrespective of the sign of leptons. Therefore, while aZ-veto (removing events containing same flavour, opposite-sign leptons with invariant massaround the Z-boson mass) is often used to reduce the SM backgrounds in the sign-inclusive3 ℓ and 4 ℓ channels, we cannot use such a veto here. Also, we use kinematic variables thatonly depend upon the lepton p T ’s and the E T / in an event. We find it useful to select eventsin terms of the variables m ℓeff and m eff , defined as follows: m ℓeff = X p leptonsT (1) m eff = X p leptonsT + E T / , (2)where the missing transverse energy is given by E T / = r(cid:16)X p x (cid:17) + (cid:16)X p y (cid:17) . (3)Here the sum goes over all the isolated leptons, the jets, as well as the ‘unclustered’ energydeposits. Cut W ± ( Z /γ ⋆ ) t ¯ t t ¯ t ( Z /γ ⋆ ) t ¯ tW ± TotalBasic cuts 34.50 9.88 2.82 0.73 47.93 m ℓeff >
100 GeV 33.53 8.23 2.80 0.71 45.27 m ℓeff >
200 GeV 5.01 0.00 1.43 0.33 6.77 m eff >
150 GeV 32.06 8.23 2.80 0.72 43.81 m eff >
250 GeV 6.18 1.65 1.81 0.48 10.12Table 1: SM contributions to the trilepton channel at 14 TeV LHC. The m ℓeff or m eff cutis applied one at a time. All the cross-sections are in femtobarns.Cut ( Z /γ ⋆ )( Z /γ ⋆ ) t ¯ t ( Z /γ ⋆ ) TotalBasic cuts 9.33 0.46 9.79 m ℓeff >
100 GeV 9.25 0.46 9.71 m ℓeff >
200 GeV 3.71 0.32 4.03 m eff >
150 GeV 7.87 0.45 8.32 m eff >
250 GeV 1.67 0.36 2.03Table 2: SM contributions to the four-lepton channel at 14 TeV LHC. The m ℓeff or m eff cut is applied one at a time. The t ¯ t contribution is zero after the basic lepton selection andisolation cuts. All the cross-sections are in femtobarns.The SM contributions coming from the sign-inclusive 3 ℓ and the 4 ℓ channels are shownin Tables 1 and 2 respectively. The predictions for the 14 TeV run only are presented here;4lthough the predictions for 7 TeV, too, are very small, we do not expect enough statisticsfor performing our suggested analysis there. We show the cross-sections after different cutson the m ℓeff and m eff variables. In the 3 ℓ channel the major backgrounds are W ± ( Z /γ ⋆ ), t ¯ t , t ¯ t ( Z /γ ⋆ ) and t ¯ tW ± . Here, the W ± ( Z /γ ⋆ ) and t ¯ t ( Z /γ ⋆ ) processes include the effect of Z , γ ∗ and their interference. In the 4 ℓ channel, the dominant SM contributions come from( Z /γ ⋆ )( Z /γ ⋆ ), t ¯ t and t ¯ t ( Z /γ ⋆ ). The processes W ± ( Z /γ ⋆ ) and t ¯ t ( Z /γ ⋆ ) were simulatedusing MadGraph 5 [18] and PYTHIA, t ¯ tW ± using ALPGEN and PYTHIA and t ¯ t and( Z /γ ⋆ )( Z /γ ⋆ ) using PYTHIA alone. For the t ¯ t process we have multiplied the leadingorder cross-section from PYTHIA by a K-factor of 2.2 according to the analysis in Ref. [19].We have taken showering, hadronisation and multiple interaction effects into account in allof our simulations. ℓ in L-violating SUSY: a brief review of the dif-ferent cases In this section, we shall very briefly describe how SS3 ℓ can arise in different scenarios oflepton-number (L) violating supersymmetry. For a detailed discussion on this, we refer thereader to our previous work on this subject [5].The superpotential in R-parity violating SUSY can contain the following ∆ L = 1 terms,over and above those present in the MSSM: W L/ = λ ijk L i L j ¯ E k + λ ′ ijk L i Q j ¯ D k + ǫ i L i H (4) Case 1 : With the λ -type terms, we consider two possibilities, namely, having (a) thelightest neutralino ( ˜ χ ) and (b) the lighter stau ( ˜ τ ) as the lightest SUSY particle (LSP).In (a), SS3 ℓ can arise if ˜ χ decays into a neutrino, a tau ( τ ) and a lepton of either of thefirst two families. When the τ decays hadronically, the two leptons from two ˜ χ ’s producedat the end of SUSY cascades are of identical sign in 50% cases. An additional lepton of thesame sign, produced in the decays of a chargino ( ˜ χ ± ) in the cascade, leads to SS3 ℓ . If thereis just one λ -type coupling (we have used λ for illustration), there is no further branchingfraction suppression in LSP decay, and one only pays the price of ˜ χ ± -decay into a leptonof the same sign. In (b), two same-sign ˜ τ ’s can be produced from two ˜ χ ’s, due to itsMajorana character. Each of these ˜ τ ’s goes into a lepton and a neutrino; these two leptons,together with one of identical sign from the cascade, lead to SS3 ℓ signals. Case 2 : With λ ′ -type interactions, a ˜ χ -LSP decays into two quarks and one chargedlepton or neutrino. If the LSP is not much heavier than the top quark, and if the effect ofthe difference between up and down couplings of the neutralino can be neglected, we obtainSSD’s from a pair of ˜ χ ’s roughly in 12.5% of the cases. If another lepton of the same signarises from a ˜ χ ± , SS3 ℓ is an immediate consequence. Therefore, the overall rate of SS3 ℓ canbe substantial in this case as well. Here, (and also partially in case 1(b)), the large boostof the ˜ χ can lead to collimated jets and leptons, making the latter susceptible to isolationcuts. 5lthough most of the analysis we have presented for such couplings is based on a ˜ χ -LSPscenario, we shall see later that one with ˜ τ -LSP, too, has potential for SS3 ℓ events. Case 3 : With bilinear R-parity breaking terms ( ∼ ǫ i ), the most spectacular consequenceis the mixing between neutralinos and neutrinos as well as between charginos and chargedleptons. Consequently, over a substantial region of the parameter space, a ˜ χ LSP in thisscenario decays into
W µ or W τ in 80% cases altogether, so long as the R-parity breakingparameters are in conformity with maximal mixing in the ν µ − ν τ sector [20]. From the decayof the two ˜ χ ’s, one can obtain SSD’s either from these µ ’s, or from the leptonic decay of the W ’s or the τ ’s. An additional lepton from the SUSY cascade results in SS3 ℓ again. Addingup all the above possibilities, the rates can become substantial.Again, in addition to a ˜ χ -LSP, a ˜ τ -LSP also can lead to the signals under consideration.We shall briefly mention such possibilities later in our discussion.
14 TeV
In [5], the SS3 ℓ cross-sections for a few representative points from the mSUGRA parameterspace were presented, for both the 7 TeV and 14 TeV runs. Those benchmark points, cor-responding to the various cases discussed in the previous sub-section, are shown in Table 3.We show the values of M and M / ( M and M / being respectively the universal scalarand gaugino mass at high scale), the ratio of the vacuum expectation values of the two Higgsdoublets tan β , as well as the values of other relevant SUSY parameters at the electroweakscale (fixed here at √ m ˜ t m ˜ t , where ˜ t and ˜ t are the two mass eigenstates of the top squarks).We use fixed values for the other mSUGRA parameters, namely, the universal soft-breakingtrilinear scalar interaction A = 0 and the Higgsino mass parameter µ >
0. Since the valuesof the L-violating couplings are very small, they do not affect the renormalisation grouprunning of mass parameters from high to low scale [21]. We have therefore generated thespectrum using SuSpect 2.41 [22] and interfaced it with SDECAY [23] by using the pro-gramme SUSY-HIT [24] (for calculating the decay branching fractions of the sparticles) andfinally have interfaced the spectrum and the decay branching fractions to PYTHIA, whichis used to generate all possible SUSY production processes. Also, we have neglected the roleof R-violating interactions in all stages of cascades excepting when the LSP is decaying. Thevalue of each trilinear coupling ( λ, λ ′ ) used for illustration is 0.001. For case 3, The values ofthe ǫ -parameters are chosen consistently with the neutrino data; essentially, they are tunedto sneutrino vacuum expectation values of the order of 100 keV, in a basis where the bilinearterms are rotated away from the superpotential. The values of ǫ i are also of this order in theabsence of any additional symmetry. The exact values of ǫ i that correspond to points 3(1)and 3(2) in Table 3 depend also on other parameters of the model, such as the L-violatingsoft terms in the scalar potential [25]. However, the range of values of these parameters isof little consequence to the neutralino decay branching ratios. Therefore, with appropriatevalues of these soft terms, ǫ ≈
100 keV, ǫ = ǫ = 0 is consistent with all our results. Inorder to demonstrate the reach of the LHC in the SS3 ℓ channel, we show in Figure 1, theboundary contours of regions in the M − M / plane, where at least 5 signal events (withzero background event expected) can be obtained with a given integrated luminosity. Thisscan was performed for a sample case (case 1) with fixed values for the other mSUGRAparameters (tan β = 10 , A = 0 , µ > M - M / plane. In addition, in Figure 1 we have used a 5 signal events discovery criterion while inRef. [5] we used a 10 signal events discovery criterion. Since we do not expect any backgroundevent in the SS3 ℓ channel even with 30 fb − integrated luminosity, 5 signal events should besufficient for a discovery. Note that there is a sharp fall observed in each curve of Figure 1.As we increase M for a given M / , the first two family sleptons eventually become heavierthan the chargino, thereby reducing the branching fraction of ˜ χ ± → l ± ν ˜ χ . This leads toa drop in the SS3 ℓ cross-section, giving rise to the faster fall in the curves.We refer the reader to [5] for the total signal cross-sections for the various other casesof R-parity violation. It is clear that, with at least 30 fb − of integrated luminosity, theycan enable one to perform the analysis suggested in later sections for extracting the exactdynamics of R-parity violation.Case M M / tan β m ˜ g m ˜ χ ± m ˜ χ m ˜ τ m ˜ e L RPV(GeV) (GeV) (GeV) (GeV) (GeV) (GeV) (GeV) Coupling1a(1) 75 275 15 661 200 108 ∗
115 204 λ ∗
139 265 λ ∗
191 309 λ ∗
246 418 λ ∗ λ ∗ λ ∗ λ ∗ λ ∗
115 204 λ ′ ∗
139 265 λ ′ ∗
191 309 λ ′ ∗
246 418 λ ′ ∗
191 309 ǫ i ∗
246 418 ǫ i Table 3: mSUGRA benchmark points defined in Ref. [5] for the various cases discussed inthe text (e.g., 1a(1) corresponds to the first example in case 1a). The LSP in a given pointis indicated by a * against its mass. The low-scale MSSM parameters were generated in anmSUGRA framework (with A = 0 and µ > λ and λ ′ couplings are set at 0.001,and the ǫ i are within the limits set by neutrino data. The SS3 ℓ cross-sections after variouscuts in these benchmark points can be found in Ref. [5]. results In our previous study [5], for the 7 TeV run, we presented the points which can be discoveredwith an integrated luminosity of 2 fb − . Since the LHC experiments are collecting data ata fast pace and there is every chance of continuing the 7 TeV run upto at least 5 fb − , weupdate our 7 TeV results in cMSSM to include more points which can now be accessed. In7 / ( G e V ) M (GeV)tan β =10A =0, µ >0 Stau LSPLEP Excluded1 fb -1 -1
30 fb -1 Figure 1: (Color online) 5-events LHC reach with SS3 ℓ in the M − M / plane for R-parityviolating mSUGRA, at √ s = 14 TeV, with λ = 0 . ℓ channel. These benchmarkpoints include cases with ˜ χ LSP and λ -type couplings (points 1a(3) and 1a(4)) and also˜ τ LSP with λ -type couplings (point 1b(3)). For ˜ χ LSP with λ ′ -type couplings, the SUSYsparticle mass-reach is somewhat smaller, and we can access masses slightly higher than650 GeV during the 7 TeV run (point 2(1) in Table 4), if we insist on seeing 10 signal eventswithout backgrounds with 5 fb − of integrated luminosity. For 3 signal events with ≤ We now discuss some other possible cases in L-violating SUSY where one can also get SS3 ℓ events. In case of a ˜ τ LSP with λ ′ ijk -type couplings, the ˜ τ will directly decay to two quarksif the index i takes the value 3. For the other two cases where i takes the value 1 or 2,˜ τ cannot decay via two-body L-violating modes. In this case, it will go through a 4-bodydecay via an intermediate off-shell chargino or neutralino. In mSUGRA type of models, thelighter stau is mostly composed of the right-chiral field, in which case it will couple primarilyto the bino component of the neutralino. Also, the lighter chargino there is mostly heavierthan the lightest neutralino, and therefore the propagator suppression is more for off-shellchargino. Thus, the mode through off-shell neutralino will dominate. Thus, we shall findthe dominant decay pattern for a ˜ τ to be ˜ τ → τ ˜ χ ∗ ) → τ l ± qq ′ . SS3 ℓ events arise then in8ase σ SS l (fb)1a(1) 19.821a(2) 29.451a(3) 4.291a(4) 2.011b(1) 30.741b(2) 6.461b(3) 3.352(1) 2.072(2) 4.03Table 4: SS3 ℓ cross-sections after all selection cuts ( σ SS l ) at √ s = 7 TeV for the differentcases defined in Table 3.a very similar fashion as in the case of a ˜ χ LSP with λ ′ -type couplings.Since the intermediate neutralino in ˜ τ ± -decay is a Majorana particle, we shall not haveequal rates for the τ ± l + qq ′ and the τ ± l − ¯ q ¯ q ′ final states. Also, the production of the ˜ τ inin the decay of each neutralino has also an accompanying tau, which is another source ofleptons. Consequently, with two taus decaying together with two staus, there is a favourablecombinatoric factor for SS3 ℓ , which partially offsets the suppression due to branching ratios.The exact numerical evaluation of the relevant branching fractions and the resulting eventrates is a detailed exercise by itself. In any case, we expect substantial cross-sections inthe SS3 ℓ channel, with the usual reduction of events in the presence of λ ′ -type couplingscompared to the presence of λ -type couplings.In presence of bi-linear L-violating couplings, a ˜ τ which is the LSP can mix with acharged Higgs, thereby leading to the decay mode ˜ τ → τ ν τ , since the charged Higgs willcouple more to the tau lepton than to electrons or muons. Thus, starting from a pair ofneutralinos which can be produced in cascades, one can obtain two same-sign tau leptons,whose further leptonic decays can give rise to two leptons of the same sign. The third leptonof the same sign can come in the usual way from ˜ χ ± decay giving rise to SS3 ℓ . Evidently, therates in this case are expected to be rather small for various branching fraction suppressions.A detailed study of SS3 ℓ in the ˜ τ -LSP scenario for both of the above cases will be reportedin a forthcoming publication [26]. ℓ in phenomenological MSSM (pMSSM) Next we discuss the case of phenomenological MSSM, which includes many more possibilitiesthan mSUGRA, as far as the mass spectra are concerned. In particular, the three gauginomass parameters at the weak scale then need not be in the approximate ratio M : M : M = 1 : 2 : 6. Thus the lighter chargino may not be about twice as massive as the lightestneutralino, a fact that can affect electroweak phenomenology considerably. Since one of the9eptons in the SS3 ℓ signal comes from the cascade decay of the chargino (via on or off-shell W ’s and sleptons) ˜ χ ± → ˜ χ l ± ν , we need to look into other hierarchies between M and M .If M ≃ M , ˜ χ ± , ˜ χ and ˜ χ are all very close in mass, and therefore the lepton comingfrom chargino decay is rather soft in the ˜ χ ± rest frame. But, if the ˜ χ ± is resulting fromthe decay of the gluino or squarks, which could be much heavier, it can have a large boost,giving rise to high p T leptons which will pass the required cuts.Another interesting situation arises if M > M . Here, the ˜ χ and the ˜ χ ± are mostlycomposed of wino components. This is what happens, for example, in the case of anomalymediated SUSY breaking. The degeneracy in their masses is even more severe in this case,and some fine-tuning is necessary to make their mass difference of the order of pion mass.Here, one can have an additional channel in the cascade, from which a third lepton can arise.The second lightest neutralino can decay to a charged lepton, a neutrino and the ˜ χ ± . Thelepton produced in this way can have sufficient p T to be detectable. The ˜ χ ± , on the otherhand, goes to the ˜ χ and an extremely soft pion (or lepton + neutrino), and the ˜ χ paircan be the source of same-sign dileptons, which, when of the same-sign as that of the initiallepton, leads to SS3 ℓ . We also look into the case of M < M in pMSSM but with a widermass separation than expected in mSUGRA, namely, M = 3 M . Here the rates of SS3 ℓ aresomewhat enhanced. Finally, we look into a kind of non-universality between the low-energyselectron (or smuon) and stau soft masses. This can lead to a scenario where all the sleptonsexcept stau are lighter than ˜ χ ± and the BF of ˜ χ ± to leptons is around 95%. Needless tosay, this enhances the SS3 ℓ rates.In order to be conservative, we fix the squark soft masses and M at 1 TeV. We have al-ready shown in Ref. [5] that the strongly interacting sparticle mass scale of around 600 GeV iseasily accessible at the LHC in the SS3 ℓ channel during the 7 TeV run. The benchmark pointschosen here are just to emphasize that the SS3 ℓ signal can probe a generic MSSM modelupto considerable higher masses of strongly interacting superparticles even during the earlyrun. In addition, the situation of relatively closely spaced low-lying charginos/neutralinos,including those with an inverted hierarchy compared to mSUGRA, also turn up with sub-stantial event rates. We present the most important parameters in the pMSSM benchmarkpoints in Table 5 and the SS3 ℓ cross-sections at these points in Table 6. As mentioned above,we have fixed the squark soft masses and M at 1 TeV while A t , A b , A τ and the µ parameterhave been fixed at − − −
250 and 975 GeV respectively. tan β has been fixed at 10,and the R-parity violating coupling used for illustration is λ = 10 − . The cross-sectionshave been calculated for both the 7 TeV and the 14 TeV runs at the LHC, and we alsogive the required luminosities for a five-event discovery, with no events expected from thebackgrounds. The overall usefulness of SS3 ℓ in probing low missing-energy SUSY scenariosis thus brought out quite emphatically by the results presented by us. To this is added therather striking prospect of extracting dynamic information (like the presence of Majoranagauginos and the exact nature of L-violating couplings) from the SS3 ℓ and SS4 ℓ channels,as will be explained in detail in section 5, again on the basis of a model-independent scan ofthe SUSY parameter space . 10P M M M ˜ χ M ˜ χ ± M ˜ e L M ˜ τ (GeV) (GeV) (GeV) (GeV) (GeV) (GeV)1 150 150 146.54 154.80 254.13 180.912 160 150 154.08 154.80 254.13 217.693 100 300 97.69 395.30 254.10 180.684 125 250 121.65 254.35 156.76 217.52Table 5: Values of M , M and some other relevant parameters for the SS3 ℓ channel in thepMSSM benchmark points. The squark and gluino masses are fixed at ∼ σ L σ
14 TeV L
14 TeV ( fb) ( fb − ) ( fb) ( fb − )1 0.91 5.49 4.60 1.092 0.41 12.20 1.62 3.093 2.81 1.78 20.67 0.244 8.78 0.57 42.93 0.12Table 6: SS3 ℓ cross-sections in the different pMSSM benchmark points at 7 TeV and 14 TeVLHC. We also show the luminosities required to obtain 5 signal events at the two centre ofmass energies. If lepton number is conserved in the MSSM, then it is extremely difficult to find a sce-nario where one can obtain a same-sign trilepton signal (We specifically design the cuts tosuppress leptons coming from b-decays, since otherwise they can boost the standard modelbackgrounds as well.) In fact, we do not find any such scenario in the simple mSUGRA pic-ture. If one considers a purely phenomenological MSSM , one can of course generate a widevariety of mass spectra. We find one particular such spectrum where one can obtain SS3 ℓ ,but at a negligibly low rate because of branching fraction suppressions which are difficultto avoid. Thus, as far as we could analyze the MSSM processes with conserved R-parity, itis not possible to generate SS3 ℓ with significant cross-section. Therefore, it seems, within asupersymmetric framework, a reasonably large cross-section of SS3 ℓ is a clear indication ofL-violation.To convince the reader of this, let us outline a scenario in MSSM, where, in principle,it is possible to obtain an SS3 ℓ signal, albeit with a small rate. Consider a situation wherethe sbottom is lighter than the stop. In this case, let us look at stop pair production( ˜ t ˜ t ∗ ), followed by the decay ˜ t → ˜ b W + (and a charge-conjugate decay process for ˜ t ∗ ).The produced ˜ b can then decay to t ˜ χ − , although with a very low branching fraction.The top quark, of course, then decays to bW + . Thus starting from the initial ˜ t ˜ t ∗ wecan obtain a final state ( W + ˜ χ − bW + )( W − ˜ χ ¯ bW − ). We can re-write this final state as( b ¯ b )( W + W + ˜ χ )( W − W − ˜ χ − ). Now, it can be clearly seen that if a set of three same-charge W ± ’s and ˜ χ ± ’s decay leptonically and the other set decays hadronically, we have a same-signtrilepton signal. In order to demonstrate the branching fraction suppression of this SS3 ℓ final11tate, let us consider a typical pMSSM spectrum with M ˜ t = 522 GeV and M ˜ b = 482 GeV.We keep the first two generation squark masses at ∼ ℓ channel.The gluino mass is ∼ ℓ cross-section after all the cutsturns out to be 2 . × − fb at the 14 TeV LHC, which is evidently very small. We have now reasons to feel reasonably confident that substantial SS3 ℓ (or SS4 ℓ ) rates areunlikely to be seen in R-parity conserving SUSY, and that R-parity (read lepton number)violation will be strongly suggested by them. More pointedly, L-violation by odd units andthe existence of more than one Majorana fermions in the scenario work together towards theenhancement of such signals.The total rate of SS3 ℓ in a particular L-violating scenario depends not only on the L-violating coupling and the LSP involved, it is also dictated by SUSY production cross-sectionand other parameters determining the cascade decay patterns. We shall now show that itis possible to extract the information on the different L-violating couplings, through which aMajorana neutralino LSP decays, once we make use of the SS ℓ and SS ℓ final states. With this in view, we construct certain variables which involve not only the SS3 ℓ andSS4 ℓ rates in a given scenario, but also on the total rates in the 3 ℓ and 4 ℓ channels. In ageneric MSSM scenario with a particular L-violating coupling, it is possible to make definitepredictions involving these variables based on simple probability arguments and neutralinobranching fraction information in different combinations of charged lepton final states. Wethen verify these predictions using Monte Carlo simulations, where we also show the effect ofselection and isolation cuts, as well as the effect of adding the SM backgrounds in the 3 ℓ and4 ℓ channels. Although we have demonstrated the results using some mSUGRA benchmarkpoints for simplicity, the conclusions are generic to phenomenological scenarios. λ -type couplings A neutralino LSP in presence of λ ijk -type couplings contributes to same-sign trileptons onlyif one of the indices in { ijk } is 3. As λ ijk is anti-symmetric in i and j , there are nineindependent couplings of λ -type. Out of these nine couplings, seven have 3 as one index,and only two do not have the index 3 anywhere. Now consider the generic decay mode of the˜ χ where ˜ χ → τ ± l ∓ ν ( l = e, µ ) . The produced τ ± will decay leptonically in ∼
35% of thetime, and hadronically in rest of the cases. Now consider the ratio of the number of same-sign trilepton (SS3 ℓ ) events to the total number of trilepton events (which includes bothsame-sign trileptons (SS3 ℓ ) and mixed-sign trileptons (MS3 ℓ )). This ratio can be calculatedindependent of the other SUSY parameters as follows. In the above case, in a trileptonevent, we know that at most one of the leptons is coming from the cascade as the pair ofneutralinos produced at the end of the decay chains will always give rise to at least 2 leptons.As mentioned before, the produced τ ± ’s decay to a semi-leptonic final state in ∼
35% of thecases, and to hadronic final states in 65% cases. Therefore, as the two ˜ χ decays will produce12wo leptons when both the τ ± ’s decay hadronically, the fraction of cases a pair of ˜ χ ’s goesto 2 leptons and jets and neutrinos is (0 . = 0 . × . × .
35) = 0 .
455 of all cases (i.e., when one τ ± decaysleptonically and the other one decays hadronically). In rest of the cases they decay to afour-lepton final state (when both the τ ± ’s decay leptonically) which we are not consideringin this case. Thus out of all possible trilepton events, in ≃
42% cases one lepton comes fromthe cascade and in ∼
46% cases no lepton comes from the cascade. We can summarise thesituation in Table 7.No. of leptons No. of leptons Fraction SS3 ℓ Fraction MS3 ℓ Fraction(Cascade) (LSP Decay) of cases1 2 0.42 0.25 0.750 3 0.46 0 1Table 7: Fraction of trilepton events with different origins for the leptons, and the fractionsof SS3 ℓ and MS3 ℓ events among them (see explanation in text).In Table 7, the first two columns represent the number of leptons coming from the twodifferent sources that we distinguish, namely, from the cascade and from the decay of thetwo ˜ χ LSP’s. As explained above, there are only two such possibilities in a trileptonevent. Those two possibilities are described in the two rows of the table. The third columndescribes the fraction of cases in which each of these possibilities occur. We have explainedthe numbers in this column above. Finally, the last two columns represent the fraction ofSS3 ℓ and MS3 ℓ events in each of the possible ways of obtaining a trilepton event, as explainedbelow.From Table 7, we see that in the first case where two of the leptons come from theLSP-pair decay, and one from the cascade, the probability of getting an l + l + pair from theLSP’s is 0 .
25, and same for obtaining an l − l − pair (this stems from the fact that the ˜ χ isMajorana). Now, in a trilepton event, let P be the probability of the single lepton comingfrom the cascades being of positive charge, and P for it to be of negative charge. Then,the probability of obtaining an SS3 ℓ event is 0 . × P + 0 . × P = 0 .
25 as P + P = 1.Therefore, the probability of obtaining an MS3 ℓ event is 1 − .
25 = 0 .
75. In the second case,where all three of the leptons are coming from the LSP decay, all the trilepton events are ofMS3 ℓ -type. Note that, we are demanding only three leptons in the final state, therefore anyevent with additional leptons (four or more) are vetoed out. Let us now define the ratio x = σ SS ℓ σ SS ℓ + σ MS ℓ (5)From Table 7, we see that we can easily calculate this ratio as follows x = σ total × . × . σ total × [(0 . × .
25) + (0 . × .
75 + 0 . ≃ . , (6)where σ total is the total SUSY production cross-section which cancels out among thenumerator and the denominator. As we have explained above, the trilepton events are afraction of all possible SUSY events and SS3 ℓ and MS3 ℓ events are subsets of all 3 ℓ events.13his value of the ratio x ≃ .
12 is therefore a prediction stemming from the L-violatingdecay mode of the neutralino under study and also the Majorana character of the neutralino.Whatever be the values of the other SUSY parameters, as long as we have a ˜ χ LSP decayingvia a λ type of coupling, this ratio is fixed. In particular, this ratio is independent of theprobabilities of obtaining a charged lepton of either sign from the cascade. One should note,however, that if the L-violating couplings are so large as to compete with the gauge couplingsfor the decay of sparticles other than the LSP, this result can change. But, flavour physicsand neutrino physics experiments suggest that these Yukawa couplings would take rathersmall values if SUSY models are to explain the above phenomena.Point σ SS ℓ + σ MS ℓ σ SS ℓ x (fb) (fb)1a(1) 928.32 75.11 0.081a(2) 1084.26 110.06 0.101a(3) 228.24 27.51 0.121a(4) 149.47 14.20 0.10Table 8: The 3 ℓ (signal+SM background) and SS3 ℓ (signal) cross-sections at 14 TeV LHCafter the m eff >
250 GeV cut and the ratio x calculated including the SM backgroundcontribution. The total SM background in the 3 ℓ channel after the above cut is 10 .
12 fb.Note that the predicted value of x in this case is ∼ .
12, which shifts somewhat after includingthe effects of lepton isolation, detection efficiencies, other cuts and the SM backgrounds. Theagreement with the predicted value is within 20% in most cases.In realistic situations, where we have to consider the experimental triggers, detectorefficiencies etc., the ratio x can fluctuate around the predicted value of ∼ .
12. Unfoldingthese effects in an event by event basis is not an easy exercise, and we abstain from trying todo so. In Table 8 we present the ratio x obtained by Monte Carlo simulations with propercuts in different benchmark points with widely varying SUSY parameters. We see thatto within 20% one always gets a ratio as predicted, thereby validating the above analysis.Thus we find that this ratio of SS3 ℓ to the total trilepton production cross-section givesus dynamic information about the underlying SUSY theory, in particular the L-violatingcoupling involved and the Majorana nature of the decaying LSP.What happens if we change the L-violating coupling? Note that, in the presence of ageneric λ ijk -type coupling a ˜ χ decays to two charged leptons and a neutrino. Only if oneof these leptons is a tau, which in turn can decay hadronically, one can obtain an SS3 ℓ signal. Therefore, one of the indices in { ijk } has to be 3. Moreover, we find the ratio x ≃ .
12 only for the none-zero coupling λ . The reason for this is that if i = 3 or j = 3(which are equivalent due to the antisymmetry of λ ijk in the indices i, j ), then the ˜ χ canalso decay to a ν τ instead of a τ ± , thereby changing the ratio. For example, for the set ofcouplings { , , , } we find this ratio to be approximately x ∼ .
14, while for theset { , } , x = 0, since no SS3 ℓ events are expected in these cases .The above analysis thus shows that the dynamic information of a Majorana ˜ χ decayingvia L i L j E ck -type couplings can be captured in a quantity easily measurable at the LHCexperiments. Since the cross-sections in the 3 ℓ and SS3 ℓ channels are rather large (see14able 8) at the 14 TeV LHC, one can acquire a reasonably good statistics within 1 − − of integrated luminosity. Therefore, these cross-sections can be measured and the ratio x calculated fairly accurately in the early periods of the 14 TeV run. λ ′ -type couplings The case for ˜ χ LSP with λ ′ -type couplings is somewhat more complicated than that for the λ -type couplings. No unique prediction (which is independent of the other SUSY parameters)can be made there about the ratio x . One can, however, construct a similar ratio with four-lepton events. Subsequently, we obtain a linear relation between these two ratios, which isthen independent of the parameters determining the cascade decays.In the presence of a λ ′ -type coupling, a ˜ χ decays either to two quarks and a neutrino,or to two quarks and a charged lepton. SS3 ℓ signals can arise in the second case. But nowwe have more ways in which one can obtain trilepton events. Let us define the fraction ofcases in which a ˜ χ decays via ˜ χ → l ± q ′ q to be α . Now let us note the various possibleways of obtaining trilepton events in Table 9. The structure and meaning of the differententries in this table are same as explained in detail for Table 7.No. of leptons No. of leptons Fraction SS3 ℓ Fraction MS3 ℓ Fraction(Cascade) (LSP Decay) of cases3 0 (1 − α ) α (1 − α ) − P P α ℓ and MS3 ℓ events among them (see explanation in text).Since α denotes the probability that a ˜ χ will decay leptonically, the fraction of cases apair of ˜ χ ’s give rise to two leptons is α . Similarly, when both the ˜ χ ’s decay to neutrinosand quarks, we do not obtain any leptons from LSP decays. This happens in (1 − α ) fractionof trilepton events. And, finally, in the remaining 2 α (1 − α ) fraction of cases, we obtain onelepton from the decay of the two LSP’s. In the first case, when all three of the leptons comefrom the cascade, we do not obtain any SS3 ℓ event, making the MS3 ℓ fraction unity. Inorder to understand the second case, note that in Table 9, when two leptons come from thecascade, we define P to be the probability of them being oppositely charged ( l ± l ∓ ). Thus,(1 − P ) is the probability of them being of same charge ( l ± l ± ). In such a case, in a trileptonevent, evidently the third lepton comes from LSP decay. In half of such events the leptoncoming from LSP decay will also have the same sign, thereby giving rise to an SS3 ℓ event.Thus the probability of obtaining an SS3 ℓ event is − P . Consequently, the probability forobtaining a MS3 ℓ event is (cid:0) − − P (cid:1) = P . In the third case, where two of the leptonscome from LSP decay, because of the Majorana nature of the decaying ˜ χ LSP, we get thecorresponding fractions in the same way as in the previous sub-section, where we considered˜ χ decay via λ -type terms.In this case, therefore, we find the following formula for the ratio x defined in eqn. 5.15 = α − α − P (cid:0) α − α (cid:1) (7)Now, the ratio α is very weakly dependent on the sparticle mass spectra, especially thedifference between the up and down-type squark masses entering the off-shell propagatorsin the 3-body ˜ χ decays. In most scenarios this difference is rather small, especially for thefirst two families. On the whole, α is close to 0.5 in most cases.As mentioned before, there is a residual dependence of x on P , thereby making this ratiovary as the other SUSY parameters vary (also the parton distribution functions affect P ).In order to eliminate P and obtain a prediction that follows just from the Majorana natureof the ˜ χ and the L-violating coupling involved, we introduce another ratio y defined as y = σ SS ℓ σ SS ℓ + σ MS ℓ (8)where σ SS ℓ and σ MS ℓ are the same-sign four-lepton and mixed-sign four-lepton cross-sections respectively.To calculate y , we make a table similar to the one made for calculating x .No. of leptons No. of leptons Fraction SS4 ℓ Fraction MS4 ℓ Fraction(Cascade) (LSP Decay) of cases4 0 (1 − α ) α (1 − α ) 0 12 2 α − P P Table 10: Fraction of four-lepton events with different origins for the leptons, and the frac-tions of SS4 ℓ and MS4 ℓ events among them (see explanation in text).Since, the fraction of cases for the different possibilities are only dependent on the num-ber of leptons coming from LSP decays, the entries in the third column of Table 10 can beunderstood in the same way as in the trilepton case, which we explained before while dis-cussing Table 9. In the first two cases, where four and three leptons come from the cascaderespectively, the MS4 ℓ fraction is 1, since we cannot get more than two same-sign leptonsfrom the cascade. In the third case, we define P as before. Since (1 − P ) is the probabilityto have a same-sign lepton pair from the cascade, in order to obtain a same-sign four leptonevent, we need the other two leptons coming from LSP decay to be of the same-sign as that ofthe cascade leptons. Now, since the ˜ χ is a Majorana particle, when it decays leptonically,the probability to obtain a same charge lepton as in the cascade is 1 /
2, and similarly for thesecond ˜ χ , thus giving us a probability of − P to obtain an SS4 ℓ event. The rest of theevents are of MS4 ℓ variety, which come with a fraction of (cid:0) − − P (cid:1) = P . This completesthe explanation of Table 10.From Table 10 and eqn. 8 we find that y = α − α P . (9)The total SUSY production cross-section σ total cancels out in the ratio as in the case for x . Combining these two equations for x and y , we can eliminate P to obtain the followingequation relating x and y : 16 = α y (cid:18) α − (cid:19) (10)This equation is therefore a prediction based just on the Majorana nature of the decaying˜ χ LSP and the presence of λ ′ -type couplings. In order to verify the above claim and also tosee the deviations due to lepton selection and isolation effects we note the values of x and y obtained in different benchmark points and compare them with the above prediction taking α ∼ . y SMC x SMC x Seqn. y S + BMC x S + BMC x S + Beqn. x and y after the m eff >
250 GeV cut, before and after adding theSM background cross-sections. Here, y SMC and x SMC refer to the ratios x and y calculatedonly with the signal whereas y S + BMC and x S + BMC denote the ratios calculated adding up boththe signal and the background cross-sections in the appropriate channels. x Seqn. and x S + Beqn. denote the values of x calculated using eqn. 10 taking α = 0 .
5, with y SMC and y S + BMC as therespective inputs.The entries of Table 11 have been explained in the caption of the table. The ratios x and y have been evaluated from cross-sections calculated for the 14 TeV LHC. As the total 3 ℓ and 4 ℓ cross-sections in the case of a ˜ χ LSP with λ ′ -type coupling are comparable to theSM backgrounds, the ratios x and y change after adding the backgrounds. In order to showthat we present the ratios both before and after adding the SM background cross-sections.In order to validate the prediction derived in eqn. 10, we take the Monte Carlo prediction for y as an input, and then calculate the value of x from eqn. 10, and denote it by x eqn. . This x eqn. is then compared with x MC , the value obtained from Monte Carlo. The rather excellentagreement between the entries in the third and fourth columns in Table 11 demonstrates theviability of our claim in eqn. 10. As noted before, here we have used the approximate valueof 0 . α . We then again repeat the same calculation after adding the SM backgroundsin the 3 ℓ and 4 ℓ channels. Since the backgrounds are comparable to the signal in this case,the ratios change somewhat after the background addition, and the agreement between theprediction of eqn. 10 and the MC is not as good as with only the signal, which is expected.Also note that, in the benchmark points 2(2) and 2(4) we have the ˜ χ ± lighter than the˜ e L . This reduces the ˜ χ ± branching fraction to leptons, thereby leading to a reduction oftrilepton and four-lepton events of same-sign and mixed-sign varieties. The lower branchingfraction is compensated by the much larger total SUSY production cross-section in point2(2). Point 2(4) thus suffers from lower number of multi-lepton events, and the accurateevaluation of the ratios x and y here would require much larger statistics. Also if SS3 ℓ signals are indeed seen in the mass range of, say point 2(4), then the further reduction ofbackgrounds may be a pressing need in order to extract dynamics out of this signal.17 .3 Neutralino LSP with bi-linear couplings In the presence of bi-linear L-violating couplings, the decay branching fractions of ˜ χ indifferent channels are dependent on various other soft SUSY-breaking parameters, too. Thusit is not possible to predict a specific equation which will be valid generically for all possiblechoices of the relevant parameters. Instead, we focus in a region where the ˜ χ decays eitherin the W ± µ ∓ /τ ∓ or in the Zν channel. This is largely the case when the slepton/sneutrinostates have not-too-large mixing with the Higgs states [20]. In this case, we find an equationrelating the x and y -variables which is very similar to the equation of straight line foundfor the case of ˜ χ LSP with λ ′ -type couplings (with a different slope for the straight line!).Since the detailed evaluation of the relevant branching fractions in different combinations ofcharged-lepton final states is straightforward but cumbersome, we just note down the finalresults in the following tables.No. of leptons No. of leptons Fraction SS3 ℓ Fraction MS3 ℓ Fraction(Cascade) (LSP Decay) of cases3 0 0.146 0 12 1 0.366 − P P ℓ and MS3 ℓ events among them, in the case of a ˜ χ LSP with bi-linear L-violatingcouplings (see explanation in text).No. of leptons No. of leptons Fraction SS4 ℓ Fraction MS4 ℓ Fraction(Cascade) (LSP Decay) of cases4 0 0.146 0 13 1 0.366 0 12 2 0.335 0 . − . P .
83 + 0 . P ℓ and MS4 ℓ events among them, in the case of a ˜ χ LSP with bi-linear L-violatingcouplings (see explanation in text).From Table 12 we find that x = 0 . − . P (11)and similarly, from Table 13 we find an expression for yy = 0 . − P ) (12)We can eliminate P from equations 11 and 12, to obtain an equation of straight linerelating x and y = 3 . y + 0 .
063 (13)As mentioned before, this equation is very similar to the equation obtained for the caseof ˜ χ LSP with λ ′ -type couplings. The slope in the x − y plane, however, is slightly differentin this case. Point y SMC x SMC x Seqn. y S + BMC x S + BMC x S + Beqn. y calculated from MC as input. We find thatthe predictions agree with the MC calculations to within ∼
20% or better. As for the λ ′ case, the prediction and MC calculations deviate a little bit more after adding the SMbackgrounds, since the total signal cross-sections in the 3 ℓ and 4 ℓ channels are comparableto the backgrounds. Also, in this case as the total rates for multi-lepton events are rathersmall for the chosen benchmark points (with the squark and gluino masses ∼ We have performed a detailed study of SS3 ℓ and SS4 ℓ signals in the context of the LHC,to arrive at a number of important conclusions. First, such signals are enhanced, to sucha degree as to be appreciable even during the 7 TeV run (and also the 14 TeV run withlow integrated luminosity), if there is (a) L-violation by odd units, and (b) the presence ofself-conjugate fields. The outstanding theoretical scenario meeting the above requirementsis SUSY with R-parity violated via lepton number. Therefore, we strongly advocate theinvestigation of such signals, especially as they are complementary to signals with largemissing E T .We have gone beyond the mSUGRA scenario and focused on different regions of theparameter space of a general SUSY model. It has been shown that sizable SS3 ℓ rates areexpected over various regions of interest in the parameter space, so much so that upto a TeVin the scale of strongly interacting superparticle masses can be explored at the 7 TeV runitself. This in itself is quite remarkable for signals with such high multiplicity of leptons, andcan be attributed to almost non-existent SM backgrounds. It is further shown that eventrates of comparable magnitude are almost impossible to achieve in an L-conserving SUSYscenario of a general kind. This, we argue, further strengthens the motivation of studyingsame-sign multileptons.The other really useful feature of SS3 ℓ and SS4 ℓ signals that we have emphasized is thatthey enable us to extract information on the dynamics of R-parity violation, namely, whetherlepton number is violated through the λ , λ ′ or the bilinear terms. Using SS3 ℓ and SS4 ℓ event19ates in conjunction with their mixed-sign counterparts, one is able to define certain ratiosand their relationships which are typical of the type of R-parity violating terms, taken oneat a time. More importantly, these ratios and their relations are largely independent of theSUSY spectrum and the nature of cascades, and depend centrally on the Majorana characterof neutralinos, making our conclusions extremely general. We perform detailed simulationfor a number of benchmark points to substantiate this claim. The simulations include theeffects of experimental cuts as well the SM backgrounds for mixed-sign trileptons and fourleptons.Thus the overwhelming recommendation is for a careful analysis of SS3 ℓ and SS4 ℓ signalsat the LHC. Such analysis should be concurrent with the search for events with large missingenergy, because of its complementary nature. Acknowledgments
We thank Sanjoy Biswas and Kaoru Hagiwara for useful discussions. This work was partiallysupported by funding from the Department of Atomic Energy, Government of India for theRegional Centre for Accelerator-based Particle Physics, Harish-Chandra Research Institute(HRI). We also acknowledge the cluster computing facility at HRI (http://cluster.hri.res.in).
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