Probing compressed mass spectra in electroweak supersymmetry with Recursive Jigsaw Reconstruction

Journal of High Energy Physics, May 2018

Abstract The lack of evidence for the production of colored supersymmetric particles at the LHC has increased interest in searches for superpartners of the electroweak SM gauge bosons, namely the neutralinos and charginos. These are challenging due to the weak nature of the production process, and the existing discovery reach has significant gaps in due to the difficulty of separating the supersymmetric signal from SM diboson events that produce similar final states and kinematics. We apply the Recursive Jigsaw Reconstruction technique to study final states enriched in charged leptons and missing transverse momentum, focusing on compressed topologies with direct production of charginos and neutralinos decaying to the lightest neutral supersymmetric particle through the emission of W and Z bosons. After presenting prototype analysis designs for future LHC runs, we demonstrate that its detectors have the potential to probe a significant amount of unexplored parameter space for chargino-neutralino associated production within the next few years, and show that the very challenging successful search for chargino pair production with compressed spectra might be possible by the end of the LHC lifetime.

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Probing compressed mass spectra in electroweak supersymmetry with Recursive Jigsaw Reconstruction

JHE Probing compressed mass spectra in electroweak supersymmetry with Recursive Jigsaw Reconstruction M. Santoni 0 1 0 North Terrace , Adelaide, South Australia, 5005 Australia 1 ARC CoEPP, Department of Physics, University of Adelaide The lack of evidence for the production of colored supersymmetric particles at the LHC has increased interest in searches for superpartners of the electroweak SM gauge bosons, namely the neutralinos and charginos. These are challenging due to the weak nature of the production process, and the existing discovery reach has signi cant gaps in due to the di culty of separating the supersymmetric signal from SM diboson events that produce similar nal states and kinematics. We apply the Recursive Jigsaw Reconstruction technique to study nal states enriched in charged leptons and missing transverse momentum, focusing on compressed topologies with direct production of charginos and neutralinos decaying to the lightest neutral supersymmetric particle through the emission of W and Z bosons. After presenting prototype analysis designs for future LHC runs, we demonstrate that its detectors have the potential to probe a signi cant amount of unexplored parameter space for chargino-neutralino associated production within the next few years, and show that the very challenging successful search for chargino pair production with compressed spectra might be possible by the end of the LHC lifetime. Supersymmetry Phenomenology - HJEP05(218) 1 2 4 5 10 16 19 21 Compressed electroweakino production in leptonic channels Chargino-neutralino associated production in nal states with three leptons and missing transverse momentum Chargino pair production in nal states with two leptons and missing transverse momentum B Cut- ow for the ~1 ~20 analysis C Cut- ow for the ~1+ ~1 analysis A Selection criteria for the individual SM backgrounds and ~1+ ~1 samples 18 1 Introduction 2 3 3.1 3.2 1 Introduction Although the Standard Model (SM) of particle physics provides a successful explanation for a multitude of phenomena, it is considered an e ective eld theory of an underlying model valid at higher energies. Supersymmetry [1{8] (SUSY) refers to an invariance under generalized space-time transformations linking bosons and fermions. For each Standard Model particle, it is postulated that there exists a partner with spin di ering by one-half unit, and other quantum numbers unchanged. Evidence of supersymmetric particles with masses at the electroweak-TeV scale is a sought-after experimental outcome, providing an explanation for the stabilization of the Higgs mass and potential gauge coupling uni cation. R-parity conserving SUSY phenomenology demands an even number of superparticles in each interaction. Consequently, in collider experiments, super-partners would be pairproduced, providing in the nal state two stable lightest supersymmetric particles (LSPs). As the LSP interacts only weakly, escaping the detector, it assumes the characteristics compatible with a dark matter candidate. At the Large Hadron Collider (LHC) the missing transverse momentum, 6E~T , can infer the presence of unmeasured weakly interacting particles. As the momentum in the transverse plane is conserved, any missing momentum can be assumed to arise from missing particles including the LSPs. Reconstruction techniques su er from the lack of information related to the multiplicity and the masses of the particles not interacting with the detector. The di culty is exacerbated in situations when the momenta of the weakly interacting particles are { 1 { low. This is the case for supersymmetric spectra in which the di erence in mass between the pair-produced parent superparticles, P~, and the LSPs is low. Scenarios with a small mass-splitting are referred to herein as compressed [9]. In the compressed regime, visible and invisible decay products have low transverse momenta, as the center-of-mass system of the parent superparticles does. In this scenario, the e cacy of typical variables [ 10 ] exploited to distinguish signal from background, based on large object transverse momenta and missing transverse energy, is limited. One can gain indirect sensitivity by observing the reaction of the LSP pair to a probing force. The initial state radiation (ISR) from the interacting partons is the natural probe provided in the laboratory of a hadron collider. The ISR can boost the sparticles produced in these reactions and, in turn, endow their decay products with its momentum. The Recursive Jigsaw Reconstruction technique has been used by the ATLAS collaboration to probe supersymmetric scenarios in cases involving the production of colored superpartners of SM particles [11]. In the compressed regime, a general basis of kinematic observables designed for the analysis of events with initial state radiation can be used independently of the topology investigated. In this study, we focus on applications of this technique to nal states in the electroweak SUSY sector. Electroweakinos are a linear combination of the fermionic partner of the gauge bosons and the two Higgs bosons. Neutral higgsinos and gauginos mix to form four eigenstates of mass called neutralinos ( ~i0 with i = 1; 2, 3 or 4), while charged winos and higgsinos form two eigenstates of mass referred to charginos ( ~i with i = 1 or 2). Herein, one assumes the lightest neutralino is the LSP and focuses on cases with small mass di erence between it and the ~ 1 and/or ~20. Compressed scenarios involving electroweakinos have been studied in detail elsewhere in the literature [12{18], and they are common in supersymmetric theory. For example, in naturalness-inspired models [19], the higgsino components are light, hence extremely small mass splittings are expected for the lower eigenstates of mass of higgsino-like charginos and neutralinos. At the same time, the masses of the wino components, appearing in the one-loop corrections to the Higgs mass, are expected to be limited. Dedicated techniques, as the monojet analysis, can be used for probing the extremly compressed regime. Mass di erences between the parent superparticle and the LSP, M = MP~ M ~0 ; 1 between 15 GeV and 75 GeV are probed in this work. The lightest chargino and the next-tolightest neutralino are assumed the next-to-LSP of the theory, with the branching fractions for the decay modes ~1 ! W ~01 and ~ 2 ! Z ~01 assumed to be 100%. Final states arising 0 from intermediate sleptons are not considered. For a mass splitting below the W -boson mass, two-body decays are kinematically suppressed, and we generate three-body decays involving o -shell bosons and assume other mediators do not contribute. 2 The simpli ed compressed decay tree Recursive Jigsaw Reconstruction (RJR) [20] is a HEP technique based on the imposition to as jigsaw rules, are applied to solve nal state ambiguities due to unknown kinematic degrees of freedom, when weakly interacting particles are present, and combinatoric challenges, due to the presence of indistinguishable visible particles from a detector prospective. The result is an estimate of the relevant reference frames and, hence, the de nition of a complete basis of kinematic variables. These observables are sensitive to the masses and decay angles of the resonances appearing in the chosen tree, and can be used to distinguish signatures of new physics from the SM background. In RJR involving compressed scenarios, the simpli ed decay tree shown in gure 1 is used for analyzing topologies with initial state radiation. A transverse view of the event is considered, namely all the z-momenta of the visible objects are set to zero. We follow the procedure outlined in [21]. The estimate for the center-of-mass system of the whole reaction, SUSY + ISR, is labeled by CM; ISR is the system assigned to the radiation from the initial state, S is the signal or sparticle system decaying to visible and invisible products: the V and I systems. In each event, the missing transverse momentum is assigned to the I-system, while a jigsaw rule speci es the reconstructed objects hypothesized to come from the decay of sparticles, and assigned to the V-system, with respect to those associated with ISR. Jigsaw rules are implemented using the RestFrames software package [22]. Topology independent observables include: jp~IC;TM p^ICSMR;T j : variable sensitive to the mass ratio between LSP and parent ated in the CM frame. pICSMR;T : magnitude of the vector-sum of the jets transverse momenta of the ISR-system evaluated in the CM frame. ISR;I: transverse opening angle between the ISR-system and the I-system, evalu{ 3 { nal states with two LSPs and no other weakly interacting particles, the observable RISR can be written in the laboratory frame as RISR ~ T 6ET p^ISR pISR T ~ 1 0 q P A sin : (2.1) ~ pP~0 and sin M~0 This approximation is valid for the extremely compressed scenarios, hence in the limit of a low-momentum of the LSP in the parent superparticle rest frame (pP~~0 ) with respect to 1 the parent superparticle mass (MP~). In eq. (2.1), mP~P~ is the true mass of the S-system is a quantity which is zero on average. The observable scales with the mass ratio MP~1 and width of order 2MP~ 1 in the limit pITSR mP~P~. When visible decay objects are not reconstructed in the V-system, or additional neutrinos in the nal state contribute to the missing transverse momentum, RISR is expected to assume values between the mass ratio and unity, while the last term in eq. (2.1) decreases. 3 Compressed electroweakino production in leptonic channels where [23]. These samples are proton-proton collisions at p Simulated Monte Carlo (MC) samples of Standard Model backgrounds and SUSY signals are used to study distributions of the performance of the RJR observables. The SM background processes expected to be the largest contributions have been generated elses = 14 TeV generated with MadGraph 5 [24]. The parton shower and hadronization is performed with Pythia 6 [25] followed by a detailed detector simulation with Delphes 3 [26]. The parameterization incorporates the performance of the existing ATLAS [27] and CMS [28] experiments. Jets are reconstructed by the anti-kT clustering algorithm [29] with R = 0:5 and pmin = 20 GeV, T implemented with the FastJet [30] package. The simulation procedure involves generation of events at leading order in bins of the scalar sum of the generator level particles transverse momenta, with jet-parton matching and corrections for next-to-leading order (NLO) contributions [31]. The same procedure and parametrization are used to generate the signal samples. MP~ The topologies considered are associated chargino-neutralino production and chargino pair production assuming degenerate masses, M ~ 1 = M ~02 ; M ~1+ = M ~1 , in the range 100 GeV 500 GeV. The compressed regime is probed: the mass splittings considered are in The cross sections for pure wino chargino pair production and chargino-neutralino the range 15 GeV M associated production at p NLL cross sections at p uncertainties in the range 4:5% . s = 13 TeV at NLL can be found elsewhere [32, 33], with relative . 9% for the masses investigated. We estimate the s = 14 TeV, evaluating the NLO cross sections for the wino-like electroweakino pair production at 13 and 14 TeV with MadGraph, and assuming the same NLL/NLO k-factors for the corrections. The resulting NLL cross sections are shown in gure 2a and used as inputs for the analysis of the simpli ed supersymmetric topologies. This procedure provides small corrections (. 5%) from the k-factors, and it is a check for { 4 { σ 10−1 σ ( p p → Χ∼+ Χ∼- ) 1 1 σ ( p p → Χ∼1± Χ∼02 ) chargino-neutralino associated production (red curve) at p s = 14 TeV (a). Feynman diagrams for nal states with missing transverse momentum and three charged leptons (b) and two charged leptons (c). the matched MadGraph cross sections and their potential dependences on the cuto scales chosen. The focus of this work is on the leptonic decay channels of o -shell W and Z bosons, as depicted in the Feynman diagrams in gure 2b and gure 2c. Leptonic nal states from charmonium and bottomonium are expected to be negligible in the phase space probed. Focusing on electrons and muons as visible decay products provides several advantages. Firstly, the signal-to-background ratio increases progressively with lepton multiplicity in the nal state. Secondly, the channels result in clean nal states with high e ciencies for the lepton reconstruction. Although the minimum value for reconstructed lepton pT of 10 GeV is assumed in this study, recent work by the CMS collaboration has demonstrated improvements in the e ciency of identi cation of soft isolated electrons and muons (down to 3{4 GeV) [34], where dedicated triggers are described. Moreover, for our purposes, all the leptons are identi able as reconstructed objects produced via sparticle decays and assigned to the V-system, while all the jets can be assigned to the ISR-system with no ambiguity. A minimal value of the transverse momentum of the ISR-system, in concert with 6ET , can elicit an increase in the transverse momenta of the decay products of the SUSY system. For compressed scenarios, the lack of combinatoric ambiguity allows us to leverage the RJR technique without requiring a restrictive event selection based on a huge value of the ISR transverse momentum. The two phenomenological studies, treated separately, are presented in the next two sections emphasizing the role of the RJR observables for discriminating compressed electroweakino signals with respect to the individual SM processes. In appendices B and C two examples of cut- ows are shown in table 3 and gure 16, and table 4 and gure 17 respectively, for the overall SM background and two benchmark signal samples. 3.1 Chargino-neutralino associated production in nal states with three leptons and missing transverse momentum The signal samples are the simpli ed topologies as in gure 2b generated within the mass ranges 125 GeV (M ~ 1 = M ~02 ) 500 GeV, with ve mass splittings 106 Di-Boson t+V the preselection criteria. All the contributions are scaled with an integrated luminosity of 300 fb 1 and analyzed to probe compressed spectra for a projection of R M ~01 = 15; 25, 35, 50 and 75 GeV. Event-by-event a basis of RJR variables is extracted L dt = 300 fb 1. To the previous variables, additional transverse observables for this study include: MTV is the transverse mass of the V-system. M`+` is the transverse mass of the two same avor opposite sign leptons in nal states where the third lepton has di erent avor (corresponding to MT; e+e , when the third lepton is a muon, and MT; + , when the third lepton is an electron). CM;I is the transverse opening angle between the CM-system and the I-system. Three leptons (electrons and muons) are required in the nal state with pT > 10 GeV, while at least one jet, with pT > 20 GeV, is associated with the ISR-system. A minimal value for the missing transverse momentum, 6ET > 50 GeV, is the last preselection requirement. chargino-neutralino production samples with di erent masses and mass splittings. The observable RISR provides a remarkable signal-to-background discrimination in the absence of more stringent selection criteria as shown in gure 3a. The assignment of the di erent objects in the compressed tree is performed with no ambiguity, and it is not necessary to focus on the high ISR regime in order to improve the observable resolution for the signal samples. Notice that RISR can assume larger values than unity when some objects are forced in the V-system. The observable is expected to be peaked for values beyond M ~=MP~ due to the additional contribution to 6ET , deriving from one or more neutrinos. Values larger than the mass ratio will be considered for the de nition of the RISR requirements together with RISR < 1. { 6 { ]V 60 s=14TeV ]V 60 [eG 50 V T 40 M 30 90 80 70 20 10 0 0 0 0 3 3 3 / / / ) ) V V x x 5 5 5 1 E E E 125 GeV (c). One demands preselection criteria, NbI-SjRet = 0, pICSMR;T > 50 GeV and MTV < 100 GeV. ground samples are similar, and the variable has limited impact. In the absence of other requirements, the slope of the signal distributions is paradoxically more severe than the background one, since events with non-radiative jets forced into the ISR-system. A minimal requirement on pICSMR;T is essential to exploit the RJR technique with multi-lepton nal states. The requirement applied to this variable, the only large-scale observable in this study together with 6ET , will be moderately tighter for the largest mass splittings probed since the criterion on RISR is relaxed. It is interesting to note that the number of events passing the preselection criteria is smaller for the signal sample with M ~ pared to the sample with M ~ 1 = M ~02 = 300 GeV and 1 = M ~02 = 200 GeV and conservative minimal choice of transverse momentum for electrons and muons of 10 GeV and, consequently, when the mass splitting approaches a much more compressed regime, the kinematics are such that one of the three leptons is less likely to satisfy this transverse momentum constraint. In order to probe the extreme compressed regime ( M < 15 GeV), a parametrization of the e ciency in the reconstruction of soft electrons and muons (pT . 10 GeV) must be implemented. This is considered beyond the scope of this paper, due to the di culty of getting these details correct outside of an experimental M = 15 GeV comM = 50 GeV. There has been a collaboration. dominant Standard Model background and two representative signal samples for events passing the preselection criteria, and after applying a veto for jets tagged as being initiated by a b-quark (NbI-SjRet = 0). The nal state signal events populate low values of MTV with a complementarity with high values of RISR. Vice versa, for the diboson background, simultaneous low values of MTV and RISR close to one are disfavored, as shown in gure 4a. Using the two RJR observables in concert provides an increasingly powerful discrimination the smaller the absolute and relative mass splitting of the signal sample. In the low MTV regime (MTV < 100 GeV), and for values of the ratio close to unity (RISR > 0:6), additional handles to decrease the SM background yield are provided by the compressedtransverse RJR angles and M`+` . Figure 5 shows the distribution of Tri-Boson Boson+jets Madgraph+Pythia+Delphes, pp→SM, Χ∼1± Χ∼20 →W±(*)Z(*) Χ∼0 ∼0 Di-Boson t+V CM;I(b) and M`+` (c) for the events satisfying the (b) and M`+` for nal state events with only two of the three leptons with same avor (c). For the signal events, the transverse mass of the two leptons has a clean end-point at the expected M . Selection criteria applied on the compressed RJR observables, as shown in table 1, can be used to de ne signal regions for probing chargino-neutralino associated pair production in nal states with three leptons and missing transverse momentum. One or more additional jets are assumed to be radiated from the initial state, and a minimal requirement on pICSMR;T (and 6ET ) allows us to focus on the nal states of interest and probe the compressed spectra. The signal regions target ve particular mass splittings. A special treatment is assumed for the selection criteria applied to RISR, since this observable is related to the mass ratio, M ~=MP~ , rather than the absolute value of the mass splitting. For the largest mass di erences ( M = 50, 75 GeV), tighter selection criteria are used for the only large-scale variables (pICSMR;T and 6ET ), the jet multiplicity and the RISR requirement is relaxed. An upper bound is imposed for MTV, progressively more CM;I, since stringent to the decrease of M ; while for M`+` , the maximum required coincides with the mass splitting itself. In nal states with three electrons or three muons, only the MTV requirement is applied; while for events with two same and one di erent avor leptons, the selection on M`+` is imposed together with MTV <100 GeV. The selection criteria applied to the observable RISR are progressively more stringent the closer the mass ratio to unity, and the values are separated by 0.05, which provides a moderate optimization. Figure 6 shows the distributions of CM;I and MTV applying respectively the N-1 requirements in column 2 and 3 of table 1; namely all the selection criteria except for the one imposed on the observable plotted. The signal regions expressed by the selection criteria of the RJR observables de ned in Figures 7 shows the value of ZBi, calculated assuming the metric [35], at p an integrated luminosity of 300 fb 1. A systematic uncertainty of 20% is assumed constant in the SUSY phase space, with the dominant contribution to the background arising from associated WZ production. The signal yields in the extreme compressed scenarios can bene t from an improvement in the e ciencies of the detector in the reconstruction of low-momentum leptons, which { 8 { chargino neutralino production in trilepton nal states. Madgraph + Pythia + Delphes, p p → SM, Χ1 Χ2 → W±(*) Z(*) Χ∼0 ∼0 ∼± ∼0 1 Χ1, ∫L=300 fb-1 s=14 TeV 0.5 1 2 2.5 3 0 background events passing the N-1 selection criteria in one of the signal regions of table 1 S HJEP05(218) p p → Χ∼± Χ∼0 → W± * Z* Χ∼01 Χ∼01, 300 fb-1 s=14 TeV, ΔB/B =20% 1 2 M(Χ1), M(Χ2) < M(Χ∼10) ∼± ∼0 2σ 5σ M(Χ1), M(Χ2) > M(Χ∼10) + M(Z) ∼± ∼0 150 200 ∼ ± 250 M(Χ1), M(Χ2) [GeV] is outside the scope of this work. On the other hand, the signi cances decrease for mass di erences close to the W pole mass, due to the di culty to discriminate background events derived from topologies with absolute and relative mass scales very close to the signal ones. The value M =15 GeV must not be considered as a threshold: the minimum mass difference achievable with any technique is strongly related to the e ciencies for the detector to reconstruct low-momentum leptons. For extremely compressed scenarios, a similar analysis could be used to probe the same nal state topologies with only two low-momentum leptons reconstructed. Although the background would di er in that case, one could require two same-sign leptons to suppress the SM yield. The highest impact of the compressed RJR observables is for the samples of mass excluded up to 300 GeV for the best scenarios. splittings in the range 20{40 GeV, a challenging phase space for SUSY searches [36]. For an integrated luminosity of 300 fb 1, degenerate charginos and neutralinos would be discovered with masses M ~ 1 = M ~02 > 150 GeV, for a large portion of the samples investigated, and Overall, one can improve the performance of the RJR technique by adopting a strategy based not only on transverse observables, exploiting a three-dimensional reconstruction, as in the following study. 3.2 Chargino pair production in nal states with two leptons and missing transverse momentum p We now move on to consider a di erent and still more complicated compressed electroweakino investigation. The signal samples are simulated proton-proton collisions at s = 14 TeV producing a pair of lightest charginos with opposite electric charge and with Visible States Set Invisible Rapidity Contra-boost Invariant S ∼ Χ I b l ISR. The substructure of the S system is speci ed: each chargino decays to a visible (lepton) and an invisible (neutrino + LSP) object. ~ 1 ! W (! ` ) ~01. The focus is on nal states with two leptons as illustrated in the simpli ed topology in gure 2c. The samples are generated within the mass ranges 100 GeV 50 and 75 GeV. M ~ 1 300 GeV, with the ve mass splittings The lepton multiplicity of the nal state determines the main contributions of the Standard Model processes. In the absence of hadronic jets, the dileptonic channel of a pair of W bosons, constitutes the dominant process, producing a nal state with two opposite sign leptons and missing transverse momentum. Searches for chargino pair production in a nal state with two leptons are challenging for open mass spectra due to the W +W irreducible background, while other contributions are often negligible. In the compressed regime, the di culty is exacerbated by the low momenta of invisible and visible objects and by the subsequent kinematics. Moreover, requiring a transverse momentum for the ISRsystem introduces an additional complication for the analysis in the compressed regime: Standard Model backgrounds other than W W will contribute quite signi cantly. In order to improve the signal-to-background discrimination, the simpli ed version of the compressed RJR tree in gure 1 is enriched specifying the substructure of the S-system. This is feasible for the dilepton nal state, since the provenance of the reconstructed visible sparticle decay products is unambiguous. These decay products can then be assigned to the appropriate position in the tree. The RJR decay tree is shown in gure 8. Electrons and muons are associated with the `+ and ` systems, depending on the electric charge, while the jets are assigned to the ISR-system. The S-system frame is the approximation for the center-of-mass of the two charginos, and each one decays to a lepton and an invisible system. Each invisible system collects the ~01 + contribution of the hemisphere a or b. In this approach, a three-dimensional view of the event is considered, and jigsaw rules are applied for reconstructing the topology and the relevant frames of reference. In the overall center-of-mass frame, the ISR and S systems are back-to-back. A Lorentz invariant jigsaw rule is assumed for the estimate of the mass of the invisible objects, while the rapidity is assigned as to the chargino center-of-mass (equal to the rapidity of the visible objects in the S-system). Finally, a contra-boost invariant jigsaw rule partitions the remaining unknown degrees of freedom associated with Ia and Ib. More information can be found elsewhere [37, 38]. The useful transverse variables of the simpli ed tree can be computed along with additional experimental observables. Having in mind the simpli ed tree in gure 1, one can reconstruct the I-system, corresponding to the sum of the two invisible systems, I = Ia + Ib, and V, as the sum of the two lepton systems, V = `++` , and hence compute the transverse observables: RISR, pICSMR;T and ISR;I. Three-dimensional scale-sensitive variables and additional angular observables include: M V is the mass associated with the V-system: invariant mass of (`+ + ` ). M ~ is the mass associated with the chargino system. 6E~ T , computed in the Lab frame. `+;I ( ` ;I) is the polar angle between the positive (negative) charge lepton and CM;I is the opening angle between the CM-system and the I-system. cos S-frame. ^CM S pIS;T is the dot product between the direction of the boost from CM to the reconstructed S-frame and the transverse momentum of the I-system in the Finally, jet multiplicities are considered. For the signal samples, the mass-observable associated with the chargino system, M ~+ = M ~ , do not reproduce the actual chargino mass since the true LSPs are massive. The Ia;b systems, assumed massless by RJR, are simpli cations of the lightest neutralino plus neutrino contribution in each hemisphere. The dominant SM backgrounds are categorized into four groups: 1) Vector boson + jets, mainly populated by Z ! `+` + jets; 2) Production of at least one top quark (t+X), with single-top and dileptonic tt both contributing; 3) Irreducible diboson processes mostly arising from W +W with two leptons and missing transverse momentum; and 4) Contributions such as vector boson fusion, tri-boson, and gluon fusion plus jets with H ! W +W , are categorized as \others". Two leptons (electrons and muons), with pT > 10 GeV, are required in the nal state and at least one jet, with pT > 20 GeV, which is assigned to the ISR-system. Figure 9 shows the distribution of the invariant mass of the two leptons for same and di erent avor, assuming a minimal value for the missing transverse momentum 6ET > 20 GeV. Standard Model background samples are stacked together, while the overlaid dashed curves refer to chargino pair production samples with di erent masses and mass splittings. Notice the peak around 90 GeV for same avor leptons, due to the Standard Model backgrounds containing Z bosons produced in association with jets (in blue), with a moderate contribution from W Z (in green), and vector boson fusion and tri-boson (in red). In the compressed regime, the nal state events for all the signal distributions tend to populate lower values of M V, and the requirement M V < 70 GeV, or tighter, will be used to specify the signal regions. 1011 Madgraph + Pythia + Delphes, p p → SM, Χ∼1+ Χ∼-1 → W*+ W*- Χ∼0 ∼0 Boson + jets 1010 Notice the additional peak for low values of M V, arising from Z+ jets and vector boson fusion contributions, resulting in a comparable number of events for the cases with two leptons with same or di erent avor. The dominant process that contributes in this region , and sub-dominant contributions arise from Drell-Yan processes ) ! + ), or W boson production decaying is Z ! + ! `+` with missing transverse momentum (Z ( leptonically, with an additional lepton faked by a jet or a photon. For the dileptonic decay of the Z boson via taus, the value for M V is reconstructed to be below the Z mass, representing a challenge to the analysis in search of compressed charginos. Herein, we consider the preselection criteria as follows: nal states with two leptons and at least one light jet. A veto is applied for the jets tagged as b, N IS-jRet = 0 and NfIaStR = 0.1 A minimal value for the missing transverse momentum (6ET > 50 GeV) in concert with pICSMR;T > 50 GeV is imposed. In addition, preselection includes the criterion M V < 70 GeV. This last requirement excludes a large portion of the Standard Model background events, in particular tt and multi-bosons processes, independently of the avor of the two leptons reconstructed. Standard Model processes involving a meson decaying in two same avor leptons are expected with a small value of the invariant mass and fat: NbI-SjRet = 0, (. 10 GeV); notably, signal sample events tend to assume larger values. In the following, the impact of the main RJR observables in reducing the speci c Standard Model contributions is presented. Selection criteria will be imposed progressively on the observables sensitive to probe compressed chargino pair mass spectra, with distributions shown in appendix A. Numerous Standard Model processes result in a low value of M V, in particular, the boson plus jets contribution. The focus is on the process Z ! + ! `+` plus jets. For such events, the role of the chargino system in gure 8 is assumed by the tau's leptonic decay, while the I systems reconstruct the information of the two neutrinos in each hemisphere. The kinematics of these background events is such that M ~ is a reconstruction of the mass of the lepton and two neutrinos resulting from the decays. 1In this work a fat jet is de ned with M > 60 GeV and is a candidate for boosted SM Higgs, vector bosons and top-quark decaying hadronically. The rst two plots in gure 12 show the two-dimensional distributions between M ~ and the ratio RISR for the boson plus jets backgrounds and the signal sample M ~ 200 GeV and M ~0 = 150 GeV, gure 12c shows the distribution of M ~ for the ve signal 1 samples and for the on-shell/o -shell boson plus jets backgrounds. The lower bound M ~ = > 1 24 GeV is required to suppress the V+jets background. With this requirement the SM background is dominated by top processes, speci cally a pair of (on- or o -shell) top quarks in the dileptonic channel. Figure 13 shows the distribution of the light jet multiplicity as a function of the ratio. In order to attenuate the tt contribution, we demand only one jet in the nal state. Despite the requirement of NjIeStR = 1, and vetoing on jets coming from the fragmentation of bottoms, the tt background is still not suppressed. Although the requirement NfIaStR = 0 attenuates the contribution with the two jets reconstructed in similar directions, one of the two jets could be outside the geometrical acceptance, mismeasured, or of too low momentum to be reconstructed. Also if these events are relatively rare, their contribution is not negligible due to their high cross section, collisions. pp!tt O(103 pb), at 14 TeV LHC Figure 14a shows the distribution of `+;I for the signal samples and the t + X backgrounds, categorized in four sub-processes and stacked together. The events from the top pair contributions tend to populate value close to , while signal-like events populate low values. Figures 14b and 14c show the two-dimensional distribution `+;I vs. ` ;I for the tt background and the signal sample M ~ 1 = 200 GeV and M ~0 = 150 GeV, assuming 1 the same selection criteria, and requiring RISR > 0:6. The requirements select background events with kinematics similar to the signal events, and in particular, a simultaneously large value of ` ;I is disfavored. Such events contain predominantly two top quarks produced with low transverse momenta resulting in nal states with two reconstructed leptons and one jet not properly tagged. In the transverse plane, one of the two leptons is expected to y close to the reconstructed jet (associated with the ISR-system), while the other is expected to be closer to the invisible system. Consequently, background events tend to assume larger values of ` ;I than signal events. A similar two-dimensional distribution as in gure 14c is demonstrated by all signal samples studied. A unique light jet associated with the ISR-system together with ` ;I < 2 dramatically reduce the t+X background. Applying these selection criteria, the dominant Standard Model contribution is the irreducible diboson background: W +W : The goal is to distinguish between signal and background events with similar event topologies and kinematics, in particular when selection criteria close to the nal con guration are imposed. The key di erence to exploit is that of the I-system (Ia + Ib) for the W +W background composed of two neutrinos. For signal events, on the contrary, a minimum of four weakly interacting particles comprises the invisible system. and used to separate events resulting from compressed chargino samples with respect to W W events. Figure 15a shows the distribution of values closer to , as the mass di erence ISR;I. Signal events tend to populate M ~ is reduced. Figure 15b shows the 0:5 3:12 0:9 50 0:5 3:10 0:85 2 OS Leptons (e and ) with plep > 10 GeV, T NjIeStR = 1, NbI-SjRet = 0; N IS-jRet = 0 and NfIaStR = 0 50 2 24 3:06 0:8 nal states with two leptons and missing transverse energy. distribution of the angle between the CM-system and I-system, where in this case signal events are towards zero, almost independently of cos ^CM S S pI;T is shown in gure 15c. M or MP~=M ~. The distribution of Selection criteria de ned with the compressed RJR observables result in signal regions used to investigate chargino pair production in nal states with two leptons and missing transverse momentum. The requirements for the observable RISR are tuned depending on the mass ratio, and are more stringent than the chargino-neutralino associated study, due to the larger multiplicity of weakly interacting particles in the nal state. sample events passing the selection criteria in table 2. For the lowest mass splitting the requirement RISR > 0:85 is applied only for the sample M ~ 25 GeV, one demands this criterion for three samples (M ~ 1 1 = 100 GeV, while for M = The signal regions expressed by the selection criteria of the RJR observables de ned in at p given signal, expressed in standard deviations, in the presence of a background hypothesis, s = 14 TeV for an integrated luminosity of 3000 fb 1 . One considers a systematic uncertainty of 20% for the overall Standard Model background: a compromise between a large data sample projection and stringent selection criteria assumed to suppress the individual background yields. Exploiting the RJR technique, one can set limits for the compressed chargino pair production topology at the high luminosity LHC14, with masses 150 GeV being excluded in the best scenarios. Madgraph + Pythia + Delphes, p p → SM, Χ∼1+ Χ∼-1 → W*+ W*- Χ∼10 Χ∼01, .02102 0 / s t E f o t + X column 1 (a) and of M ~ , with the requirements in column 2 and RISR > 0:85 (b). p p → Χ∼ + Χ∼ - → W*+ W*- Χ∼ 01 Χ∼ 01, 1 1 3 ab-1 s=14 TeV 2σ M(Χ1) > M(Χ∼10) + M(W) ∼± 100 120 140 160 180 200 220 240 ∼ ± M(Χ1) [GeV] 6 5 4 3 2 1 0 ) σ Z e c n a c i f i n g i S for an integrated luminosity of 3000 fb 1 s = 14 TeV assuming a systematic uncertainty of 20% for the SM background, and We have introduced an original approach to searches for compressed electroweakinos based on the imposition of the decay trees as in gures 1 and 8 for the interpretation of reconstructed events, using the Recursive Jigsaw Reconstruction technique. Putative wino-like ~ 1 and ~02 could be discovered at the LHC14 with masses M ~ M ~02 > 150 GeV, for a large portion of the samples investigated (15 GeV . assuming an integrated luminosity of 300 fb 1, and leveraging only transverse observables. M . 50 GeV), 1 = The RJR technique is sensitive to the extremely challenging chargino pair topology scenarios in the compressed regime. A strategy based on several experimental observables has been used to reduce the W +W and the other main background yields due to the necessity of requiring jets in the nal state to be associated with the ISR-system. A potential 95% con dence level exclusion limit can be obtained for an assumed dataset of 3 ab 1, assuming a 20% of systematic uncertainty, for sample spectra with M . 50 GeV. For both the topologies, the signal yields in the extreme compressed scenarios can bene t from an improvement in the e ciencies of the detector in the reconstruction of low transverse momentum leptons (< 10 GeV). On the other hand, for large mass splittings ( M & MZ ), the bulk analysis should be preferred to a compressed investigation, while for intermediate scenarios (50 GeV . M . MZ ), one can exploit the complementarity of observables based on a reconstruction of the event with or without the ISR-system and include cases with vector bosons decaying hadronically. The method is expected to have still more impact in the cases of nal state topologies with larger lepton multiplicity: pair production of charginos and/or neutralinos with slepton mediated decays. The RJR technique can be extended to these studies and to the pair production of heavy neutralinos in nal states with four leptons, exploiting the simpli ed tree in gure 1, with a modi cation in the assignment of the objects in the case of sleptons of the third generation. The results from the simpli ed models investigated in this work can be partially reinterpreted assuming di erent compositions for the electroweakinos. The method can be applied for higgsino-dominated charginos and neutralinos, with the latter decaying via an o -shell SM Higgs boson, requiring two b-jets and one lepton in the V-system. When decay modes via o -shell gauge bosons are dominant, the comparison would be straightforward. In particular, for chargino pair production with a mixed higgsino-wino nature, one can simply re-weight the signal yields with the appropriate cross sections: typically, the contributions from o -shell charged Higgs or other sparticles can be neglected since MS; MH MW in most SUSY models. 1π06 / 0 12005 x 1ts04 n e Di-Boson(V*) M(~P)=100GeV,M(Χ∼ )=75GeV M(~P)=125GeV,M(Χ∼ )=110GeV M(~P)=150GeV,M(Χ∼ )=75GeV M(~P)=200GeV,M(Χ∼ )=150GeV M(~P)=250GeV,M(Χ∼ )=215GeV Di-Boson(V*) M(~P)=100GeV,M(Χ∼ )=75GeV M(~P)=125GeV,M(Χ∼ )=110GeV M(~P)=150GeV,M(Χ∼ )=75GeV M(~P)=200GeV,M(Χ∼ )=150GeV M(~P)=250GeV,M(Χ∼ )=215GeV 1106 . 1/005 ts 1en04 v E 1f03 o r 1eb02 m u N10 1 Model background, for events passing preselection criteria and the additional requirements M ~ > 24 GeV, NjIeStR = 1, RISR > 0:6 and 0:85 < RISR < 1, 3SF leptons 0:85 < RISR < 1 and MTV < 100 GeV, 2SF leptons 3SFL: MTV < 65 GeV, or 2SFL: M`+` < 35 GeV (MTV < 100 GeV) p s = 14 TeV and for R 1 Ldt = 300 fb 1 criteria in this table. The number of expected signal and background events resulting from each selection requirement is displayed up to three signi cant gures. 0 1105 x se 1tn04 v 1fE03 o 1re02 b cos θ 125000 113000 83900 33800 1170 367 257 43 35 S1 699 698 612 374 66 54 100 65 58 S2 170 170 148 88 20 16 31 23 20 1 for the ~ + analysis Madgraph + Pythia + Delphes, p p → SM, Χ∼1+ Χ∼-1 → W*+ W*- Χ∼0 ∼ 0 1 Χ1, M 1 [GeV] (a) Preselection criteria. Madgraph + Pythia + Delphes, p p → SM, Χ∼1+ Χ∼-1 → W*+ W*- Χ∼0 ∼ 0 1 Χ1, 10−1 106 105 10−1 π104 / 0 20103 x s t 10−1 10−1 106 105 10−1 104 .25103 0 / 10−1 3.05 3.06 3.07 3.08 3.09 3.1 3.11 3.12 3.13 3.14 0 states with two opposite sign leptons (electrons and muons). The distributions show the number of expected Standard Model background and two compressed ( M = 25 GeV) signal sample events passing the selection criteria accumulated, and with the previous selection requirement plotted. ! ~ + 1 ~ 1 + jets; ( ~ ! W 1 0 ~ ); in nal Δφ Preselection and M V < 50 GeV M ~1 > 24 GeV `+;I < 2 33900 11900 9190 2270 1490 577 154 103 65 8350 3920 2920 658 511 196 54 35 19 = = 200 GeV (S2), with 125 GeV (S1) and M~ and for R 10 GeV, NbI-SjRet = 0, N IS-jRet = 0; NfIaStR-jet = 0, 6ET > 50 GeV and pICSMR;T > 50 GeV. The ordering in gure 17 corresponds to apply the selection criteria in this table. The number of expected Ldt = 3000 f1b 1. Preselection criteria include two opposite sign leptons with plep > T signal and background events resulting from each selection requirement is displayed up to three signi cant gures. A more stringent criterion (0:9 < RISR < 1) is imposed on the sample S2 for the 1 M = 25 GeV, at the LHC with p s = 14 TeV computation of ZBi. Open Access. Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. [INSPIRE]. [2] P. Ramond, Dual Theory for Free Fermions, Phys. Rev. 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M. Santoni. Probing compressed mass spectra in electroweak supersymmetry with Recursive Jigsaw Reconstruction, Journal of High Energy Physics, 2018, 58, DOI: 10.1007/JHEP05(2018)058