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Search for Anomalous Production of Di-lepton Events with Missing Transverse Momentum in e+e- Collisions at sqrt(s) = 183-209 GeV

In total 1317 di-lepton events with significant missing transverse momentum were identified in a total data sample of 680 pb-1 collected at e+e- centre-of-mass energies ranging from 183 GeV to 209 GeV. The number of di-lepton events, the dependence on centre-of-mass energy, and the event properties are consistent with expectations from Standard Model processes, predominantly W+W- production with both W bosons decaying leptonically. This topology is also an experimental signature for the pair production of new particles that decay to a charged lepton accompanied by one or more invisible particles. No evidence for new phenomena is apparent. Upper limits are presented on the production cross-section multiplied by the relevant branching ratio squared for sleptons, leptonically decaying charginos and charged Higgs bosons. Mass limits are also given.


Introduction
We report the final results from an investigation of events containing two oppositely charged leptons and significant missing transverse momentum recorded with the OPAL detector at LEP. These events were produced between 1997 and 2000 in the highest energy e + e − collisions achieved to date, at centre-of-mass energies ( √ s) ranging from 183 to 209 GeV. The data used in this analysis amount to a total integrated luminosity of 680 pb −1 . The event topology which is studied, henceforth called acoplanar di-lepton events, consists of low multiplicity events with two oppositely charged leptons, significant missing transverse momentum and the possible presence of additional photons.
The number of observed events and their properties are compared with the expectations for Standard Model processes, which are dominated by the ℓ + ν ℓ − ν final state (ℓ = e, µ, τ ) arising from W + W − production in which both W bosons decay leptonically. This topology is also an experimental signature for the pair production of new particles that decay to produce a charged lepton accompanied by one or more invisible particles. The invisible particles may be neutrinos, or the lightest stable supersymmetric [1] particle (LSP), or weakly interacting neutral particles with long lifetimes, which decay outside the detector volume. The LSP may be the lightest neutralino,χ 0 1 , the lightest sneutrino,ν, or the gravitino,G. We present the results of searches for the pair production and stated decay mode of the following new particles: charged scalar leptons (sleptons):l ± → ℓ ±χ0 1 (orl ± → ℓ ±G ), wherel ± may be a selectron (ẽ), smuon (μ) or stau (τ ) and ℓ ± is the corresponding charged lepton.
The slepton searches are also relevant to interpreting the results of searches for chargino and neutralino production since the chargino and neutralino production cross-sections and branching ratios depend on the sneutrino and charged slepton masses. The search for charged sleptons provides constraints on the slepton masses, notably the selectron mass, while indirect limits on the sneutrino masses, notably the electron-sneutrino mass, can be obtained in models where the charged slepton and sneutrino masses are related. The search results described here will also be used in a separate publication regarding the search for sleptons with non-negligible lifetime.
In most respects the analysis is similar to our published searches at centre-of-mass energies of 161, 172, 183 and 189 GeV [2][3][4]. This paper supersedes the results of [3,4]. The analysis is performed in two stages. The first stage consists of a general event selection designed for all possible low multiplicity events containing a lepton pair plus missing transverse momentum (Section 3). In this context the Standard Model ℓ + ν ℓ − ν events are considered as signal in addition to possible new physics sources. All Standard Model processes that do not lead to ℓ + ν ℓ − ν final states, e.g. e + e − ℓ + ℓ − and ℓ + ℓ − (γ) , are considered as background and are reduced to a rather low level (≈ 3%) by the event selection. The observed numbers of events and kinematic distributions for the data are compared with expectations from Standard Model processes in Section 4. In the second stage the detailed properties of the events (e.g. the type of leptons observed and their momenta), which vary greatly depending on the type of new particles considered and on free parameters within the models, are used to separate as far as possible the events consistent with potential new physics sources from W + W − production and other Standard Model processes (Section 5). Constraints on new physics are discussed in Section 6.
Slepton search results from the ALEPH collaboration at √ s ≤209 GeV [5] have been published recently. The L3 and DELPHI collaborations have published searches for sleptons in this channel using data with √ s ≤189 GeV [6].

OPAL Detector and Monte Carlo Simulation
A detailed description of the OPAL detector can be found elsewhere [7,8] and only the general features are described here.
The central detector consisted of a system of chambers providing charged particle tracking over 96% of the full solid angle inside a 0.435 T uniform magnetic field parallel to the beam axis. It consisted of a two-layer silicon micro-strip vertex detector, a high precision vertex drift chamber, a large volume jet chamber and a set of z-chambers that measured the track coordinates along the beam direction.
A lead-glass electromagnetic calorimeter (ECAL) was located outside the magnet coil. It provided, in combination with the gamma-catchers (GC) and forward detectors (FD), which were lead-scintillator sandwich calorimeters and, at smaller angles, silicon tungsten calorimeters (SW), geometrical acceptance with excellent hermeticity down to approximately 25 mrad 1 from the beam direction.
The magnet return yoke was instrumented for hadron calorimetry and consisted of barrel and endcap sections along with pole tip detectors that together covered the region | cos θ| < 0.99. Outside the hadron calorimeter (HCAL), four layers of muon chambers covered the polar angle range of | cos θ| < 0.98. Arrays of thin scintillating tiles were installed in the endcap region to improve trigger performance, time resolution and hermeticity for operation at LEP 2 [8].
Of particular relevance to this analysis are the four layers of scintillating tiles (the MIP-plug) installed at each end of the OPAL detector covering the angular range 43 < θ < 220 mrad. These tiles were commissioned in 1997 and became fully operational for data taken from 1998 at √ s ≥ 189 GeV. Time-of-flight (TOF) scintillators in the barrel region aided cosmic ray rejection.
The following Standard Model processes are simulated. Four-fermion production is simulated using the Koralw [9] generator which uses the grc4f [10] matrix elements to calculate the four-fermion cross-sections including interference effects and includes a detailed description of hard radiation from initial and final state charged particles. Two-photon production of muon pairs and tau pairs is generated with the BDK generator [11] and the program of Vermaseren [12] is used for the two-photon production of electron pairs. The grc4f event generator excluding multi-peripheral processes is used for e + e − ℓ + ℓ − and e + e − qq. The Phojet [13] and Herwig [14] event generators are used to study backgrounds from two-photon production of hadrons. The production of lepton pairs is generated using Bhwide [15] and Teegg [16] for e + e − (γ), and KK2f [17] for µ + µ − (γ) and τ + τ − (γ). The final state ννγ(γ) is generated with Nunugpv98 [18].
Slepton pair production is generated using Susygen [19]. Chargino pair production is generated using Dfgt [20] for three-body decays, and Susygen for two-body decays. Charged Higgs boson pair production is generated using Hzha [21].
Backgrounds from the accelerator or cosmic-ray interactions can lead to additional hits, energy deposition and even reconstructed tracks being superimposed on triggered data events. Such effects of detector occupancy are simulated for all Monte Carlo samples by adding to the Monte Carlo events the hits, energy depositions and additional jets found in randomly triggered beam-crossing data events (BXRSA trigger [22] with a constant 0.1 Hz rate) corresponding to the same centre-of-mass energy. Systematic checks showed that this constant rate model adequately described the average inefficiency during a LEP fill, despite the instantaneous luminosity decreasing typically by a factor of 2 or 3.
All Standard Model and new physics Monte Carlo samples are processed with a full simulation of the OPAL detector [23] and subjected to the same reconstruction and analysis programs as used for the OPAL data.

Introduction
The general event selection is formed by requiring that an event be selected by either or both of two independent event selections, referred to here as selection I and selection II. Selection I is designed to retain efficiency for events with low visible energy. This is characteristic of slepton or chargino events where the mass difference, ∆m , between the parent particle and the invisible daughter particle (e.g.χ 0 1 ) is small. Selection II is optimised to maximise the efficiency for W + W − → ℓ + ν ℓ − ν events, while keeping other Standard Model background events to a minimum.
Both selections require evidence for two 2 charged leptons and an invisible system carrying significant missing transverse momentum (p miss t ). The maximum p miss t which can be carried away by undetected particles travelling close to the beam is set by the maximum angle to the beam at which such a particle will not be detected. This is 25 mrad -the angle to which the silicon tungsten detector extends. A particle with energy of E beam may thus carry away p miss t = 0.025 E beam without being detected.
Some background processes containing secondary neutrinos (particularly from tau decay) may have large values of p miss t with the direction of the missing momentum vector pointing away from the beam axis. Such events tend to be fairly coplanar, and the component of p miss t which is perpendicular to the event thrust axis in the transverse plane (called a miss t ) is much less sensitive than p miss t to the presence of neutrinos from tau decays or to poorly measured particles. This can be seen by considering electrons produced in tau decay. Low momentum electrons produced from this source can have a large angle relative to the original tau direction, but their momentum transverse to the original direction (and hence their contribution to a miss t ) is small.
The event selection as it was first implemented was described in detail in [2]. In [3] we made use of the improved hermeticity for non-showering particles in the forward direction provided by the MIP-plug 3 . Subsequent improvements have been made for the analysis of the data taken at 189 GeV [4] by reducing the sensitivity to mis-measurements of p miss t and using the much improved background rejection capabilities of the MIP-plug to increase substantially the efficiency of selection II. For this paper, selection I has been consolidated and much refined. In particular, a selection has been added for single lepton events in which a single high transverse momentum charged lepton is observed in the central detector. These are usually events where the second charged lepton is produced at a polar angle sufficiently close to the beam direction that it does not produce a visible track in the central detector. In the context of this paper, this "single-lepton" selection is used to recuperate di-leptons where the second lepton was missed. Various small modifications were made to selection II in order to reduce sensitivity to poorly modelled backgrounds. An example of this is using stricter track quality criteria to reduce the possibility of tracks from overlaid beam-gas events affecting the measurement of the event kinematics.
The current event selection is summarised below.

Selection I
Selection I is designed to retain efficiency for events with very low visible energy, but nevertheless significant p miss t . This is typical of new physics signal events with small ∆m. The selection requires evidence that a pair of leptons has been produced and of significant missing transverse momentum. Subsequent cuts reduce the probability that the signature of missing transverse momentum is faked by events with secondary neutrinos from tau decay or poorly measured particles.
At least one lepton in the event is required to be well identified and to satisfy requirements on isolation and transverse momentum. Much looser requirements are made on the possible presence of a second lepton in the event.
In order to be considered in the event selection, tracks in the central detector are required to satisfy p t > 0.1 GeV. Clusters in the barrel ECAL are required to satisfy E > 0.1 GeV and clusters in the endcap ECAL are required to satisfy E > 0.2 GeV. Converting photons are identified and the tracks and clusters associated to the conversion are replaced by a single 4-vector representing the photon.

Lepton Candidates
The first stage is to look for lepton candidates in the event. A track is identified as a lepton candidate if it has p > 1.5 GeV and it is identified as an electron, muon or hadronic tau decay 4 . The electron ID is based on the ratio of ECAL energy to track momentum (E/p), and dE/dx information. Muons are identified using muon chamber or HCAL hits which match with a track in the central detector, or from a high momentum track which matches with a low energy ECAL cluster. To identify a hadronic tau the following criteria are applied: • Within a cone of half-opening angle 35 • around a track of p t >1.5 GeV there are no more than three tracks in total.
• The invariant mass of all tracks and clusters within the cone is less than the tau mass. This is calculated assuming the pion mass for each track and correcting for double counting of tracks and clusters.
The lepton candidates are also required to be isolated. There must be no more than 2 additional tracks and no more than 2 additional clusters in an isolation cone defined around the lepton candidate (half opening angle 20 • for electrons and muons, half opening angle 60 • for hadronic tau decays), and the energy sum of the tracks or of the clusters must be less than 2 GeV.

Di-lepton Event Selection
Firstly evidence for a pair of leptons is required: • There must be at least one and no more than two isolated lepton candidates with p t > 1.5 GeV.
• If the event contains two isolated lepton candidates then all tracks in the event must be associated with the lepton candidates.
• If there is only one isolated lepton candidate then the other tracks and clusters in the event are considered as a possible second lepton candidate provided the following: (a) There must be between 1 and 3 additional tracks, at least one of which must have p t > 0.3 GeV.
(b) The invariant mass of the additional tracks must be less than 3 GeV and the invariant mass of the additional tracks and clusters must be less than 8 GeV.
(c) γβ, the net momentum of the additional tracks and clusters divided by their invariant mass, is required to be greater than 2.0.
Next, significant missing transverse momentum is required. For events with a large acoplanarity angle (φ acop > π/2 where φ acop is the supplement of the azimuthal opening angle), the following cut is applied 5 : • x t > 0.045, where x t is the scaled missing transverse momentum of the event (p miss t /E beam ).
For events with small acoplanarity angle (φ acop < π/2): is the total momentum of the observed particles in the z direction) are used to reduce background from processes such as τ + τ − and e + e − τ + τ − . Events are divided into subsets using variables which help estimate how likely they are to originate from τ + τ − or e + e − τ + τ − . The cut values vary according to the subset (in increasing order of similarity to τ + τ − or e + e − τ + τ − background): Further cuts are applied to reduce the effect of processes which may fake the signature of missing transverse momentum. These are mostly vetoes against energy in the forward region (GC, FD, SW or MIP-plug). However care is taken to ensure that the activity in the forward region is only used to veto the event if the activity could possibly explain the apparent missing momentum. Also different requirements are made depending on the amount of missing transverse momentum observed.
Radiative lepton pair events containing high energy isolated photons form a potentially serious source of background, because quantities such as p miss t and a miss t may be poorly measured. However, in order to retain efficiency for potential signal events containing isolated photons, events are rejected only if the presence of the isolated photon could possibly have caused the observed p miss t and a miss t . 5 The effect of measurement errors is taken into account in selection I by taking each lepton in turn and shifting its momentum up and down by one standard deviation of its estimated measurement error. At each stage the values of p miss t and a miss t are recalculated and the minimum of all the values obtained is the one used for comparison to the cut values.

Single Lepton Selection
Selection I also includes a selection for events with only one lepton visible in the central detector, and the other lepton travelling sufficiently close to the beam axis that no track is produced in the central tracking chambers.
The principal single lepton selection criteria are: • The event must contain one and only one identified, isolated lepton candidate, and no other tracks.
In order to veto events which may fake the missing transverse momentum signature, events are rejected if they contain activity in ECAL, GC, FD, SW, muon endcap or MIP-plug which is back-to-back with the observed lepton.

Selection II
Selection II is optimised to select high visible energy events typical of the W + W − → ℓ + ν ℓ − ν process. A low multiplicity preselection is applied such that the events contain at least one track but no more than 8. Also the sum of the number of tracks plus the number of ECAL clusters is required to be less than 16.
A cone-based jet finding algorithm [24] is applied requiring a minimum jet energy of 2.5 GeV and a cone half angle of 20 • . Events are required to contain 1, 2 or 3 jets, and a separate selection is used for each value of n jet . The majority (about 90%) of W + W − → ℓ + ν ℓ − ν events have n jet = 2. One-jet events are usually those where the decay products from one of the W bosons are poorly reconstructed (for example if the lepton is travelling close to the beam pipe). Three-jet events can occur if there is an energetic photon in the event.
Electron and muon identification, similar to that in selection I, is applied to the most energetic track in each jet. Jets not identified as electrons or muons are classified as hadronic tau decays.
The most important cuts for each n jet class are summarised below.

Di-jet Selection
where θ acol is the acolinearity angle between the two jets (defined as the supplement of the three-dimensional opening angle).
2. x t > 0.05. It is further required that the significance by which x t exceeds 0.05 be greater than 1 standard deviation.
3. For events with φ acop > π/2 it is required that the direction of the missing momentum satisfy | cos θ miss p | < 0.95. For events with φ acop < π/2 it is required that a miss t /E beam > 0.022 and that sin θ miss a > 0.06.
Further cuts are made on the quality of each jet, and for background rejection (mainly for events at low x t ): • Events are rejected if there are any tracks which are not associated with either jet.
• Events with low x t (x t < 0.15) are rejected if there is evidence of activity in the MIPplug with azimuthal angle within 60 • of the missing transverse momentum direction. For events with medium x t (0.15 < x t < 0.23), the veto uses only the outer MIP-plug scintillators.

Tri-jet Selection
For events classified as tri-jet, significant missing momentum is required: • The sum of the opening angles among the three two-jet pairings should be less than 359 • .
• x t of the three-jet system should exceed 0.05 with a significance exceeding 1 standard deviation.
Further requirements depend in part on the three-jet event topology in the transverse plane characterised by ∆φ max . This is calculated by ordering the jets by increasing azimuth, and finding the maximum azimuthal di-jet separation angle when rotating clockwise from one jet to the next 6 .
The most important additional requirements are: • For ∆φ max > 185 • , there should be no pair of vertex drift chamber axial tracks with an azimuthal opening angle exceeding 165 • . These tracks are reconstructed independently from standard jet chamber based tracks and this criterion helps to reduce cases where the wrong jet chamber left-right ambiguity is chosen in the standard tracking.
• For ∆φ max < 185 • it is explicitly required that two of the jets have associated tracks (charged jet) and the third jet has no associated tracks (neutral jet). For the events with ∆φ max < 180 • an axis in the transverse plane is defined using the most energetic charged jet. The event is rejected if the transverse momentum of the neutral jet with respect to this axis exceeds 80% of the transverse momentum of the less energetic charged jet. This cut is effective against τ + τ − γ events.
• Events are rejected if there is evidence for a particle passing through the MIP-plug (similar to di-jet MIP-plug veto but without the directional requirement).

Single-jet Selection
The single-jet selection applies to events where one lepton with high transverse momentum is observed at wide angle | cos θ| < 0.82 with evidence for a partially reconstructed lepton at small polar angle, or events where the two leptons fall within the same cone (massive mono-jet) for | cos θ| < 0.90. In contrast to the single lepton category of selection I, it is required here that there be some activity in the forward region (endcap ECAL, GC, FD, SW, muon endcap, MIP-plug) when there is evidence for only one lepton at wide angle.
Backgrounds from cosmic rays are reduced by requiring in-time TOF hits (within 20 ns) for tracks in the barrel region, and that the most energetic track in the jet be associated with hits in the silicon micro-vertex detector.
Three different minimum requirements on x t are applied (0.20, 0.30 and 0.25) depending on whether the event satisfies the massive mono-jet criteria and whether the forward activity is solely due to the MIP-plug or not, respectively.

Comparison of Data with Standard Model Processes
The numbers of events passing the general selection at each centre-of-mass energy in the data are compared with the Standard Model Monte Carlo predictions in Table 1. The total number of events predicted by the Standard Model is given, together with a breakdown into the contributions from individual processes. The data have been binned by centre-of-mass energy in bins which reflect the predominant centre-of-mass energies where data was collected. The number of observed candidates is consistent with the expectation from Standard Model sources, which is dominated by the ℓ + ν ℓ − ν final state arising mostly from W + W − production.  Table 1: Comparison between data and Monte Carlo of the number of events passing the general selection in each centre-of-mass energy bin. The total number of events predicted by the Standard Model is given, together with a breakdown into the contributions from individual processes. The Monte Carlo statistical errors are shown. Also listed for each bin is the mean √ s (in GeV) and the integrated luminosity, L, in pb −1 .

Lepton Identification and Kinematic Distributions
Information about the type of lepton found in the selected events and measurement of the event kinematics was used to compare the data with expectations from Standard Model processes. Some of these distributions are then used as likelihood variables to distinguish between Standard Model and new physics sources of acoplanar di-lepton events (section 5). We examine the • Di-lepton identities; • Acolinearity of the event, defined as the supplement of the three-dimensional opening angle between the two leptons; • Momentum asymmetry of the event, (|p 1 −p 2 |/(p 1 +p 2 )), where p 1 and p 2 are the momenta of each lepton; • Scaled momentum of each lepton, (p/E beam ) using the best estimate combining tracking and calorimetry information; • −q cos θ of each lepton, where q is the particle charge and θ is the polar angle with respect to the electron beam direction.
The lepton identification algorithm has been improved using techniques developed for tau lepton decay analyses such as described in [25]. The efficiencies for correctly identifying leptons as electrons, muons or hadronically decaying tau leptons are shown in Table 2 for a sample of leptons representative of the geometrical and kinematical acceptance of the general selection. Note that we have six separate mutually exclusive lepton identification decisions: electron (e), muon (µ), hadronically decaying tau (h), electron-hadron ambiguous (e/h), muon-hadron ambiguous (µ/h) and "rest-of-event" (x). The ambiguous categories correspond to cases where the lepton candidate has properties which do not permit clear identification between the two lepton types, while the rest-of-event category arises mostly from tau leptons which fail to pass basic lepton identification criteria.
We show in Figure 1 the observed di-lepton identities and the above kinematic variables are shown in Figure 2. Additional kinematic variables, which are not directly used in the likelihood, are also shown in Figure 3. Reasonable agreement is observed between the data and the Standard Model Monte Carlo in all these distributions as quantified using χ 2 tests.

Method
The method used in the second stage of the analysis, in which we distinguish between Standard Model and new physics sources of lepton pair events with missing momentum, is essentially described in [4]. Discrimination is provided by information on the lepton identification, the acolinearity and momentum asymmetry of the event, the scaled momentum and −q cos θ of the observed lepton candidates. These variables are combined using a likelihood technique. The discriminating quantity used is the relative likelihood, L R , defined by: where L S is the likelihood of the event being consistent with the signal hypothesis (a particular new physics scenario) and L B is the likelihood of the event being consistent with the background hypothesis (Standard Model sources of lepton pair events with missing transverse momentum). The distributions depend on ∆m and on the parent particle mass, m.
In our previous publications we justified the inclusion of most of these variables and described how they were used [4]. In particular the −q cos θ variable is not used in the selectron and chargino searches because the t-channel neutralino (selectron search) and sneutrino exchange (chargino search) contributions make this signal distribution model-dependent.
The new momentum asymmetry variable describes the correlation between the momenta of the two leptons and is thus complementary to the two scaled momentum variables which are implemented in the likelihood function as independent variables. It is correlated with the acolinearity variable, and so the information was included using a two-dimensional probability distribution of momentum asymmetry versus acolinearity. Sensitivity studies for the selectron and smuon searches justified this addition. However similar studies for the other channels (stau, chargino and charged Higgs), where momentum distributions are broader, showed no net gain in sensitivity and so for these channels the acolinearity distribution alone was used. Also for these channels, we removed the distinction between leptons being identified as electrons and muons and merged them into one category since we found that there was no significant difference in search sensitivity.
For the selectron search, we required that at least one lepton be identified as an electron and that no lepton in the event be compatible with being a muon (i.e. the other lepton was not identified as a muon and it was not muon-hadron ambiguous). Similarly for the smuon search we required at least one identified muon and required that no lepton be compatible with being an electron. Some additional requirements were used to reject events from these searches if the second lepton was identified as a hadronically decaying tau or a "rest-of-event" candidate and if it had properties strongly incompatible with being an electron for the selectron search and with being a muon for the smuon search. These additional requirements cut the background by 21% and 14% while only reducing the signal efficiency by 2.1% and 0.8% for the selectron and smuon searches respectively.
For each search channel, reference histograms were constructed for each of the likelihood variables at each point in m and ∆m for which signal Monte Carlo had been generated (each point corresponds to a table entry in tables [3][4][5][6][7][8]. A smoothing algorithm [26] was applied to the histograms to reduce the effects of statistical fluctuations. The reference histograms were then used to construct L R distributions. An interpolation procedure was developed which allowed us to interpolate among neighbouring signal Monte Carlo (m, ∆m , √ s) points to intermediate values of (m, ∆m and √ s). Further details are given in [27].
L R distributions for signal Monte Carlo, Standard Model Monte Carlo and data are shown in Figure 4 for the specific example of the analysis for staus with a mass of 80 GeV and a stau-neutralino mass difference of 60 GeV. There is considerable variation in the shapes of these distributions with m and ∆m but agreement between data and Standard Model Monte Carlo is generally good.

Calculation of Cross-section Upper Limits
For each search channel and for each set of kinematic parameters (m and ∆m) we wish to test the consistency of the data with the sum of background and an additional signal contribution. The signal contribution depends on σ s , the cross-section multiplied by branching ratio to leptonic final states squared. We use an extended maximum likelihood technique as described in [4] to measure σ s and, in the absence of a significant signal, to set 95% confidence level (CL) upper limits on σ s . We form a likelihood, L(σ s ), of the set of L R values for the data being consistent with the expected L R distribution for Standard Model plus a signal contribution of σ s . The upper limit on the cross-section multiplied by branching ratio squared at 95% confidence level, σ 95 , is calculated as the value of σ s below which 95% of the area under the likelihood function lies. Details of the likelihood function and method as well as cross-checks of the method are described in [4]. Data from different centre-of-mass energies are combined by weighting them using an assumed cross-section dependence on √ s. For this paper the reference centre-of-mass energy for the weighting is √ s = 208 GeV instead of √ s = 189 GeV.
We have also evaluated results based on the number of events passing an optimised cut on the L R value. These results are used as a cross-check, as a direct comparison between data and background and as a simpler basis for combining this analysis with other experiments or other analyses.

Constraints on New Physics
We present limits on the pair production of charged scalar leptons, leptonically decaying charged Higgs bosons and charginos that decay to produce a charged lepton and invisible particles.
The 95% CL upper limit on new particle production at √ s = 208 GeV obtained by combining the data at different centre-of-mass energies is calculated at each kinematically allowed point on a 1 GeV by 1 GeV grid of m and ∆m, using the L R distributions for signal and background, the L R values of the data events, and the efficiency of the general selection at that point as input.
In addition to the Monte Carlo statistical error on the signal efficiency, we assess a 10% relative systematic error on the estimated selection efficiency to take into account deficiencies in the Monte Carlo generators and the detector simulation (5%), uncertainties in the interpolation procedure (5%), effect of tau polarisation in stau decay [28] (5%), fluctuations in the shape of the signal L R distribution (2%), uncertainties from lepton identification efficiency (2%), detector occupancy (1%), trigger efficiency (< 1%), and luminosity measurement (0.5%).
At high values of ∆m the dominant background to the searches for new physics results from W + W − production. High statistics Monte Carlo samples for this process are available and these samples describe the OPAL data well [29]. In addition to the Monte Carlo statistical error, we assess a 5% relative systematic error on the estimated background to take into account uncertainties in the shapes of the L R distributions and reference histograms, in the interpolation procedure, and deficiencies in the Monte Carlo detector simulation. At low values of ∆m the dominant background results from two-photon e + e − ℓ + ℓ − events. The background uncertainty at low ∆m is dominated by the limited Monte Carlo statistics; the uncertainty is typically 20-80% at low ∆m.
We have examined distributions of the cut variables and background enriched samples in assessing these systematic errors. The systematic errors on the selection efficiency and the estimated background are considered as global errors applicable to each search and for all values of m and ∆m . In setting limits, the Monte Carlo statistical errors and the systematic uncertainties on the efficiency and the background expectation are taken into account using numerical convolution.

Limits on σ s
Limits on σ s , the production cross-section for new physics processes multiplied by the branching ratio squared, are presented in a manner intended to minimise the number of model assumptions. The 95% CL upper limits at √ s = 208 GeV shown in Figures 5 -10 are obtained by combining the data at the various centre-of-mass energies using the assumption that the cross-section varies as β 3 /s for sleptons and charged Higgs and β/s for charginos, where β is the particle's velocity in units of c. The chosen functional forms are used for simplicity in presenting the data and represent an approximation, most importantly for processes in which t-channel exchange may be important, namely selectron pair and chargino pair production. In these cases the cross-section dependence on centre-of-mass energy is model dependent, depending on the mass of the exchanged particles and the couplings of the neutralinos and charginos. The selectron Monte Carlo events were generated with µ = −200 GeV and tan β = 1.5 using Susygen. We have found by varying µ and tan β, over the range 100 < |µ| < 1000 GeV and 1 < tan β < 50, that the above choice gives a conservative estimate of the selection efficiency for selectrons.
Upper limits at 95% CL on the selectron pair cross-section at √ s = 208 GeV multiplied by the branching ratio squared for the decayẽ − → e −χ0 1 are shown in Figure 5 as a function of selectron mass and lightest neutralino mass. These limits are applicable toẽ + Lẽ − L andẽ + Rẽ − R production. The corresponding plots for the smuon and stau pair searches are shown in Figures 6  and 7, respectively. Note that if the LSP is the effectively massless gravitino,G , then for prompt slepton decays to a lepton and a gravitino the experimental signature would be the same as that forl − →ℓ −χ0 1 with a massless neutralino. In this case the limits given in Figures 5 -7 for mχ0 1 = 0 may be interpreted as limits on the decayl − → ℓ −G . The upper limit at 95% CL on the chargino pair production cross-section multiplied by the branching ratio squared for the decayχ ± 1 → ℓ ±ν ℓ (2-body decay) is shown in Figure 8. The limit has been calculated for the case where the three sneutrino generations are mass degenerate. The upper limit at 95% CL on the chargino pair production cross-section multiplied by the branching ratio squared for the decayχ ± 1 → W ±χ0 1 → ℓ ± νχ 0 1 (3-body decay) is shown in Figure 9. The upper limit at 95% CL on the charged Higgs boson pair production cross-section multiplied by the branching ratio squared for the decay H ± → τ ± ν τ is shown as a function of m H + as the solid histogram in Figure 10. The branching ratio for the decay H ± → τ ± ν τ may be the dominant one for the charged Higgs masses explored with this data-set. The dashed line in Figure 10 shows the prediction from HZHA at √ s = 208 GeV for a 100% branching ratio for the decay H ± → τ ± ν τ . With this assumption we set a lower limit at 95% CL on m H + of 92.0 GeV. 1. The signal efficiency for the general selection at 208 GeV with statistical error (the efficiencies at lower energies differ by less than 3%).

Expected Limits and Consistency with Expectation
2. The 95% CL upper limit on the cross-section multiplied by the branching ratio squared at 208 GeV, obtained by combining the data from each centre-of-mass energy.
3. The expected 95% CL upper limit on the cross-section multiplied by the branching ratio squared in the absence of signal, σ 95 . This is calculated using an ensemble of 1000 Monte Carlo experiments to simulate the data. In each Monte Carlo experiment, the total number of candidates is drawn from a Poisson distribution with mean equal to the number of events expected from the Standard Model. For each candidate, a value of L R is assigned, chosen randomly according to the expected L R distribution for Standard Model processes. The expected limit at a given point in m and ∆m is the mean value of the limit for the ensemble of simulated experiments.
4. The confidence level for consistency with the Standard Model, calculated as the fraction of the simulated experiments for which the upper limit on the cross-section multiplied by the branching ratio squared is greater than or equal to the value calculated using the actual data. In the absence of signal, a CL of 50% is expected on average 7 .
Note that the number of candidate events with high values of relative likelihood varies greatly from search to search and with m and ∆m . For the selectron and smuon searches where particular di-lepton identities are required and the kinematics of the lepton from the slepton decay are measured directly (in contrast to events with tau leptons), relatively few events may be present at high relative likelihood. For searches where the signal di-lepton identities are not that dissimilar to W + W − → ℓ + ν ℓ − ν and a range of lepton momenta are expected, hundreds of events may potentially have high values of relative likelihood.
For some points in m and ∆m in these tables, the confidence level for consistency with the Standard Model is relatively small (of order 1%). The probability of getting a low confidence level for one or more points in m and ∆m for one or more of the search channels depends on the degree of correlation among the different (m, ∆m) points and among the different channels. The correlation between adjacent points is strong when the momentum distributions for those points are similar. The momentum distributions vary slowly with both m and ∆m when ∆m is high (hence the clustering of low confidence level values in Table 4), but vary considerably with ∆m when ∆m is low. This effect was investigated by generating 1000 Monte Carlo experiments with the Standard Model Monte Carlo as described above. For each experiment and each point on the (m, ∆m) grid at which signal Monte Carlo has been generated, the CL was calculated. It was found that 56% of the experiments had at least one point with a CL of 0.9% or less; this is the lowest value observed in Tables 3 to 8.

Limits on Slepton Masses
We can use our data to set limits on the masses of right-handed sleptons 8 based on the expected right-handed slepton pair production cross-sections and branching ratios. The cross-sections were calculated using Susygen at each centre-of-mass energy and take into account initial state radiation. In Figure 11 we show limits on right-handed smuons as a function of smuon mass and lightest neutralino mass for several assumed values of the branching ratio squared forμ ± R → µ ±χ0 1 . The expected limit, calculated using Standard Model Monte Carlo only, is also shown for a branching ratio of 100%. For a branching ratioμ ± R → µ ±χ0 1 of 100% and for a smuon-neutralino mass difference exceeding 4 GeV, right-handed smuons are excluded at 95% CL for masses below 94.0 GeV. The 95% CL upper limit on the production of right-handed τ +τ − multiplied by the branching ratio squared forτ ± R → τ ±χ0 1 is shown in Figure 12. The expected limit for a branching ratio of 100% is also shown. For a branching ratioτ ± R → τ ±χ0 1 of 100% and for a stau-neutralino mass difference exceeding 8 GeV, right-handed staus are excluded at 95% CL for masses below 89.8 GeV. No mixing betweenτ L andτ R is assumed. However, the cross-section ratio στ+ GeV varies between 0.90 and 1.17 depending only on the mixing angle. Using this information, the limits shown in Figure 12 can be applied to any degree of stau mixing by multiplying the predicted cross-section forτ +

Rτ
corresponding to the mixing angle considered. The two broken lines in Figure 12 show the range of possible positions of the line defining the excluded region for a branching ratioτ ± 1 → τ ±χ0 1 of 100% for any degree of stau mixing. For the case of a massless neutralino (or gravitino) and 100% branching ratio, right-handed smuons and staus are excluded at 95% CL for masses below 94.3 GeV and 89.8 GeV, respectively, andτ ± 1 is excluded at 95% CL for masses below 88.7 GeV, for any degree of stau mixing. An alternative approach is to set limits taking into account the predicted cross-section and branching ratio for specific choices of the parameters within the Minimal Supersymmetric Standard Model (MSSM) 9 . For µ < −100 GeV and for two values of tan β (1.5 and 35), Figures 13, 14 and 15 show 95% CL exclusion regions in the (ml± R , mχ0 1 ) plane for righthanded selectrons, smuons and staus, respectively. For µ < −100 GeV and tan β = 1.5, righthanded sleptons are excluded at 95% CL as follows: selectrons with masses below 97.5 GeV for mẽ− − mχ0 1 > 11 GeV; smuons with masses below 91.0 GeV for mμ− − mχ0 1 > 3 GeV; and staus with masses below 85.2 GeV for mτ − − mχ0 1 > 6 GeV.

Search for Unequal Mass Particle Production
All the search results described above are for the pair production of new particles with equal mass. New physics signals with unequal mass, such as the production ofẽ LẽR in which the two selectrons have different mass and each selectron decays to eχ 0 1 , can potentially be observed in the acoplanar di-lepton event sample.
We have examined the data for di-electron, di-muon and arbitrary di-lepton identity events consistent with unequal mass particle production. The search hypothesis is e + e − → XY, with subsequent decays, X → ℓ ± N and Y → ℓ ∓ N, where X and Y are two massive charged particles, and N is an invisible particle such as the LSP. The free parameters in the search are the masses of particles X, Y and N. The kinematics of producing two particles with different mass constrain the lepton momenta to be within well defined ranges depending on the new particle masses. The data have been examined by scanning the three particle masses in steps of 10 GeV for the three different di-lepton identity hypotheses and requiring the measured lepton momenta to be within the ranges specified by kinematics.
The consistency of the data with the Standard Model expectations is then examined. The lowest probability mass hypothesis occurs for di-leptons of arbitrary flavour with particle mass m X = 130 GeV, m Y = 60 GeV and m N = 20 GeV, where 242 events are observed with 197.3 expected from Standard Model sources (Poisson probability of 0.7%). From an ensemble of 1000 Standard Model Monte Carlo experiments it is found that 12.5% of the experiments had at least one mass hypothesis with a Poisson probability of 0.7% or lower. In general, the agreement with expectation is good. In conclusion, we have explored this potential weakness of the standard equal mass pair production search and found no significant evidence for unequal mass particle production.

Summary and Conclusions
A selection of di-lepton events with significant missing transverse momentum is performed using a data sample with an integrated luminosity of 680 pb −1 collected at e + e − centre-of-mass energies ranging from 183 to 208 GeV. The observed number of events, 1317, the dependence on centre-of-mass energy and the event properties are consistent with expectations from Standard Model processes, dominantly arising from W + W − production with both W bosons decaying leptonically. 9 In particular regions of the MSSM parameter space, the branching ratio forl ± → ℓ ±χ0 1 can be essentially zero as a result of competing cascade decays and so it is not possible to provide general limits on sleptons within the MSSM on the basis of this search alone. The predicted cross-sections and branching ratios within the MSSM are obtained using Susygen and are calculated with the gauge unification relation, Discrimination techniques are employed to search for the pair production of charged scalar leptons, leptonically decaying charged Higgs bosons and charginos that decay to produce a charged lepton and invisible particles. No evidence for new phenomena is apparent. Upper limits on the production cross-section multiplied by the branching ratio squared for each new physics process are presented in a manner intended to minimise the number of model assumptions.
Assuming a 100% branching ratio for the decayl ± R → ℓ ±χ0 1 , we exclude at 95% CL: righthanded smuons with masses below 94.0 GeV for mμ− − mχ0 1 > 4 GeV and right-handed staus with masses below 89.8 GeV for mτ − − mχ0 1 > 8 GeV. Right-handed selectrons are excluded at 95% CL for masses below 97.5 GeV for mẽ− − mχ0 1 > 11 GeV within the framework of the MSSM assuming µ < −100 GeV and tan β = 1.5. Charged Higgs bosons are excluded at 95% CL for masses below 92.0 GeV, assuming a 100% branching ratio for the decay H ± → τ ± ν τ .            Figure 9: Contours of the 95% CL upper limits on the chargino pair cross-section times branching ratio squared forχ ± 1 → ℓ ± νχ 0 1 (3-body decay) at √ s = 208 GeV. The limit is obtained by combining the 183 -208 GeV data-sets assuming a β/s dependence of the cross-section. The kinematically allowed region lies below the dashed line. The unshaded region at very low ∆m is experimentally inaccessible in this search. The solid histogram shows the 95% CL upper limit on the charged Higgs pair production cross-section times branching ratio squared for the decay H ± → τ ± ν τ at √ s = 208 GeV.
The limit is obtained by combining the 183 -208 GeV data-sets assuming a β 3 /s dependence of the cross-section. For comparison, the dashed curve shows the prediction from HZHA at √ s = 208 GeV assuming a 100% branching ratio for the decay H ± → τ ± ν τ . The expected limit calculated from Standard Model Monte Carlo alone is indicated by the dotted line.  : 95% CL exclusion region for right-handed stau pair production obtained by combining the √ s = 183 -208 GeV data-sets. The limits are calculated for several values of the branching ratio squared forτ ± R → τ ±χ0 1 . The selection efficiency forτ +τ − is calculated for the case that the decayτ − → τ −χ0 1 produces unpolarised τ ± . Otherwise the limits have no supersymmetry model assumptions. The two broken lines adjacent to the limit for BR 2 = 1.0 show the region in which this limit can vary if stau mixing occurs (see text). The kinematically allowed region is shown by the dashed line. The expected limit for BR 2 = 1.0, calculated from Monte Carlo alone, is represented by the indicated broken line.      sets. The excluded regions are calculated taking into account the predicted branching ratio for τ ± R → τ ±χ0 1 . The gauge unification relation, M 1 = 5 3 tan 2 θ W M 2 , is assumed in calculating the MSSM branching ratios. The selection efficiency forτ +τ − is calculated for the case that the decayτ − → τ −χ0 1 produces unpolarised τ ± . The kinematically allowed region lies below the dashed line.