Physics performances for Scalar Electron, Scalar Muon and Scalar Neutrino searches at 3 TeV and 1.4 TeV at CLIC

The determination of scalar lepton and gaugino masses is an important part of the programme of spectroscopic studies of Supersymmetry at a high energy e+e- linear collider. In this article we present results of a study of the processes: e+e- ->eR eR ->e+e- chi0 chi, e+e- ->muR muR ->mu mu- chi0 chi0, e+e- ->eL eL ->e e chi0 chi0 and e+e- ->snu_e snu_e ->e e chi+ chi-in two Supersymmetric benchmark scenarios at 3 TeV and 1.4 TeV at CLIC. We characterize the detector performance, lepton energy resolution and boson mass resolution. We report the accuracy of the production cross section measurements and the eR muR, snu_e, chi+ and chi0 mass determination, estimate the systematic errors affecting the mass measurement and discuss the requirements on the detector time stamping capability and beam polarization. The analysis accounts for the CLIC beam energy spectrum and the dominant beam-induced background. The detector performances are incorporated by full simulation and reconstruction of the events within the framework of the CLIC_ILD_CDR detector concept.


Introduction
One of the main objectives of linear collider experiments is the precision spectroscopy of new particles predicted in theories of physics beyond the Standard Model (SM), such as Supersymmetry (SUSY). In this article, we study the production of the supersymmetric partners of the muon, electron and neutrino in two specific SUSY benchmark points, where we assume R-parity conservation within the so-called constrained Minimal Supersymmetric extension of the SM (cMSSM). In this model the neutralino (χ 0 1 ) is the lightest supersymmetric particle. Table 1 shows the masses and the branching ratios of the supersymmetric particles for the two benchmark points P1 and P2.
For both benchmark points the Higgs boson mass is 120 GeV. Smuons are produced in pairs through s-channel γ/Z exchange, selectrons and sneutrinos are pair produced through s-channel γ/Z exchange or t-channelχ 0 1 andχ ± 1 exchange respectively, see Figure 1. The cross sections, the decay modes, and the cross sections times the branching ratio of the signal processes are given in Table 2. In the processes e + e − →l + Rl − R eachl ± R decays into an ordinary lepton and aχ 0 1 ; theχ 0 1 is stable and escapes detection due to its weakly  and e + e − →ν eνe → e + e −χ+ 1χ − 1 the signature is an e + e − pair, four jets, and missing energy. Measuring the lepton energy distributions of these four processes allows the determination of their production cross sections and of theẽ R ,μ R ,ν e ,χ ± 1 , andχ 0 1 masses. The aim of this study is to: • Characterize the detector performance, namely lepton energy resolution, and boson mass resolution.
• Assess the statistical accuracy of the cross section measurements and the mass determination.
• Estimate the systematic errors, affecting the mass measurements, related to the event selection and the luminosity spectrum knowledge.
• Set the requirements for the detector time stamping capability and beam polarization.
The results presented in this article improve and supersede the previous results [1] obtained at 3 TeV only.

Event Simulation
SUSY signal events and SM background events are generated using the WHIZARD program [2], assuming zero polarisation of the electron and positron beams. WHIZARD is interfaced to Pythia 6.4 [3] for fragmentation and hadronization. For the generation of processes involving supersymmetric particles, the SUSY parameters are entered into WHIZARD using the Les Houches format [4]. The physics backgrounds simulated for this study are listed in Table 3. Beamstrahlung effects on the luminosity spectrum are included using results of the CLIC beam simulation for the CDR accelerator parameters [5]. There are three sources of the centre-of-mass energy spread: the momentum spread in the linac, the beamstrahlung which creates a long tail, and initial state radiation (ISR). The first two are collectively refererred to as "luminosity spectrum". The luminosity spectrum is obtained from the GuineaPig [6] beam simulation; it is used as input to WHIZARD in which initial state radiation and final state radiation (FSR) are enabled. Figure 2 Table 3. Taking into account the luminosity assumptions, the simulation and reconstruction of the background events would require very large computing and storage resources. To optimize the use of these resources preselection cuts are applied after generation of the background events. The preselection requires two opposite charged leptons (L1 and L2) and the following conditions: • p T (L1 and L2) > 4 GeV and 10 • < θ(L1 and L2) < 170 • where p T is the transverse momentum, θ the polar angle of the lepton, ∆φ(L1, L2) the acoplanarity of the leptons, p T (L1, L2) the vector sum of the p T of the two leptons, and M (L1, L2) the invariant mass of the two leptons. Table 3 shows the decay modes, and the cross section times branching ratio values without and with preselection cuts. For the signal samples, these cuts are also applied after full simulation and reconstruction. The simulation is performed using the Geant4-based [7] Mokka program [8] with the CLIC ILD CDR detector geometry [9], which is based on the ILD detector concept [10] being developed for the ILC.

Event Reconstruction
Events are subsequently reconstructed using the Marlin reconstruction program [11]. The tracking systems of the CLIC detectors are designed to provide excellent momentum measurement for charged particle tracks. The track momenta and calorimeter data are input to the PandoraPFA algorithm [12,14] which performs particle flow (PFO) reconstruction, including particle identification and returns the best estimate for the momentum and energy of the particles.

Two Lepton final states
The energy of the lepton is reconstructed from the momentum of the charged particle track and corrected for final state radiation and bremsstrahlung. The energy of photons and e + e − pairs from conversions within a cone of 20 • around the reconstructed lepton direction is added to the energy from the track. Figure 3 shows, for the process e + e − →ẽ +   smaller. For both processes there is a good agreement between the true and reconstructed lepton energy distributions when photon radiation corrections are applied. Table 4 shows the reconstruction efficiencies, ǫ R , for the signal processes. For the process e + e − →l + Rl − R , ǫ R is the number of good reconstructed lepton pairs divided by the number of generated lepton pairs. A lepton is considered as good when the reconstructed lepton matches the generated particle in space within 2 • . For the process e + e − →μ + Rμ − R , at 3 TeV and 1.4 TeV, there is an inefficiency of about 2.5%; 2.0% is due to the cut on the lepton angle and 0.5% is coming from muon misidentification. For the process e + e − →ẽ + Rẽ − R , at 3 TeV, there is an inefficiency of 6.5%; 4.0% is due to the cut on the lepton angle and 2.5% is coming from electron reconstruction or misidentification. At 1.4 TeV the inefficiency is 5.5%; 3.0% is due to the cut on the lepton angle and 2.5% is coming from electron reconstruction or misidentification.
The energy resolution is characterized using: ∆E/E 2 True , where ∆E = E True − E Reco , E True is the lepton energy at generator level before final state radiation or bremsstrahlung, and E Reco is the reconstructed lepton energy with photon radiation corrections. resolution is parametrised using the sum of two Gaussian functions G1 and G2; G1 for the peak and G2 for the tails. For the muons the r.m.s. of G1 is 1.5 · 10 −5 GeV −1 , and the r.m.s. of G2 is 4.9 · 10 −5 GeV −1 . Only 4.1% of the events are outside of the central region; the central region of the distribution is defined within the interval ∆E/E 2 True = ±0.5 · 10 −3 GeV −1 . The electron energy resolution is described by the Gaussian G1 with a very similar r.m.s. as that for muons, 1.4 · 10 −5 GeV −1 , however, even with bremsstrahlung recovery, about 30% of the events are outside the central region. These are due to cases where final state radiation and bremsstrahlung are not sufficiently well accounted for; the tails are reasonably well described by the Gaussian G2 with r.m.s. = 7.7 · 10 −5 GeV −1 .

Two leptons and four jets final states
For the processes e + e − →ẽ + Lẽ − L and e + e − →ν eνe , the parton topology signature required is two leptons and four quarks. After the reconstruction of all the particles in the event, the jet finder program FastJet [16] is used to reconstruct jets. The jet algorithm used is the inclusive anti-kt method [17]; The choice of cylindrical coordinates is optimal since the γγ → hadrons events are forward boosted, similarly to the underlying events in pp collisions for which the anti-kt clustering has been optimised. The R parameter cut value is 1 and the minimum jet energy required is 20 GeV at √ s = 3 TeV and 10 GeV at 1.4 TeV.
An event is retained if six jets are found and if two of the jets are identified as isolated leptons. Table 4 shows the reconstruction efficiencies of both processes, ǫ R is the number of reconstructed six jet events, with two leptons, divided by the number of generated events with two leptons and four quarks. Figure 4 shows the electron energy distribution for the processes e + e − →ν eνe (a) and There is good agreement between the true and reconstructed electron energy distributions when photon radiation corrections are applied.
For the processes with two electrons and four jets, see Figure 5 (c) and (d), despite the presence of four jets, the electron energy resolution is consistent with the energy resolution obtained for the isolated electrons process, see Figure 5 (b).

Reconstruction with beam-induced background
The creation of electron-positron pairs and the production of hadrons in γγ interactions are expected to be the dominating source of background events originating from the interaction region [15]. The beam-beam interaction leading to the production of these background particles was simulated with the GUINEAPIG program [6]. The average number of γγ interactions for each bunch crossing is 3.2 at 3 TeV and 1.3 at 1.4 TeV. At 3 TeV the pile-up of this background over the entire 156 ns bunch-train deposits 19 TeV of energy in the calorimeters, of which approximately 90% occurs in the endcap and 10% in the barrel regions. On average, there is 1.2 TeV of reconstructed energy from γγ → hadrons that are in the same readout window as the physics event. To reduce this energy deposit, p T and additional timing cuts are applied. The presence of the γγ → hadron background sets strong requirements for the design of the CLIC detector and its readout.  To investigate the effect of beam-induced background, the reconstruction software is run overlaying particles produced by γγ → hadrons interactions [18]. The γγ → hadrons event sample was generated with Pythia and simulated. From this sample we randomly select for each physics event the equivalent of 60 bunch crossings, assuming 3.2 events per bunch crossing at 3 TeV [15] and 1.3 events per bunch crossing at 1.4 TeV.
The detector hits from these events are merged with those from the physics event before the reconstruction. A time window of 10 nsec on the detector integration time is applied for all detectors, except for the HCAL barrel for which the window is 100 nsec. After particle reconstruction timing cuts in the range of 1 to 3 nsec are applied in order to reduce the number of particles coming from γγ → hadrons interactions and to optimize the energy resolution. The cut values vary according to the particle type (photon, neutral hadron, charged particle), the detector region, (central, forward) and the p T of the particle. Table 5 shows the cut values for the tight particle flow (PFO) selection.  Table 4. At 1.4 TeV the γγ → hadron background is a factor two lower, no  In final states with four jets and two leptons, the background from γγ →hadrons cannot be removed using a similar p T cut, as this would significantly degrade the jet energy reconstruction. Figure 6 (c) shows the bias in the reconstructed electron energy when the γγ →hadron background is included. This bias is due to additional background particles being associated with the electron in the attempt to account for FSR and bremsstrahlung. Without PFO cuts, the energy resolution is not degraded but the central value is shifted. Figure 6 (d) shows the lepton energy resolutions without and with γγ → hadrons overlaid after tight PFO selection cuts. The cuts restore the central value and preserve the energy resolution, but reduce the reconstruction efficiency ǫ R by 6%, see Table 4. Figure 7 shows, for the process e + e − →ν eνe at 3 TeV, the W boson mass distribution without and with overlaid background: without PFO cuts (a) and with tight PFO selection cuts (b). The tight selection cuts give a similar mass distribution as the one obtained without overlaid background. To estimate the mass resolution degradation, Figure 8 shows the W boson mass distribution fit, for the process e + e − →ν eνe without overlaid background (a) and with overlaid background and tight selection cuts (b). The mass distributions are fitted with a Breit-Wigner convoluted with two Gaussians, one Gaussian takes into account the resolution in the peak, the second the tails. The most probable mass value is fixed as well as the natural width of the W . The width of the peak convoluted Gaussian is 4.1 GeV without overlaid background, it increases to 4.7 GeV with overlaid background and tight PFO selection cuts. The fraction of events in the peak gaussian is 90% without overlaid background and 89% with overlaid background. Figure 9   which correspond to an integrated luminosity of 2000 fb −1 are fitted with two Breit-Wigner functions. The mass distribution of the Higgs boson is broader than the W one, due to a 10% background component from Z boson decays and due to semi-leptonic heavy flavour decays in the H → bb process. In this analysis, no flavour tagging is applied. Figure 9 (b) shows the boson mass distributions for all inclusive SUSY processes with four jet final states [13]. It illustrates that adding b-tag information in the analysis would improve the separation of W and H final states.

Event Selection
All signal processes have two undetectedχ 0 1 's in the final state. Therefore, the main characteristics of these events are missing energy, missing transverse momentum and acoplanarity. Despite this signature, the large Standard Model backgrounds make the analysis rather challenging. To distinguish signal events from background events the following set of discriminating variables is used:   • dilepton velocity β(L1, L2), • cos θ(L1, L2); θ(L1, L2) is the polar angle of the vector sum of the two leptons, • dilepton acollinearity π − θ 2 − θ 1 , where L1 and L2 are the two leptons. For illustration, Figure 10  TMVA [19], is used to implement the event selection. Firstly the discriminating variables of the Monte Carlo sample are input to the BDT method which trains the BDT probability classifier and computes the weights allowing to distinguish signal from background. Next the weigths are used to the evaluate the "Data" sample, computing for each event a probability value allowing to rank the events to be signal or background-like. The cut value is chosen to optimise the significance S M C / √ S M C + B M C versus the signal efficiency and the background rejection; S M C and B M C are the number of signal and background events of the MC sample. The cross section and the masses are determined after background subtraction and efficiency correction; the errors on the masses depend on √ S data + B data + B M C . A stronger BDT cut reduces slightly the significance but decreases significantly the errors on the masses. Figure 11 shows for the process e + e − →ẽ +  electron energy distribution for signal and background events with a loose BDT cut (a), and with an optimized BDT cut (b). At 3 TeV the BDT selection efficiency is 95% for the dimuon events, 90% for the dielectron events and 94% for the dielectron and four jet events. At 1.4 TeV the efficiency is 90% for the dimuon events, 80% for the dielectron events, and 90% for the dielectron and four jet events.

Slepton and Gaugino Mass Determination
After the final selection, the slepton, neutralino or chargino masses are extracted from the position of the kinematic edges of the lepton energy distribution, a technique first proposed for squarks [20], then extensively applied to sleptons [21]: and mχ0 1 or mχ± where E L and E H are the low and high edges of the lepton energy distribution The masses are determined using a three-parameter fit to the background subtracted energy distribution, with σl ± , ml ± and mχ0 1 or mχ± 1 as parameters. The background subtraction is done using the "Monte Carlo" event sample used to train the classifier. The fit is performed with the Minuit minimization package [22]. The fit function is: L( √ s) is the luminosity spectrum prior to initial state radiation (ISR), ISR( √ s) is the √ s variation due to ISR and σl ± ( √ s) is the slepton cross section. U is a uniform distribution of E, and depends on the process cross section σl ± , the slepton and gaugino masses and √ s ; the boundaries E L , E H of U are given by 5.2. D is the detector resolution function obtained from the fits shown in Figure 5. Figure 12 shows, for the processes e + e − → e + Rẽ − R (a) and e + e − →ν eνe (b) at √ s = 3 TeV the lepton energy distributions and fit results. Table 6 shows the values of the measured slepton cross sections, slepton masses, and gaugino masses at √ s = 3 TeV, assuming 2 ab −1 of integrated luminosity. For the process e + e − →ẽ + 2χ 0 2 , the cross section is determined from the fit to the boson mass distribution, Figure 9. Table 7 shows the results at 1.4 TeV, assuming 1.5 ab −1 of integrated luminosity.

Systematic Uncertainty related to the event selection
For the event selection described in section 4 the signal sample, used to train the classifier allowing to distinguish signal events from background events, was generated with the same slepton and gaugino masses as the data sample. With real data the masses are unknown.
In this section we describe the procedure allowing to determine the masses and assess the error on the masses introduced when the MC masses are different from the true masses; the evaluation is done for the process e + e − →μ + Rμ − R at 1.4 TeV. Firstly signal events for lower smuon and neutralino masses are simulated and reconstructed; the smuon and neutralino masses are 459 GeV and 257 GeV respectively, that is to say, data masses -100 GeV. These events are used to train a classifier in which three variables are removed, namely the dilepton energy, dilepton velocity and dilepton energy imbalance. These variables are most correlated with the masses. The 6 variables classifier is then used to select the events. Figure 13 (a) shows the the stacked muon energy distribution for signal and background events selected with the 6 variables classifier trained with masses lower by 100 GeV. The energy distribution of the MC training sample is the black dotted line; the energy distribution of the selected signal data sample is the black full line; and the energy distribution of the signal data sample without selection is the black dashed line.
Next signal events for larger smuon and neutralino masses are simulated and reconstructed. The smuon and neutralino masses are 659 GeV and 457 GeV respectively, this is to say, data masses + 100 GeV . These events are used to train the classifier which is then used to select the events.  The beam energy is derived from the beam deflection measurement using high precision beam position monitors (BPM) pairs placed before and after the first dipole in the energy collimation section. This setup provides a relative energy resolution better than 0.04% [23]; therefore the impact on the slepton and gaugino masses is considered as negligible.
In this section the systematic uncertainty on the slepton and gaugino masses, related to uncertainties in the the knowledge of the luminosity spectrum, is investigated. The assessment is done at 3.0 TeV where the beamstrahlung is largest. As can be seen from equation (5.3), the slepton and gaugino masses depend on the effective luminosity The details about the method used to reconstruct the luminosity spectrum L( √ s, − → p ) using Bhabha events are reported in [24]. The luminosity spectrum is parametrized with a function F (x 1 , x 2 , − → p ) where x 1,2 = 2E 1,2 / √ s; E 1,2 is the energy of the e + e − particles before ISR; the vector − → p has 19 parameters. The model takes into account the longitudinal boost, the correlation between the two particle energies and accounts for asymmetric beams. A fit of F (x 1 , x 2 , − → p ) to the Bhabha events using the energy and the acollinearity of the outgoing e + e − particles allows to determine the parameters − → p of the luminosity function and their errors. The  parameters were determined at 3 TeV, using 2.2 · 10 6 events and taking into account the e + e − energy resolution.
To estimate the systematic error on the masses due to the luminosity spectrum, the mass fit is performed 38 times. Prior to each fit the effective luminosity spectrum L Ef f ( √ s, − → p ) is computed; one parameter p i is changed to p i + C ij is the correlation matrix obtained from the luminosity spectrum fit and: ). (7.2) where m is the the result of the mass fit described in section 5. Table 8 shows the values of the slepton and gaugino masses, the corresponding statistical uncertainty, and the systematic errors from the knowledge of the shape of the luminosity spectrum. For 2 ab −1 of integrated luminosity, the statistical errors are dominant.

Polarization
Beam polarization is very helpful in the study of SUSY processes both to improve the signalto-background ratio and as an analyzer [25], in particular to establish the chirality of the  Table 8: Slepton and gaugino masses, statistical and systematic uncertainties, from the knowledge of the shape of the luminosity spectrum (lumi) , at √ s = 3 TeV.
sleptons. Table 9 shows the signal cross sections for different electron and positron beam polarization conditions. Running with left polarized electron beam would establish the chirality of the selectron which decays into two leptons and of the selectron and sneutrinos which decay into two leptons and four jets. Running with right polarized electron beam would increase the cross sections of thel R processes and reduce some of the backgrounds.

Summary
The accuracy of the slepton and gaugino mass determination and of the process cross section measurement in pair producedẽ R ,ẽ L ,μ R , andν e processes has been studied at CLIC with the CLIC ILD CDR detector model for two specific SUSY benchmark scenarios at √ s = 3 TeV and 1.4 TeV. The analysis is based on two lepton and two lepton plus four jet final states. The electron and muon energy resolution and the boson mass resolution are not affected by the beam induced background, provided the detectors have timing capabilities of the order of 1 nsec allowing for the application of PFO selection cuts. The reconstructed boson mass accuracy allows W ± and light H final states to be distinguished; b tagging improves the purity of the W ± and H samples.
Slepton cross sections, slepton and gaugino masses can be extracted from the lepton energy distributions. At 3.0 TeV, for 2.0 ab −1 of integrated luminosity the relative statistical error on the masses is in the range of 0.15 to 0.45% for the sleptons and in the range of 0.5 to 2.8% for the gauginos. At 1.4 TeV, for 1.5 ab −1 of integrated luminosity, the relative statistical errors, on the slepton and gaugino masses are in the range of 0.1 to 0.2%.
A major source of smearing of the kinematic edges of the lepton energy spectrum is beamstrahlung and ISR. The measurement of the luminosity spectrum with Bhabha events, allows a good control of the beamstrahlung. The systematic errors on the slepton and gauginos masses due to the knowledge of the luminosity spectrum were estimated. At 3.0 TeV for 2.0 ab −1 of integrated luminosity the statistical errors are larger than the systematic errors.