Search for Scalar Top and Scalar Bottom Quarks at LEP

Searches for a scalar top quark and a scalar bottom quark have been performed using a data sample of 438 pb-1 at centre-of-mass energies of sqrt(s) = 192 - 209 GeV collected with the OPAL detector at LEP. No evidence for a signal was found. The 95% confidence level lower limit on the scalar top quark mass is 97.6 GeV if the mixing angle between the supersymmetric partners of the left- and right-handed states of the top quark is zero. When the scalar top quark decouples from the Z0 boson, the lower limit is 95.7 GeV. These limits were obtained assuming that the scalar top quark decays into a charm quark and the lightest neutralino, and that the mass difference between the scalar top quark and the lightest neutralino is larger than 10 GeV. The complementary decay mode of the scalar top quark decaying into a bottom quark, a charged lepton and a scalar neutrino has also been studied. The lower limit on the scalar top quark mass is 93.0 GeV for this decay mode, if the mass difference between the scalar top quark and the scalar neutrino is greater than 10 GeV and if the mixing angle of the scalar top quark is zero. From a search for the scalar bottom quark, a mass limit of 96.6 GeV was obtained if the mass difference between the scalar bottom quark and the lightest neutralino is larger than 10 GeV.

h now at University of Liverpool, Dept of Physics, Liverpool L69 3BX, UK i and CERN, EP Div, 1211 Geneva 23 j and Universitaire Instelling Antwerpen, Physics Department, B-2610 Antwerpen, Belgium k now at University of Kansas, Dept of Physics and Astronomy, Lawrence, KS 66045, USA l now at University of Toronto, Dept of Physics, Toronto, Canada m current address Bergische Universität, Wuppertal, Germany n and University of Mining and Metallurgy, Cracow, Poland

Introduction
Supersymmetric (SUSY) extensions of the Standard Model predict the existence of bosonic partners of all known fermions. The scalar top quark (t), which is the bosonic partner of the top quark, may be light because of supersymmetric radiative corrections [1]. Furthermore, the supersymmetric partners of the right-handed and left-handed top quarks (t R andt L ) mix, and the resulting two mass eigenstates (t 1 andt 2 ) have a mass splitting which may be very large due to the large top quark mass. The resulting lighter mass eigenstate (t 1 ),t 1 =t L cos θt +t R sin θt, where θt is a mixing angle, can be lighter than any other charged SUSY particle, and also lighter than the top quark [1]. All SUSY breaking parameters are absorbed in θt and the mass oft 1 .
The scalar bottom quark (b) can also be light if tan β, the ratio of vacuum expectation values of the two Higgs doublet fields, is large. In this case, the analogous mixing between the supersymmetric partners of the right-and left-handed states of the bottom quark (b R and b L ) becomes large, and the resulting two mass eigenstates (b 1 andb 2 ) also have a large mass splitting [2]. The mass of the lighter mass eigenstate (b 1 ) may therefore be within the reach of LEP.
Assuming R-parity [3] conservation and that theχ 0 2 andl ± are heavier than thet 1 , the dominant decay mode of thet 1 is expected to be eithert 1 → cχ 0 1 ort 1 → bνℓ + , whereχ 0 1 is the lightest neutralino,ν is the scalar neutrino, and ℓ is e, µ or τ . The latter decay mode is dominant if it is kinematically allowed. Otherwise the flavour changing two-body decay, t 1 → cχ 0 1 , is dominant except for the small region where mt 1 − mχ0 1 > m W ± + m b 1 . Both of these decay modes (t 1 → cχ 0 1 andt 1 → bνℓ + ) have been searched for. The dominant decay mode of theb 1 is expected to beb 1 → bχ 0 1 . Since the decay widths of these modes are smaller than the QCD energy scale, thet 1 andb 1 produce colourless squark-hadrons before decay. Under the assumption of R-parity conservation,χ 0 1 andν are invisible in the detector. Thus, t 1t1 andb 1b1 events are characterised by two acoplanar jets 2 or two acoplanar jets plus two leptons, with missing energy. The phenomenology of the production and decay oft 1 andb 1 is described in Section 2 of Ref. [4].
The CDF Collaboration has reported lower limit values [5] on thet 1 mass of 89 and 110 GeV (95% C.L.), when the mass difference betweent 1 andχ 0 1 is larger than about 40 and 60 GeV, respectively. These limits were obtained with the assumption thatt 1 → cχ 0 1 . Searches at e + e − colliders are sensitive to smaller mass differences. The first lower limits on thet 1 mass were obtained around the Z 0 peak (LEP1) assumingt 1 → cχ 0 1 [6]. Using part of the higher energy LEP2 data sample, the 95% C.L. lower limit for a mass difference larger than 6 GeV was improved to 83 GeV [9]. Several other squark searches at various centre-of-mass energies ( √ s) have also been performed at LEP [4,7,8,10,11].
For the decay mode oft 1 → bνℓ + the first lower limit on thet 1 mass was obtained at √ s = 161 GeV [7], and successive searches were performed at LEP [4,[8][9][10][11] and the Tevatron. The D0 Collaboration has reported a lower limit [12] on thet 1 mass of 123 GeV (95% C.L.), when the mass difference betweent 1 andν is larger than 40 GeV and the branching fraction to each 1 In this region,t 1 → bχ 0 1 W + becomes dominant through a virtual chargino. This decay mode has not been studied in this paper. 2 Two jets are called 'acoplanar' if they not back-to-back with each other in the plane perpendicular to the beam axis. lepton flavour is the same. A search for the four-body decay mode,t 1 → bχ 0 1 W * + , where the W boson is off shell, was recently performed at LEP and no evidence was reported [11]. In this paper direct searches fort 1 andb 1 using this data sample are reported. The limits shown here have been obtained by combining the results obtained at these new centre-of-mass energies with those previously obtained using the OPAL data at lower √ s [4, 7-9].

The OPAL Detector and Event Simulation
The OPAL detector, which is described in detail in Ref. [13], is a multipurpose apparatus having nearly complete solid angle coverage. The central detector consists of a silicon strip detector and tracking chambers, providing charged particle tracking for over 96% of the full solid angle, inside a uniform solenoidal magnetic field of 0.435 T. A lead-glass electromagnetic calorimeter (ECAL) located outside the magnet coil is hermetic in the polar angle range of | cos θ| < 0.984. The magnet return yoke consisting of barrel and endcap sections along with pole tips is instrumented for hadron calorimetry (HCAL) in the region | cos θ| < 0.99. Four layers of muon chambers cover the outside of the hadron calorimeter. Forward detectors (FD), silicon-tungsten calorimeters (SW) and the gamma-catcher detectors (GC) are located in the forward region (| cos θ| > 0.98) surrounding the beam pipe and provide complete acceptance down to 25 mrad.
Monte Carlo simulation of the production and decays oft 1 andb 1 were performed following [14]. The squark (q) pairs were generated, and the hadronisation process was subsequently performed to produce colourlessq-hadrons and other fragmentation products according to the Lund string fragmentation scheme (JETSET 7.4) [15,16]. The parameters for perturbative QCD and fragmentation processes were optimised using hadronic Z 0 decays measured by OPAL [17]. For the fragmentation ofq, the fragmentation function proposed by Peterson et al. [15,18] was used. Theq-hadron was formed from a squark and a spectator anti-quark or diquark. For thẽ t 1 decaying into cχ 0 1 , a colour string was connected between the charm quark and the spectator. The decaysb 1 → bχ 0 1 andt 1 → bℓ +ν were simulated in a similar manner. One thousand events were generated at each point of a two dimensional grid of spacing of typically 5 GeV steps in (mt 1 , mχ0 1 ) fort 1 → cχ 0 1 , in (mt 1 , mν) fort 1 → bℓ +ν (with equal branching ratios for e, µ and τ ) andt 1 → bτ +ν , and in (mb 1 , mχ0 1 ) forb 1 → bχ 0 1 . Smaller steps were used for the case of small mass differences (∆m = mt 1 − mχ0 1 , mt 1 − mν or mb 1 − mχ0 1 ). The signal samples were generated at √ s=192, 196, 200 and 206 GeV.
The background processes were simulated as follows. The KK2f generator [19] was used to simulate multihadronic (qq(γ)) events, τ + τ − (γ), and µ + µ − (γ) events. Bhabha events, e + e − → e + e − (γ), were generated with the BHWIDE program [20]. Two-photon processes are the most important background for the case of small mass differences, since in such cases signal events have small visible energy and small transverse momentum relative to the beam direction. Using the Monte Carlo generators PHOJET [21], PYTHIA [15] and HERWIG [22], hadronic events from various two-photon processes were simulated in which the invariant mass of the photon-photon system (M γγ ) was larger than 5.0 GeV. Monte Carlo samples for leptonic two-photon processes (e + e − e + e − , e + e − µ + µ − and e + e − τ + τ − ) were generated with the Vermaseren program [23]. The grc4f [24] and KoralW [25] generators were used for all fourfermion processes except for regions covered by the two-photon simulations. All interference effects of the various diagrams are taken into account in these generators. Four-fermion processes in which at least one of the fermions is a neutrino constitute a serious background at large mass differences. The generated signal and background events were processed through the full simulation of the OPAL detector [26], and the same analysis chain was applied as to the data.

Analysis
Since the event topologies oft 1 → cχ 0 1 andb 1 → bχ 0 1 are very similar, the same selection criteria were used (Section 3.1, analysis A). In Section 3.2 (analysis B), the selection criteria fort 1 → bℓ +ν are discussed. These analyses are the same as those in Ref. [9]. Variables used to make the selections, such as the total visible energy and the total transverse momentum, and jet properties, were calculated as follows. First, the four-momenta of the tracks and those of the ECAL and HCAL clusters not associated with charged tracks were summed. Whenever a calorimeter cluster had associated charged tracks, the expected energy deposited by the tracks was subtracted from the cluster energy to reduce double counting. If the energy of a cluster was smaller than the expected energy deposited by the associated tracks, the cluster energy was not used.
The following three preselections, which are common to analyses A and B, were applied first: (1) The number of charged tracks was required to be at least four and the visible mass of the event was required to be larger than 3 GeV.
(2) The energy deposited had to be less than 5,2 and 5 GeV in each side of the SW, FD and GC detectors, respectively, to reduce the background from two-photon processes.
(3) The visible energy in the region of | cos θ| > 0.9 was required to be less than 10% of the total visible energy, and the polar angle of the missing momentum direction, θ miss , was also required to satisfy | cos θ miss | < 0.9 to reduce the two-photon and the qq(γ) background.

Analysis
The experimental signature fort 1t1 (t 1 → cχ 0 1 ) events andb 1b1 events is two jets which are not coplanar with the beam axis. The fragmentation functions oft 1 andb 1 are expected to be hard and the invariant mass of the charm (or bottom) quark and the spectator quark is small, therefore the jets are expected to be narrow and have low invariant masses. The following five selections were applied.
(A1) Events from two-photon processes were largely removed by demanding that the missing transverse momentum, P t , is greater than 4.5 GeV. Fig. 1(a) shows the distribution of P t after the preselection.
(A2) The number of reconstructed jets was required to be exactly two. Jets were reconstructed using the Durham algorithm [27] with the jet resolution parameter of y cut = 0.005(E vis / √ s) −1 , where E vis is the total visible energy. This E vis -dependent y cut parameter was necessary for good jet reconstruction over a wide range of mt 1 , mb 1 and mχ0 1 , and the distribution of the number of reconstructed jets is shown in Fig. 1(b). Both reconstructed jets were required to contain at least two charged particles to reduce the τ + τ − background.
(A3) The acoplanarity angle, φ acop , is defined as π minus the azimuthal opening angle between the directions of the two reconstructed jets. To ensure the reliability of the calculation of φ acop , both jet axes were required to have a polar angle satisfying | cos θ jet | < 0.95. The value of φ acop was required to be larger than 20 • .
(A4) Softness, S, was defined as where M 1 and M 2 are the invariant masses of the two reconstructed jets, and E 1 and E 2 are the energies of the jets. The signal events have low values of S, whereas two-photon events which pass the acoplanarity cut have relatively large values [8]. It was required that 1.5 × S < (P t − 4.5), where P t is given in units of GeV.
(A5) The arithmetic mean of the invariant masses of the jets,M jet , was required to be smaller than 8 GeV. When the invariant mass of the event, M vis , was larger than 65 GeV, a harder cut,M jet < 5 GeV, was applied to reduce background from Weν events. Fig. 1(c) shows theM jet distributions for data, the simulated background processes and typicalt 1t1 events. As shown in this figure, jets fromt 1 are expected to have low invariant masses.
The numbers of events remaining after each cut are listed in Table 2. The table also shows the corresponding numbers of simulated events for background processes. After all cuts, 13 events were observed in the data, which is consistent with the expected number of background events of 19.8±2.2. Fig. 1(d) shows the E vis distribution after all selections were applied.
The efficiencies for botht 1t1 andb 1b1 events are 30-60% if the mass difference betweeñ t 1 (b 1 ) andχ 0 1 is larger than 10 GeV. A modest efficiency of about 20% is obtained for a mass difference of 5 GeV fort 1t1 events. An additional loss of 3% (relative) arises from beam-related background in SW, FD and GC, which was estimated using random beam crossing events.  Table 2: Numbers of events remaining after each cut for various background processes are compared with data for analysis A. The simulated background processes were normalised to the integrated luminosity of the data. The errors due to Monte Carlo statistics are also shown. Efficiencies for three simulated event samples ( √ s = 206 GeV) oft 1t1 andb 1b1 are also given.

Analysis B:t 1 → bℓν
The experimental signature fort 1t1 (t 1 → bℓν) events is two acoplanar jets plus two leptons with missing transverse momentum. The momenta of the leptons and the missing transverse momentum depend strongly on the mass difference betweent 1 andν. To obtain optimal performance, two sets of selection criteria (analyses B-L and B-H) were applied for small and large mass differences, respectively.
The numbers of events remaining after each cut are listed in Tables 3 and 4. The tables also show the corresponding numbers for the simulated background processes.

Small mass difference case
For the case of a small mass difference (∆m ≤ 10 GeV), the following four selection criteria were applied. Lepton identification was not used in this analysis.
(B-L1) The event missing transverse momentum, P t , was required to be greater than 5 GeV.
(B-L2) The number of charged tracks was required to be at least six, and the number of reconstructed jets was required to be at least four, since the signal would contain two hadronic jets plus two isolated leptons. Jets were reconstructed using the Durham algorithm [27] with the jet resolution parameter y cut = 0.004. Figure 2(a) shows the distribution of the number of reconstructed jets for the data, the simulated background processes and typical t 1t1 events.
(B-L3) To examine the acoplanarity of the remaining events, the whole event was reconstructed as two jets using the Durham algorithm. To ensure a good measurement of the acoplanarity angle, | cos θ jet | < 0.95 was required for both reconstructed jets. Finally, the acoplanarity angle, φ acop , between these two jets was required to be greater than 15 • . Fig. 2(b) shows the φ acop distributions.
(B-L4) The total visible energy, E vis , was required to be smaller than 60 GeV to reject fourfermion events. As shown in Fig. 2 Table 3: Numbers of events remaining after each cut for various background processes are compared with data for analysis B-L. The simulated background processes were normalised to the integrated luminosity of the data. The errors due to Monte Carlo statistics are also shown. Efficiencies for two simulated samples oft 1t1 are also given. In these samples, produced at √ s = 206 GeV, the branching fractions to each lepton flavour are assumed to be the same.
Five events were observed in the data after all the cuts, which is consistent with the number of expected background events (5.0±1.4), mainly from two-photon processes. The detection efficiencies are 30-40% if the mass difference betweent 1 andν is 10 GeV, and if the branching fraction to each lepton flavour is the same. Even if the branching fraction into bτ +ν τ is 100%, the efficiencies are 25-35%.

Large mass difference case
The selection criteria for a large mass difference (∆m > 10 GeV) are as follows: (B-H1) The event missing transverse momentum, P t , was required to be greater than 6 GeV.
(B-H2) The number of charged tracks was required to be at least six, and the number of reconstructed jets was required to be at least three. Jets were reconstructed with the same jet resolution parameter (y cut = 0.004) as in (B-L2).
(B-H3) The same selection as (B-L3) was applied on the φ acop variable to reject qq(γ) events.
(B-H4) A candidate event was required to contain at least one lepton, since a signal event would contain two isolated leptons. The selection criteria for leptons are given in Ref. [8].
(B-H5) The invariant mass of the event excluding the most energetic lepton, M hadron , was required to be smaller than 60 GeV in order to reject W + W − → νℓqq ′ events. As shown in Fig. 3(a), a large fraction of four-fermion events was rejected using this requirement. Furthermore the invariant mass excluding all identified leptons was required to be smaller than 40 GeV.  Table 4: Numbers of events remaining after each cut for various background processes are compared with data for analysis B-H. The simulated background processes were normalised to the integrated luminosity of the data. The errors due to Monte Carlo statistics are also shown. Efficiencies for three simulated samples oft 1t1 are also given. In these samples, produced at √ s = 206 GeV, the branching fractions to each lepton flavour are assumed to be the same.
(B-H6) Finally, the visible mass of the event, M vis , must be smaller than 80 GeV to reduce W + W − background events in which one of W ± 's decays into τ ν and the other into qq ′ (g). If one jet from qq ′ (g) was misidentified as a tau lepton, this event could pass through the previous cut (B-H5). Fig. 3(b) shows the M vis distributions.
Seven candidate events were observed in the data, which is consistent with the number of expected background events (6.3 ± 1.1). The dominant background arises from four-fermion processes. The detection efficiencies are 30-60%, if the mass difference between thet 1 andν is 10 GeV, and if theν is heavier than 30 GeV. The detection efficiencies fort 1 were found to be slightly smaller for the case where it decays purely into bτ +ν τ than for the case where the branching fraction to each lepton flavour is assumed to be the same.

Results
The observed number of candidate events in each case is consistent with the expected number of background processes. Since no evidence fort 1t1 andb 1b1 pair-production has been observed, lower limits on mt 1 and mb 1 are calculated. The results shown here have been obtained by combining the results obtained at these new centre-of-mass energies with those previously obtained using the OPAL data at lower √ s [4,[7][8][9].
The systematic errors on the expected number of signal and background events were estimated in the same manner as in the previous paper [8]. The main sources of systematic errors on the signal are uncertainties in thet 1 andb 1 fragmentation (5-15%) and in Fermi motion of the spectator quark (3-10%). The main sources of systematic errors on the background are uncertainties in the generation of four-fermion processes (5%). The background from four-fermion processes evaluated with the grc4f and KoralW generators agreed within the statistical error, but the small difference was conservatively taken as a systematic error. The limited statistics of the two-photon Monte Carlo samples also give rise to a sizable systematic error. Detailed descriptions are given in Ref. [8]. Systematic errors are taken into account when calculating limits [28]. Figure 4(a) shows the 95% C.L. excluded regions in the (mt 1 , mχ0 1 ) plane fort 1 → cχ 0 1 . In this figure there is a triangular region of mt 1 − mχ0 1 > m W ± + m b , in whicht 1 → bχ 0 1 W + (on shell) through a virtual chargino becomes dominant even if the chargino is heavy. This region is not excluded. Figures 5(a) and (b) show the 95% C.L. excluded regions in the (mt 1 , mν) plane for t 1 → bℓν (ℓ= e,µ,τ ) andt 1 → bτ +ν τ , respectively. The branching fraction to each lepton flavour ℓ + depends on the composition of the lightest chargino [4]. As the chargino becomes more Higgsino-like, the branching fraction into bτ +ν τ becomes large. In the limit that the chargino is a pure Wino state, the branching fraction to each lepton flavour is the same. Two extreme cases in which the branching fraction to each lepton flavour is the same, or the branching fraction into bτ +ν τ is 100%, were considered here. The 95% C.L. mass bounds oft 1 are listed in Table 5 for two values of θt. Assuming that t 1 decays into cχ 0 1 , and the mass difference betweent 1 andχ 0 1 is greater than 10 GeV,t 1 is found to be heavier than 97.6 GeV for θt = 0.0. A lower limit of 95.7 GeV is obtained even ift 1 decouples from the Z 0 boson (θt=0.98 rad), which approximately minimizes the crosssection. Whent 1 decays into bℓν, the lower limit on mt 1 is 96.0 GeV for the zero mixing angle case, assuming that the mass difference betweent 1 andν is greater than 10 GeV and that the branching fraction to each lepton flavour is the same.  Table 5: The excluded mt 1 region at 95% C.L. (∆m = mt 1 − mχ0 1 or mt 1 − mν).
The 95% C.L. excluded regions in the (mb 1 , mχ0 1 ) plane are shown in Fig. 4(b) for two cases θb= 0 and 1.17 rad. The numerical mass bounds are listed in Table 6 for two values of θb. The lower limit on theb 1 -mass is found to be 96.9 GeV, if ∆m is greater than 10 GeV and θb = 0.0. If theb 1 decouples from the Z 0 boson (θb=1.17 rad), the lower limit is 85.1 GeV. Since the electromagnetic charge ofb 1 is half that oft 1 , the coupling between γ andb 1 is weaker than between γ andt 1 . Therefore the production cross-section ofb 1b1 is strongly suppressed when theb 1 decouples from the Z 0 boson.

Summary and Conclusion
A data sample of 437.6 pb −1 collected using the OPAL detector at √ s =192-209 GeV has been analysed to search for pair production of the scalar top quark and the scalar bottom quark predicted by supersymmetric theories, assuming R-parity conservation. No evidence was found above the background level expected from the Standard Model.
The 95% C.L. lower limit on the scalar top quark mass is 97.6 GeV if the mixing angle of the scalar top quark is zero. Even if thet 1 decouples from the Z 0 boson, a lower limit of 95.7 GeV is obtained. These limits were estimated assuming that the scalar top quark decays into a charm quark and the lightest neutralino and that the mass difference between the scalar top and the lightest neutralino is larger than 10 GeV.
Assuming a relatively light scalar neutrino (mν ≤ mt 1 − m b ), the complementary decay mode, in which the scalar top quark decays into a bottom quark, a charged lepton and a scalar neutrino, has also been studied. If the mass difference between the scalar top quark and the scalar neutrino is greater than 10 GeV and if the mixing angle of the scalar top quark is zero, the 95% C.L. lower limit on the scalar top quark mass is 96.0 GeV. This limit is obtained assuming that the branching fraction to each lepton flavour is the same. If the branching fraction to the tau lepton is 100%, a lower limit of 95.5 GeV is obtained.
The lower limit on the light scalar bottom quark mass is found to be 96.9 GeV, assuming that the mass difference between the scalar bottom quark and the lightest neutralino is greater than 10 GeV and that the mixing angle of the scalar bottom quark is zero. When the scalar bottom quark decouples from the Z 0 boson, a lower limit of 85.1 GeV is obtained. These limits are significantly improved with respect to the previous OPAL results [9], and are the best limits published to date.     Figure 4: (a) The 95% C.L. excluded regions in the (mt 1 , mχ0 1 ) plane assuming thatt 1 decays into cχ 0 1 . The solid line shows the limit for zero mixing angle oft 1 , and the dotted line shows the limit for a mixing angle of 0.98 rad (t 1 decouples from the Z 0 boson). The dash-dotted straight line shows the kinematic limit for thet 1 → cχ 0 1 decay. In the triangular region of mt 1 − mχ0 1 > m W ± + m b , the decayt 1 → bχ 0 1 W + (on shell) through a virtual chargino becomes dominant. This region is not excluded. (b) The 95% C.L. excluded regions in the (mb 1 , mχ0 1 ) plane, assuming thatb 1 decays into bχ 0 1 . The solid line shows the limit where the mixing angle ofb 1 is assumed to be zero, and the dotted line shows the limits for a mixing angle of 1.17 rad (b 1 decouples from the Z 0 boson). The singly-hatched regions in (a) and (b) are excluded by the CDF Collaboration [5].  Figure 5: The 95% C.L. excluded regions in the (mt 1 , mν) plane assuming that thet 1 decays into bℓν; (a) the branching fraction to each lepton flavour is the same; (b)t 1 always decays into bτν τ . The solid lines show the limits where the mixing angle oft 1 is assumed to be zero, and the dotted lines show the limits for a mixing angle of 0.98 rad (decoupling case). The cross-hatched region has been excluded by measurements of the Z 0 invisible decay width at LEP1 [29], and the dash-dotted diagonal line shows the kinematic limit for thet 1 → bℓν decay. The singly-hatched region in (a) is excluded by the D0 Collaboration [12].