Search for Scalar Leptons and Scalar Quarks at LEP

Scalar partners of quarks and leptons, predicted in supersymmetric models, are searched for in e^+e^- collisions at centre-of-mass energies between 192GeV and 209GeV at LEP. No evidence for any such particle is found in a data sample of 450 pb^-1. Upper limits on their production cross sections are set and lower limits on their masses are derived in the framework of the Minimal Supersymmetric Standard Model.


Data samples and Monte Carlo simulation
The data used in the present analysis were collected with the L3 detector [9] at LEP and correspond to an integrated luminosity of 450.5pb −1 at √ s = 192 − 209 GeV. Two average centre-of-mass energies are considered in the following: 196 GeV and 205 GeV, with corresponding integrated luminosities of 233.2pb −1 and 217.3pb −1 . SM processes are simulated with the following Monte Carlo (MC) generators: PYTHIA [10] for e + e − → qq(γ), e + e − → Z e + e − and e + e − → ZZ, EXCALIBUR [11] for e + e − → W ± e ∓ ν, KORALZ [12] for e + e − → µ + µ − (γ) and e + e − → τ + τ − (γ), BHWIDE [13] for e + e − → e + e − (γ) and KORALW [14] for e + e − → W + W − . Two-photon interaction processes are simulated using DIAG36 [15] for e + e − → e + e − ℓ + ℓ − and PHOJET [16] for e + e − → e + e − hadrons, requiring at least 3 GeV for the invariant mass of the two-photon system. The number of simulated events for each background process is more than 100 times the data statistics, except for two-photon processes for which the MC statistics amounts to about 7 times that of the data.
Signal events for scalar leptons are generated with the SUSYGEN [17] MC program, for scalar lepton masses, Ml, ranging from 45 GeV up to the kinematic limit, and for values of ∆M varying between 3 GeV and Ml − 1 GeV. For scalar quarks, a generator [18] based on PYTHIA is used. Scalar quark masses vary from 45 GeV up to the kinematical limit and Mχ0 1 varies from 1 GeV to Mt 1 − 3 GeV and to Mb 1 − 7 GeV, for scalar top and bottom respectively. Thẽ t 1 → bℓν andt 1 → bτν channels are generated withν mass ranging from the 43 GeV limit [19] up to Mt 1 − 8 GeV. In total, about 180 samples are generated, each with at least 1000 events.
The response of the L3 detector is simulated using the GEANT package [20]. It takes into account effects of energy loss, multiple scattering and showering in the detector materials and in the beam pipe. Hadronic interactions are simulated with the GHEISHA program [21]. Timedependent detector inefficiencies are monitored during data taking and reproduced in the simulation.
3 Event selection 3.1 Analysis procedure Besides the common signature of missing momentum in the direction transverse to the beam axis, signals from supersymmetric particles are further specified according to the number of leptons or the multiplicity of hadronic jets in the final state.
Signatures of scalar leptons are simple and the final states mostly contain just two acoplanar leptons of the same generation. To account for the three lepton flavours, three different selections are performed. For scalar electrons and muons a pair of electrons or muons is required in the event, respectively, while scalar taus are selected as low multiplicity events with electrons or muons or with narrow jets. Events from thet 1 → cχ 0 1 andb 1 → bχ 0 1 processes contain two high-multiplicity acoplanar jets originated by c or b quarks. In addition, two charged leptons are present when both scalar top quarks decay viat 1 → bℓν.
An optimization procedure is devised [5] which maximizes signal efficiency and background rejection by varying simultaneously all cuts for a given process. The signal topology depends on ∆M and therefore the optimization is repeated for different values of ∆M. Details of the selections performed for each topology are given in the following.

Acoplanar leptons
Scalar leptons are searched for in events with two isolated leptons of the same flavour. The lepton identification and isolation criteria follow those used at lower √ s [22]. An electron is isolated if the calorimetric energy deposition in a 10 • cone around its direction is less than 2 GeV. Muon isolation requires an energy below 2 GeV in the cone between 5 • to 10 • around the muon direction. A tau is isolated if the energy deposition in the cone between 10 • and 20 • around its direction is less than 2 GeV and less than 50% of the tau energy. Furthermore, the energy deposition in a cone between 20 • and 30 • must be less than 60% of the tau energy. The large background from two-photon interactions is rejected with cuts on the lepton transverse momentum, the visible mass, M vis , the transverse missing momentum, P miss T , the energy deposited at low polar angle, E 30 , and the sine of the polar angle of the missing momentum, sin θ miss . Acoplanarity and acollinearity cuts together with upper bounds on the visible energy, E vis , reduce the background from W boson and fermion pair-production. After these cuts, the distributions of selection variables for data and Monte Carlo are in good agreement, as shown in Figure 1a for the energy of the most energetic lepton, E 1 .
The final selections are optimised for each scalar lepton flavour, using a set of parameterized cuts (E vis , P miss T , M vis , E 1 ) together with fixed cuts (acoplanarity, acollinearity and sin θ miss ). The parameterised cuts depend on Z = (∆M/Ml) × E beam , to reflect the dependence of the final state topologies on ∆M and Ml. E beam is the beam energy. The variables used for each selection are described in Reference 5.
The selection efficiencies for scalar lepton pair-production, the number of candidates in data and the SM expectations are given in Table 2 for three ∆M regions.

Single electron
The single-electron analysis requires one or two identified electrons. Cuts on E vis and sin θ miss are applied in order to reject background from two-photon interactions. At least one electron with energy greater than 5 GeV is required. The electron energy has to be less than 65 GeV to reject photon conversion from the e + e − → ννγ process when the two tracks are not resolved. If two electrons are selected, their acoplanarity must be between 10 • and 160 • and the energy of the second electron must be less than 5 GeV to suppress background from W pair-production. To remove events with additional activity in the detector, the difference between the total energy and the energy of the most energetic electron must be less than 5 GeV. In addition, a cut P miss T > 15 GeV is applied. If no second electron of at least 100 MeV is detected, this cut is released to P miss T > 10 GeV. Figure 1b compares data and MC for the energy of the most energetic electron, the remaining background originates from four-fermion final states. Signal efficiencies vary from 3% at ∆M = Mẽ L − Mχ0 1 = 5 GeV up to 60% for ∆M = 60 GeV.

Acoplanar jets
The search for scalar quarks decaying into quarks and neutralino is based on events with two high-multiplicity acoplanar jets. The DURHAM algorithm [23] is used for the clustering of hadronic jets. A common preselection is applied [6] which is based on: E vis , the calorimetric cluster multiplicity, P miss T , E 30 and sin θ miss . After this preselection, the data agree well with the SM expectations, as depicted in Figures 1c and 1d.
Four selections are optimised for scalar top quarks and four for scalar bottom quarks. They depend on ∆M and cover the regions 5 − 10 GeV, 10 − 20 GeV, 20 − 40 GeV and above 40 GeV. Lower cuts on E vis / √ s and P miss T / √ s separate the signal from the two-photon background, whereas an upper cut on E vis / √ s removes events from four-fermion final states. A cut on sin θ miss also rejects the two-photon background. Cuts on the jet widths and on the absolute value of the projection of the total momentum of the jets onto the direction perpendicular to thrust, computed in the transverse plane, further suppress the two-photon as well as W + W − and qq(γ) backgrounds. For the scalar bottom selection, b-quark identification in the final state is enforced by an additional cut on the event b-tagging variable [6], D b−tag .
The expected signal efficiencies at various ∆M values are given in Table 3 together with the observed number of events and the SM background expectations.

Acoplanar jets and leptons
A selection of events with two acoplanar jets and one or two isolated leptons complements the scalar top searches in presence of thet 1 → bℓν decay. Large values of the D b−tag variables are required for the two jets and additional cuts on E vis / √ s reject part of the two-photon and four-fermion events. Lower cuts on the energy of the leptons suppress background from two-photon interactions at low ∆M and the qq(γ) final state at medium ∆M. At high ∆M, an upper cut on the lepton energy reject four-fermion events. This selection covers the ∆M region above the limit Mν > 43 GeV.
The expected signal efficiencies for scalar top detection are given in Table 3 together with data counts and the SM background expectations, for various ∆M values.

Cross section limits
As discussed above and summarized in Table 4, no excess with respect to the Standard Model expectations is observed in the data. Upper limits on the production cross section are therefore derived combining these results with those obtained at lower √ s [5,6]. This combination scales the signal cross sections with √ s and the limits refer to √ s = 205 GeV. Figures 2 and 3 show the 95% confidence level (CL) upper bounds on the production cross sections as a function of the scalar fermion masses and of the neutralino mass. The case of right handed scalar leptons and of the lightest scalar quarks is considered. These limits include [24] the systematics effects discussed below.

Systematic uncertainties
Systematic uncertainties on the signal efficiency for scalar lepton searches and on all background predictions are dominated by Monte Carlo statistics. They are smaller than 5%. The main systematic uncertainties on the scalar quark signal selection efficiency arise from uncertainties on the production mechanism, hadronisation and decay of the scalar quark [6]. These uncertainties are in the range from 7% to 18% for scalar top, with the highest uncertainty in the very low ∆M region. For scalar bottom, the highest uncertainty is about 10% and is observed in the very low and high ∆M regions.

Interpretations in the MSSM
In the MSSM, with Grand Unification assumptions [25], the masses and couplings of the supersymmetric particles as well as their production cross sections are described [2] in terms of five parameters: tan β, the ratio of the vacuum expectation values of the two Higgs doublets, M 2 ≃ 0.81 × m 1/2 , the gaugino mass parameter, µ, the higgsino mixing parameter, m 0 , the common mass for scalar fermions at the GUT scale and A 0 , the trilinear coupling in the scalar fermion sector. We investigate the following MSSM parameter space: The limits on the production cross section for scalar leptons and scalar quarks discussed above are translated into exclusion regions in the MSSM parameter space. To derive these limits, we optimise the event selection for each point in the MSSM parameter space by choosing the combination of selections which provides the highest sensitivity for each process. This sensitivity is derived by calculating at each point the production cross sections and the decay branching fractions of scalar leptons and scalar quarks. For the latter, the mixing angle θ LR is also considered. A point of the MSSM parameter space is excluded if any of these calculated cross sections exceeds its corresponding experimental limit. Mass lower limits are derived as the lowest value for the mass of a particle over all points which are not excluded. The limiting factor towards an absolute limit on the scalar electron mass is the lack of detection efficiency for very small ∆M values. This is overcome, in the constrained MSSM, by using the e + e − →ẽ RẽL process. The searches for acoplanar electrons and single electrons are combined to derive a lower limit on Mẽ R as a function of tan β and for any value of m 0 , M 2 and µ as shown in Figure 5a. For tan β < 1 the mass difference betweenẽ L andẽ R decreases, reducing the sensitivity of the single electron search. As an example, Figure 5b shows the limit as a function of m 0 for a fixed value of tan β. For tan β ≥ 1, the 95% CL lower limit for the lightest scalar electron, independent of the MSSM parameters, is:

Limits on scalar lepton masses
Assuming a common mass for the scalar leptons at the GUT scale, this limit holds for the lightest scalar muon,μ R , as well. Figure 6a shows the excludedt 1 mass region as a function of Mt 1 and Mχ0 1 at cos θ LR = 1 and cos θ LR = 0.57 for thet 1 → cχ 0 1 decay. The second value of the mixing angle corresponds to a vanishing contribution of the Z exchange in the s-channel production. For this decay mode, scalar top masses below 95 GeV are excluded at 95% CL under the assumptions cos θ LR =1 and ∆M = 15 − 25 GeV. For the same values of ∆M and in the most pessimistic scenario of cos θ LR = 0.57, the 95% CL mass limit is 90 GeV. The region in which thet 1 → bWχ 0 1 decay is kinematically accessible and becomes the dominant decay mode, is indicated. This decay is not considered in this analysis. Figure 6b shows the scalar top mass regions which are excluded if the dominant three-body decayt 1 → bℓν is kinematically accessible. Equal branching fractions for the decays into e, µ or τ are assumed and 95% CL mass lower limits are derived as 96 GeV and 93 GeV for cos θ LR = 1 and cos θ LR = 0.57, respectively. The corresponding exclusion limits for the scalar top decaỹ t 1 → bτν are shown in the Figure 6c. Mass lower limits at 95% CL in the range 93 − 95 GeV are obtained, assuming ∆M > 15 GeV. Figure 6d shows the region excluded as a function of Mb 1 and Mχ0 1 considering theb 1 → bχ 0 1 decay for cos θ LR = 1 and cos θ LR = 0.39. The latter value corresponds to a vanishing contribution of the Z exchange in the s-channel production. Scalar bottom masses below 95 GeV are excluded at 95% CL assuming cos θ LR =1 and ∆M = 15 − 25 GeV. For cos θ LR = 0.39, the 95% CL mass lower limit is 81 GeV.

Limits on scalar quark masses
For scalar quarks of the first two generations, the same selection efficiencies are assumed as for thet 1 → cχ 0 1 decay because of the similar event topologies. The cross section limits given in Figure 3a are then interpreted in terms of degenerate scalar quark masses. Figure 7a shows the scalar quark mass lower limits as a function of theχ 0 1 mass. Two scenarios are considered: left-and right-handed scalar quark degeneracy or only right-handed scalar quark production. In the first case, with four degenerate scalar quark flavours, the 95% CL mass limit is 99.5 GeV at for ∆M > 10 GeV. In the case of only right-handed scalar quark production, the 95% CL mass lower limit is 97 GeV. Regions excluded in the hypotheses that all scalar quarks but the scalar top are degenerate are also shown.
Assuming gaugino unification at the GUT scale, the results for the four degenerate scalar quarks are reinterpreted on the plane of the scalar quark and gluino masses, as shown in Figure 7b. In addition, gaugino unification [25] allows a transformation of the absolute limit on M 2 , obtained from the chargino and neutralino [26] as well as scalar lepton searches, into a lower limit on the gluino mass, also shown in Figure 7b. The ISAJET program [27] is used for the calculation of the exclusion contours. For tan β = 4, gluino masses up to about 270−310 GeV are excluded at 95% CL.
In conclusion, no evidence for the production of scalar lepton and quarks is observed in the data set collected by the L3 experiment at LEP. Stringent upper limits on the cross sections for the production of these scalar particles are derived, which correspond to lower mass limits in the MSSM. The L3 Collaboration: Low ∆M  79  84  10  151 138  29  317 270  3  Medium ∆M  19  25  45  46  47  52  146 124  29  High ∆M  50  53  35  108 105  57  122 123  29   Table 2: Results of the scalar lepton analysis: number of observed events, N D , SM background expectations, N SM , and efficiencies, ε, at √ s = 205 GeV for the scalar electron, muon and tau selections at low (Z < 10 GeV), medium (10 GeV < Z < 30 GeV) and high ∆M (Z > 30 GeV) for different values of the scalar lepton masses.      The dark shaded area is excluded by the search for scalar quarks of the first two families, assuming mass degeneracy among different flavours and between left-and right-handed scalar quarks. The light shaded area illustrates indirect limits on the gluino mass, derived from the chargino, neutralino and scalar lepton searches. The regions excluded by the CDF and D0 collaborations [8] are valid for tan β = 4 and µ = −400 GeV. The exclusions obtained by the UA1 and UA2 [28] collaborations are also shown.