DELPHI Collaboration DELPHI PHYS 611. Search for neutralinos, scalar leptons, and scalar top. R. Keranen. University of Bergen

Transcription

1 DELPHI Collaboration DELPHI PHYS 6 9 April, 996 Search for neutralinos, scalar leptons, and scalar top quarks in e + e? interactions at p s = 3GeV? 36GeV R. Keranen University of Bergen P. Andersson, K. Hultqvist, A. Lipniacka University of Stockholm Abstract Using the data accumulated by DELPHI during the November 995 LEP run at 3 GeV { 4 GeV, searches have been carried out for events with jets or leptons in conjuction with missing momentum. The results of the searches are interpreted in terms of limits on the production of neutralinos, scalar top quarks, and scalar leptons.

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3 Introduction Supersymmetric partners of neutral gauge bosons (gauginos) and neutral Higgs states (higgsinos) are postulated in supersymmetric extensions of the Standard Model []. In the Minimal Supersymmetric extension (the MSSM) these are realized in four neutralino mass states, ~ i ; i = ; 4, which are linear superpositions of the gauge and Higgs eigenstates, and which are expected to be produced at LEP in ~ i ~ j pairs. The lightest neutralino, ~, is usually assumed to be the lightest supersymmetric particle. Under the assumption of R-parity conservation ~ is stable and undetectable because of its weak interactions. Channels such as ~ ~ 2 or ~ 2 ~ 2 are visible with the second lightest neutralino, ~ 2, decaying into ~ and a fermion-antifermion pair or a photon, giving events characterised by missing energy and momentum. This would be most striking in the case of ~ ~ 2, which is also kinematically favoured. At LEP, limits have been set, based on data taken at the Z resonance [2]. Neutralinos are produced through s-channel Z exchange and t-channel exchange of scalar electrons. The present analysis is primarily sensitive to higgsino dominated light neutralinos which would have large cross sections because of the large coupling between the Higgsino and Z. In the MSSM, with a common gaugino mass at the GUT scale, such neutralinos appear when the gaugino mass parameter, M 2, is large compared to the Higgs supereld mass parameter jj. It is noteworthy that in this case there is little dependence on the common MSSM scalar mass term m, i.e. the cross section depends on three parameters: M 2,, and tan. Scalar leptons (sleptons) would be pair-produced through Z / exchange in the s- channel and, in the case of selectrons, by t-channel neutralino exchange. In the MSSM the latter contribution can enhance the selectron production for some regions of parameters space. Due to the small electron and muon masses, mixing between the scalar partners of the two chirality states is expected to be negligible, and the expected nal states are are ~`R~`R, ~`L~`L, ( ~` = ~; ~e). Because of the t-channel contribution the channel ~e L ~e R may also have a signicant cross section even if there is no selectron mixing. Sleptons are expected to decay according to ~`! `~, giving events with two acoplanar leptons. The supersymmetric partner of the top quark (the stop, ~t) could be the lightest scalar quark. Because of the large mass of the top quark, the scalar partners of its two chirality states, ~t R and ~t L, are expected to mix [3], and the lightest physical state could be significantly below the typical mass of scalar quarks, hence accessible at LEP. In the MSSM, a suciently light ~t state could explain, through virtual corrections, the large measured partial width?(z! bb) as compared to the standard model prediction [5]. If kinematically allowed, ~t is expected to decay into b~ +, and if this channel is closed into c~, in both cases with a branching ratio close to unity. The present analysis considers the c~ decay, which leads to events with two jets, missing energy and momentum, similar to the ~ ~ 2 nal state. This paper presents a search for scalar top (stop) quark, neutralinos, and sleptons in the data accumulated by DELPHI in the high energy run of LEP in November 995. The paper is organised as follows: Section 2 gives a brief description of the detector, section 3 describes the real data and the simulated signal and background samples, while section 4 describes the analyses applied for the dierent topologies. Section 5 gives the results of the selections and their interpretation. Section 6, nally, contains the conclusions.

4 2 Detector description A summary of the properties of the DELPHI detector [4] relevant to this analysis is presented below. Charged particle tracks were measured in a system of cylindrical tracking chambers immersed in.2 T solenoidal magnetic eld. These were: the Microvertex Detector (VD), the Inner Detector (ID), the Time Projection Chamber (TPC), and the Outer Detector (OD). In addition two planes of drift chambers aligned perpendicular to the beam axis (Forward Chambers A and B) tracked particles in the forward and backward directions, covering polar angles < < 33 and 47 < < 69. The VD consists of three cylindrical layers of silicon detectors, at radii 6.3 cm, 9. cm and. cm. These measured R coordinates transverse to the beam over a length of 24 cm along the beam. The closest (6.3 cm) and the outer (. cm) layers contain doublesided detectors to also measure RZ coordinates. The polar angle coverage of the VD is from 25 to 55 for the closest and from 44 to 36 for the outer layer. The ID is a cylindrical drift chamber (inner radius 2 cm and outer radius 22 cm) covering polar angles between 5 and 65. The TPC, the principal tracking device of DELPHI, is a cylinder of 3 cm inner radius, 22 cm outer radius and has a length of 2.7 m. Each end-plate is divided into 6 sector plates, with 92 sense wires used for the de/dx measurement and 6 circular pad rows used for 3 dimensional space-point reconstruction. The OD consists of 5 layers of drift cells at radii between 92 cm and 28 cm, covering polar angles between 43 and 37. The average momentum resolution for the charged particles in hadronic nal states is in the range p=p 2 ' : to : (GeV/c)?, depending on which detectors are included in the track t. The electromagnetic calorimetry consist of the High density Projection Chamber (HPC) covering the barrel region of 4 < < 4, the Forward Electromagnetic Calorimeter (FEMC) covering < < 36 and 44 < < 69 and the STIC, a scintillator tile calorimeter which as a continuation of FEMC goes down to.78 both in a forward and in backward region. The 4 taggers are a series of single layer scintillatorlead counters used to veto electromagnetic particles otherwise missed in a region between HPC and FEMC. The hadron calorimeter (HCAL) covers 98 % of the solid angle. The total photon detection eciency measured with the LEP data is above 99 %. 3 Data samples The integrated luminosities accumulated were 2.9 pb? and 3. pb?, at centre-of-mass energies of 3.4 GeV and 36.3 GeV, respectively. In addition, a small amount of data (.3 pb? ) was taken at 4 GeV. The total number of recorded events in the e + e?! qq() channel is about 7. The signal and background events were generated using dierent programs, relying on JETSET 7.4 [6] for quark fragmentation. SUSYGEN [7] was used to generate neutralino events and to calculate cross sections and branching ratios. It has been veried to agree with the results of ref [8]. SUSYGEN was also used to generate the ~`+~`? signals, while the ~t ~t signal was generated with a program based on the BASES/SPRING package [9], with gluon radiation treated according to [], and intermediate ~t -hadron fragmentation [7]. In this channel SUSYGEN was used as a cross check. 2

5 The background processes e + e?! f f(n) and processes leading to four-fermion nal states (Z =) (Z =), W + W?, We e, and Z e + e? were generated using PYTHIA [6]. The cut on the invariant mass of the (Z =) in (Z =) (Z =) process was reduced from its default value of 2 GeV=c 2 down to 3 GeV=c 2, in order to determine the background from low mass f f pairs. The calculation of the four-fermion background was veried using the program EXCALIBUR [], which consistently takes into account all amplitudes leading to a given four-fermion nal state. EXCALIBUR does not, however, include the transverse momentum of initial state radiation. Two-photon interactions were generated using TWOGAM [2]. The number of background events simulated was similar to, or in most cases several times larger than, the number expected. 4 Event Selection 4. Two jets and missing momentum This topology would result from production of ~ ~ 2 with hadronic decays of ~ 2, or from ~t ~t production. Charged particles were selected as reconstructed tracks having momentum above MeV=c, impact parameters below 5 cm in the transverse plane and 8 cm in the beam direction, measured length greater than 3 cm or at least one associated VD point. In the forward region, a track element from the ID, the VD, or the TPC was required, in addition. Neutral particles were selected as calorimetric energy clusters not associated with charged tracks, and with an energy above MeV=c 2. The following consecutive cuts were applied to the data in order to extract a possible signal:. The number of charged tracks should be greater than four, and there should be at least one track originating from within 2 m from the interaction point in the R plane. These cuts select e + e? interactions giving multihadronic nal states. Invariant mass distributions of the samples of hadronic events selected from data and simulation are shown in gure. Subsamples of events without initial state radiation and of radiative Z events are shown in separate distributions. 2. The total energy of particles with polar angle below 3 was required to be smaller than 2% of the total energy, and the polar angle of the missing momentum should satisfy < p miss < 7. The transverse missing momentum should exceed 5 GeV=c. These cuts serve to remove two-photon interactions and radiative Z events. 3. The visible invariant mass should be smaller than 55% of the centre-of-mass energy, and the missing mass should exceed 35% of that energy. This suppresses mainly e + e?!qq() events. 3

6 4. The number of jets reconstructed using the JADE algoritm [3] with a cut on minimal invariant mass of two jets y min = GeV=c 2 should not exceed two. There should be no isolated neutral particle with energy greater than 5 GeV and for which a double cone around the particle momentum with opening angles between 5 and 25 contains less than 2.5 GeVof additional energy. Similarly there should be no isolated charged particle with energy greater than GeV and energy in the double cone below 5 GeV. These cuts exclude multijet events, events with radiated photons registered in the detector and events with decays. The parameter choice in the jet denition allows for the gluon emission characteristic of scalar particles [4], thus giving a high eciency for scalar quarks. 5. In order to eliminate the residual background from two-photon events and Z events the acoplanarity angle between the jets multiplied by the minimum sin jet, was required to be larger than. Two events in the real data satisfy the selection criteria. One of them is an e + e? interaction in coincidence with a cosmic ray particle traversing the calorimeters, reconstructed as additional neutral showers. When neglecting these showers, as appropriate, the event does not satisfy the selection criteria. The observation of this event is in agreement with the expected rate of coincidences, while the estimated probability for a signal event to overlap with a cosmic particle is below a few per mille. This event is not considered further. The second event is a qq nal state, where the hard photon is partially reconstructed, but clearly registered, by the veto counters and the HCAL in the region between the FEMC and HPC acceptances. The appearance of one such an event in the selection is consistent with the Monte Carlo simulation of the qq process, while hard photons are not expected in signal events. In conclusion, the data contain no events with acoplanar jets due to hadronic decays of heavy states in association with invisible particles. 4.2 Multijets, or jets and a pair of isolated leptons, with missing energy These channels could signal pair production of the second lightest neutralino according to e + e?! ~ 2 ~ 2 with one ~ 2 decaying into ~ qq and the other into either ~ qq or ~ `+`?. The charged and neutral particles were selected as in section 4., and the same event variables were used. The signal consists of multijet events (qqq q ) or hadronic events with isolated lepton tracks (qq`+`?), in association with missing energy and momentum from the escaping neutralinos. Such events were selected as follows :. The number of charged tracks should be greater than four, the multiplicity including neutrals should exceed six, and there should be at least one track originating from the interaction point. These criteria select multihadronic e + e? interactions. 2. The total energy of particles within 3 of the beam axis was required to be less than 2% of the total visible energy. Furthermore, the missing momentum was required to be outside this polar angle range. These cuts remove two photon events and radiative Z events. 4

7 3. If the event contained no isolated particle (charged or neutral) above 5 GeVand with the energy inside the double cone of section 4. below 3 GeV, the following set of cuts were used (qqq q selection) : { the transverse missing momentum should exceed 5 GeV=c, and { the visible invariant mass should be less than 65% of the centre-of-mass energy, the missing mass should exceed 55% of that energy, and { the scaled acoplanarity angle (see subsection 4.) should be more than 6. If there was such an isolated particle the following set of cuts were used instead (qq`+`?selection) : { there should be at least one isolated charged track in the polar angle interval j cos()j < :8 reconstructed in the TPC and with more than % of the total visible energy. The energy inside the double cone for this track was required to be below GeV, and { the transverse missing momentum should exceed 2.5 GeV=c, and { the visible invariant mass should be less than 65% of the centre-of-mass energy (To reject background this cut was reduced to 35% for events with ve or fewer charged particles), and { the scaled acoplanarity angle (see subsection 4.) was required to be greater than. One event satises these criteria (the qqq q selection). This is the qq event described in section 4.. No ~ 2 ~ 2 event was found. 4.3 Two leptons and missing momentum This topology could arise from ~ ~ 2 production with ~ 2! ~ `+`? or from ~e + ~e? production with subsequent decay : ~e! e ~. After a selection of charged and neutral particles similar to that of the previous section, events were selected by requiring two charged particles with 2 < < 6, in association with missing energy in excess of 55 GeV, and satisfying the following: It was required that for both tracks at least 4 pad signals in the TPC had been used in the reconstruction. The relative momentum errors (p=p) were required to be below.5, and the reconstructed impact parameters of the tracks in the r' and rz planes had to be smaller than 5 cm. At least one of the tracks should be identied as an electron or a muon [4]. There should be no more than 2 GeV of energy in charged tracks reconstructed within of any of the two selected track. Figure 2 shows a comparison of the missing mass and acoplanarity distributions in real data and in the simulated background sample for events where two such tracks were found. The following selection was then applied: 5

8 The total multiplicity of the event was required to be less than eight, and the transverse momentum of the pair of tracks had to be greater than 6 GeV=c if the missing energy of the event was below GeV and 4 GeV=c if the missing energy of the event was above GeV. In addition, the missing transverse momentum of the event should be larger than 4 GeV=c. The energy carried by neutral particles had to be smaller than 2 GeV, and the energy deposited in the STIC should be smaller than 5 GeV. These cuts reject background from e + e?!qq() events and two-photon interactions. The acolinearity and acoplanarity between the two selected particles was required to exceed 2 and 8, respectively, and the invariant mass of the pair had to be less than 7 GeV=c 2. These cuts reject e + e?! e + e? events One event passed the selection described above. The nal state consists of an e + e? pair with an invariant mass of 4.6 GeV=c 2 a scalar sum of momenta of 29.6 GeV=c. The large acoplanarity (7 ) and the large missing p T (5 GeV=c) are not consistent with the expectation for the two photon background. However, the event is consistent with the background of.6.3 events expected from the four-fermion process e + e?! `+`?. 4.4 Four leptons and missing energy Events of this type could be the result of ~ 2 ~ 2 production followed by the decay ~ 2! ~ `+`?. The cuts used were similar to those of section 4.3: It was required that there be at least three and not more than four isolated tracks with 2 < < 6. For these tracks it was required that at least four TPC pad signals had been used in the reconstruction, and that there was at least one associated hit in the VD. The invariant mass of any track pair should be less than 9 GeV=c 2, and at least two of the tracks should be identied leptons. In addition, the missing energy of the event was required to exceed 5 GeV, the missing transverse momentum should be greater than 3 GeV=c, and the total multiplicity was required to be smaller than. The energy carried by neutral particles was required to be smaller than 3 GeV. No events which satised these requirements were found. 5 Results Table summarises the number of accepted events in the data for the dierent selections. Also shown are the expected numbers of events from the dierent background channels. 5. Results on neutralino production To determine the eciency as a function of the neutralino masses events were generated using SUSYGEN for dierent values of M ~ and M ~?M ~ 2, and for dierent decay channels. A total of 24 ~ ~ 2 events were passed through the DELPHI full detector simulation [4] and event reconstruction programs. The selections described above were then applied to these events. Table 2 shows the selection eciencies as determined by this procedure for three ~ 2 decay modes. 6

9 qq `+`? `+`?`+`? qq`+`?,qqqq Obs. events Total background Z =! f f(n) f ff f events ! +? ! e + e? ; +?.8.8! hadrons Table : Number of observed events in the dierent search channels. Also shown is the total number of expected background events, and the number of events expected from individual background sources. M ~ M ~ 2 ~ e + e? ~ +? ~ qq M ~ M ~ 2 ~ e + e? ~ +? ~ qq Table 2: Eciencies in percent for ~ ~ 2 events with dierent decays of ~ 2 neutralino masses (in GeV=c 2 ). and for dierent For each combination of masses each of these eciencies may be used, together with the observed number of events and expected background, to derive an upper limit on the corresponding product of cross section and branching ratio. The single candidate in the ~ ~ electron channel was included in the region of the M 2 ~? M 2 ~ plane where it would be kinematically possible for such an event to arise (approximately given by M ~ 2 < 8 GeV=c 2 ). The limits obtained are shown in gure 3 for the leptonic and hadronic ~ 2 decay mode. The limit obtained with an assumption that ~ 2! ff ~ decay is mediated via Z leading to 2 % of invisible nal states is also presented. In the ~ 2 ~ 2 channel 44 events were generated and passed through the simulation and selection procedure, giving eciencies shown in Table 3. The limits obtained are shown in gure 4 for three dierent assumptions on the ~ 2 decay mode. These results were interpreted in terms of the MSSM with universal GUT scale parameters by evaluating the appropriate eciency, cross section, and branching ratio for each channel as functions M 2,, and tan. Exclusion regions were derived by comparing the expected number of events with the number actually observed and the number expected from background, using Poisson statistics in the Bayesian approach for combining the dierent channels [5]. Figures 5 show the resulting limits in the? M 2 plane for two four values of tan and for dierent values of the universal scalar mass at the GUT scale, m. The eect of changing m, and hence the mass of the scalar electron, is only noticeable for low M 2, and only in regions already excluded by lower energy LEP results. 7

10 M ~ M ~ 2 e + e? +? l + l? qq; qqqq M ~ M ~ 2 e + e? +? l + l? qq; qqqq Table 3: Eciencies in percent for ~ 2 ~ 2 events with dierent decays of ~ 2 neutralino masses (in GeV=c 2 ). and for dierent For values of M 2 below approximately GeV=c 2 the cross section for ~ ~ 2 production drops sharply, but is replaced by a signicant cross section for ~ ~ 3, where the properties and branching ratios of ~ 3 are similar to those of ~ 2 for higher M 2. This makes it possible to extend the exclusion region to lower values of M 2, based on the calculated eciencies for ~ ~ 2. For lower values of M 2 ~ 2 ~ 4 production, with radiative decays of ~ 2 and ~ 4, becomes dominant. 5.2 Results on scalar lepton production The eciency of the selection in section 4.3 for scalar electron production, calculated using 4 events for dierent mass combinations, is shown in table 4. In ~e case there is a possibility of ~ exchange in the t-channel. In the case of low jj values the t-channel and s-channel contributions may interfere destructively, giving cross sections of about.5 pb for M ~e = 4 GeV=c 2. For larger jj, however, meaningful limits may be set. Figure 6 shows the excluded regions in the case of a) production of ~e + R~e? R only (assuming heavy ~e L ), and b) production of ~e + R~e? R, ~e + L~e? L, and ~e + R~e? L with M ~el = M ~er. These limits apply for 2 GeV=c 2 < < TeV=c 2 and < tan < 5, and are computed assuming one candidate event described in 4.3. M ~ M ~f ~e~e ~~ ~t~t M ~ M ~f ~e~e ~~ ~t~t Table 4: Eciencies in percent for ~ f ~ f events for dierent sfermion types and for dierent ~ f and ~ masses (in GeV=c2 ). The search of subsection 4.3 yielded no events with nal states. The selection eciency for scalar muons was evaluated using fully simulated samples generated with SUSYGEN (a total of 4 events for dierent mass combinations) and is shown in table 4. Two cases were considered, namely the case of degenerate masses, M ~ R = M ~L, and the case of a lighter ~ R and a kinematically inaccessible ~ L, as suggested by the running of scalar mass terms in the MSSM. The limit improves on previous LEP limits only in the mass degenerate case. The excluded region is shown in gure 6 c) for ~ L;R. 8

11 5.3 Results on scalar top production The expected cross section for scalar top quark production is in the pb range close to the kinematic limit, but may be reduced if left-right mixing cause decoupling from Z in the s-channel, leaving only the photon contribution. The sensitivity of the selection of acoplanar jet events (section 4.) to scalar top production has been evaluated using fully simulated event samples for several M ~ t? M ~ combinations, supplemented by a large set of generator data passed through a very fast detector response parametrization to interpolate results obtained with the full simulation. Table 4 shows the eciency of the selection for dierent mass combinations. Figure 7 shows the mass combinations excluded, at the 95% condence level, together with results from previous searches at LEP [6] and the Tevatron [7]. Limits are shown for the left and right handed ~t. 6 Conclusion In a data sample of 5.9 pb? collected by the DELPHI detector at centre-of-mass energies of 3 and 36 GeV searches were performed for events with acoplanar jet pairs, acoplanar lepton pairs, or combinations of these, in association with missing energy. One event was selected; an acoplanar electron pair of momenta 7.6 GeV=c and.6 GeV=c, and an invariant mass of 4.6 GeV=c 2. This is consistent with the expected number of background events of.3.9. There is no candidate in the acoplanar jets topology. These results were used to set limits on the production of neutralinos, scalar leptons, and scalar top quarks. Assuming the dominant decay of ~ 2 into ~ and a virtual Z the cross section for ~ ~ 2 production is limited to be below a few pb at the 95% condence level in most of the kinematically allowed mass range. If the gaugino mass parameter M 2 is in the region between 5 GeV=c 2 and 8 GeV=c 2 (higgsino dominated case) the higgs supereld mass parameter,, is limited to satisfy?45gev=c 2 < < 95GeV=c 2 for tan =., and jj < 65 for tan = 5. A narrow window for close to zero is covered by previous LEP searches. The mass of the left scalar top quark, M ~ tl, is limited to be above 56 GeV/c2 at the 95% condence level if the dierence between this mass and that of the lightest neutralino exceeds 8 GeV=c 2. In the case of degenerate scalar electron masses, M ~el = M ~er, values below 56.5 GeV=c 2 are excluded at the 95% condence level if M ~e? M ~ > 5 GeV=c 2, 2 GeV=c 2 < jj < TeV=c 2, and tan >. For scalar degenerate muons the corresponding limit is 5 GeV=c 2, irrespective of the MSSM parameters. These results considerably extend exclusion limits obtained at LEP, and probe a relevant part of the MSSM parameter space. Acknowledgements We are eager to express our gratitude to the members of the CERN accelerator divisons and to compliment them on the fast and ecient comissioning and operation of the LEP accelerator in this new energy regime. 9

12 References [] H.P. Nilles, Phys. Rep. (984) ; H.E.Haber and G.L.Kane, Phys. Rep. 7 (985) 75 [2] ALEPH Coll., D. Decamp et al., Phys. Rep. 26 (992) 253. A. Lopez-Fernandez, DELPHI note (Dallas) PHYS 26 L3 Collaboration: M. Acciarri et al., Phys. Lett. B35 (995) 9{9 OPAL Collab., OPAL Physics Note PN94, July 995. [3] M. Drees and K. Hikasa, Phys. Lett. B252 (99) 27{34 [4] DELPHI Collaboration, P.Abreu et al. CERN-PPE-95-4, December 995, Submitted to Nucl. Instr. and Meth. [5] G. Altarelli and R. Barbieri, Phys. Lett. B253 (99) 6; M. Boulware and D. Finnel, Phys. Rev. D44 (99) 254; A. Djouadi et al., Nuclear Pyhsics B349 (99) 48. [6] T. Sjostrand, Comp. Phys. Comm. 39 (986) 347; T. Sjostrand, PYTHIA 5.6 and JETSET 7.3, CERN-TH/ [7] Proceedings of the Workshop on Physics at LEP2, CERN 96- [8] S. Ambrosanio and B. Mele, Phys. Rev. D52 (995) 39{398 S. Ambrosanio and B. Mele, ROME-95-95, Aug. 995, submitted to Phys. Rev. D [9] S. Kawabata, Comp. Phys. Comm. 4 (986) 27{53 [] W. Beenakker, R. Hopker, M. Spira, and P.M. Zerwas, Phys. Lett. B349 (995) 463{468 [] F.A. Berends, R. Pittau, R. Kleiss, Comp. Phys. Comm. 85 (995) 437{452 [2] S.Nova, A.Olshevski, and T. Todorov, A Monte Carlo event generator for two photon physics, DELPHI note (993). [3] S. Bethke et al., Phys. Lett. B 23 (988) p.235. [4] K. Hikasa and J. Hisano, Hard gluon emission from colored scalar pairs in e + e? annihilation TU-497,TIT-HEP-38, March 996. [5] V.F. Obraztsov, Nucl. Instr. and Meth. 36 (992) 388{39 [6] The OPAL Collaboration, R. Akers et al., Phys. Lett. B337 (994) [7] D Collaboration, S. Abachi et al., FERMILAB-PUB E, Dec 995. Submitted to Phys. Rev. Lett.

13 Figure : Invariant mass distributions of the hadronic events in the data, compared to the simulation for a) multihadronic events (more than four charged particles), b) a reference sample of multihadronic Z events with jet polar angles consistent with an undetected photon in the beam, and c) a reference sample of multihadronic events with no signicant undetected radiation.

14 Figure 2: The distribution of missing energy and acoplanarity for events whith two isolated tracks selected for the real data (lled circles) and Monte Carlo data (shaded area). The acoplanarity was calculated using the two selected tracks. 2

15 Figure 3: Upper limits (in pb) on the cross section for ~ ~ 2 production at 95% condence level, assuming that ~ decays exlusively into 2 (a) ~ e+ e?, (b) ~ +?, (c) ~ qq, and (d) ~ Z, respectively, for dierent values of the neutralino masses. 3

16 Figure 4: Upper limits on the cross section for ~ 2 ~ 2 production assuming that ~ 2 decays exclusively into (a) ~ `+`?, (b) ~ qq, and (c) ~ Z, respectively, for dierent values of the neutralino masses. 4

17 Figure 5: Regions in the? M 2 plane excluded at 95% condence for dierent values of tan. The solid, dashed, and dotted lines (which are often indistinguishably close) correspond to m = TeV=c 2, m Z, and 3 GeV=c 2, respectively. The light shaded areas show the regions excluded by LEP for m = TeV=c 2, while the more heavily shaded areas are only excluded for the lower m values. The thin line is the kinematic limit for ~ ~ 2 production at E cms = 36 GeV. 5

18 Figure 6: Exclusion regions in the M ~e - M ~ and M ~ - M ~ planes at the 95% condence level. a) ~e R, b) degenerate ~e R ~e L, and c) degenerate ~ R ~ L. LEP limits for acoplanar leptons and for stable charged particles (upper part) are also shown. 6

19 Figure 7: Exclusion regions in the M ~ t - M ~ plane at the 95% condence level. Limits are shown for the left and right handed stop states. Also shown are results from previous searches at LEP and the Tevatron. 7