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-ofmass energies between 192 and 209 GeV at LEP. No evidence for any such particle is found in a data sample of 4 −1. Upper limits on their production cross sections are set and lower limits on their masses are derived in the framewo Minimal Supersymmetric Standard Model.  2003 Published by Elsevier B.V. Open access under CC BY license. 40 L3 Collaboration / Physics Letters B 580 (2004) 37–49


Introduction
The minimal supersymmetric extension of the Standard Model (MSSM) [1,2] postulates a scalar partner,f L,R , for each weak eigenstate of Standard Model (SM) fermions f L,R . Generally, the left,f L , and right, f R , eigenstates mix to form mass eigenstates. This mixing is an unitary transformation of thef R andf L states, parameterised by a mixing angle, θ LR . Since the off-diagonal elements of the sfermion mass matrix are proportional to the SM partner mass, the mixing is expected to be relevant only for scalar fermions of the third family: the scalar top,t L,R , the scalar bottom,b L,R , and the scalar tau,τ L,R . The lightest scalar quarks are denoted ast 1 andb 1 .
The R-parity is a quantum number which distinguishes SM particles from supersymmetric particles. If R-parity is conserved, supersymmetric particles are pair-produced and the lightest supersymmetric particle, assumed hereafter to be the lightest neutralino, χ 0 1 , is stable. In addition, theχ 0 1 is weakly-interacting and hence escapes detection. R-parity conservation is assumed in the following, which implies that the decay chain of pair-produced supersymmetric particles always contains, besides the relevant SM particles, at least two invisible neutralinos. The typical signature of the production of scalar leptons and scalar quarks is the presence of leptons or jets in events with missing energy and momentum. The difference between the masses of the scalar fermion and theχ 0 1 , M, determines the kinematic of the event.
The pair-production of scalar fermions in e + e − interactions proceeds through the s-channel γ or Z exchange. For scalar electrons, the production cross section is typically enhanced by the t-channel exchange of a neutralino. 1  At LEP energies, all scalar fermions, but the scalar top, decay into their SM partners mainly viaf → χ 0 1 f. Cascade decays, such asf →χ 0 2 f →χ 0 1 Z * f are also possible and may dominate in some regions of the MSSM parameter space. According to the values of the scalar top mass and couplings, four channels can become dominant among the possible scalar top decays:t 1 → cχ 0 1 , bν ˜ , b ν and bχ + 1 . The additional decay into bχ 0 1 ff which can originate six-fermion final states is not considered [3]. This topology is indirectly covered by searches in the framework of Rparity violation, which revealed no excess [4]. In the following, for thet →νb decay, scalar neutrinos are assumed to be lighter than charged scalar leptons. For this decay, M refers to the mass difference between the scalar top and scalar neutrino masses.
The supersymmetric partners of the right-handed leptons,˜ R , are generally expected to be lighter than their left-handed counterparts and are considered in the following. If the mass difference between the righthanded scalar electron and the lightest neutralino is very small the search for e + e − →ẽ RẽR has little sensitivity. The e + e − →ẽ RẽL process is then considered. The left-handed scalar electron, too heavy to be produced in pairs, decays into an energetic electron, while the electron from the right-handed scalar electron decay remains often invisible, leading to a 'single electron' topology.
Scalar leptons and scalar quarks are searched for at centre-of-mass energies, √ s, up to 209 GeV. The present study supersedes previous L3 limits on scalar lepton [5] and scalar quark production [6] obtained at lower √ s. Searches for scalar fermions were also reported by other experiments at LEP [7] and at the TEVATRON [8]. Table 1 summarises the investigated processes and decay modes together with the studied topology.

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 450.5 pb −1 at √ s = 192-209 GeV. Two average centre-of-mass energies are considered in the following: 196 and 205 GeV, with corresponding integrated luminosities of 233.2 and 217.3 pb −1 .
Signal events for scalar leptons are generated with the SUSYGEN [17] MC program, for scalar lepton masses, M˜ , ranging from 45 GeV up to the kinematic limit, and for values of M varying between 3 GeV and M˜ − 1 GeV. For scalar quarks, a generator [18] based on PYTHIA is used. Scalar quark masses vary  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  Table 3 Results of the scalar quark analysis: number of observed events, N D , SM background expectations, N SM , and efficiencies, ε, for a 90 GeV scalar quark at very low (5-10 GeV), low (10-20 GeV), medium (20-40 GeV) and high M ( 40 GeV) at √ s = 205 GeṼ    from 45 GeV up to the kinematical limit and Mχ0 1 varies from 1 GeV to M˜t 1 − 3 GeV and to Mb 1 − 7 GeV, for scalar top and bottom, respectively. Thẽ t 1 → b ν andt 1 → bτν channels are generated withν mass ranging from the 43 GeV limit [19] up to M˜t 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]. Time-dependent detector inefficiencies are monitored during data taking and reproduced in the simulation.

Analysis procedure
Besides the common signature of missing momentum in the direction transverse to the beam axis, signals from supersymmetric particles are further speci- 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 → b ν.
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 • and 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 acollinear- ity 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 Fig. 1(a) 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/M˜ ) × E beam , to reflect the dependence of the final state topologies on M and M˜ . E beam is the beam energy. The variables used for each selection are described in Ref. [5].
The selection efficiencies for scalar lepton pairproduction, 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. Fig. 1(b) 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 highmultiplicity 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 Fig. 1(c) and (d).
Four selections are optimised for scalar top quarks and four for scalar bottom quarks. They depend on M and cover the regions 5-10, 10-20, 20-40 GeV and above 40 GeV. Lower cuts on E vis / √ s and P miss T / √ s separate the signal from the twophoton 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 → b ν 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. Figs. 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 neu-tralino 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 frac-tions 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 Fig. 5(a). For tan β < 1 the mass difference betweenẽ L andẽ R decreases, reducing the sensitivity of the single electron search. As an example, Fig. 5(b) shows the limit as a function of m 0 for a fixed value of tan β. For tanβ 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.  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 Collaborations [28] are also shown. 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. Fig. 6(b) shows the scalar top mass regions which are excluded if the dominant three-body decayt 1 → b ν 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 and 93 GeV for cos θ LR = 1 and cosθ LR = 0.57, respectively. The corresponding exclusion limits for the scalar top decayt 1 → bτν are shown in Fig. 6(c). Mass lower limits at 95% CL in the range 93-95 GeV are obtained, assuming M > 15 GeV. Fig. 6(d) 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 cosθ 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 Fig. 3(a) are then interpreted in terms of degenerate scalar quark masses. Fig. 7(a) 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 Fig. 7(b). 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 Fig. 7(b). 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.