Search for R-parity Violating Decays of Supersymmetric Particles in e+e- Collisions at LEP

A search, in e^+e^- collisions, for chargino, neutralino, scalar lepton and scalar quark pair-production is performed, without assuming R-parity conservation in decays, in the case that only one of the coupling constants lambda_ijk or lambda''_ijk is non-negligible. No signal is found in data up to a centre-of-mass energy of 208GeV. Limits on the production cross sections and on the masses of supersymmetric particles are derived.


Introduction
The most general superpotential of the Minimal Supersymmetric Standard Model (MSSM) [1], which describes a supersymmetric, renormalizable and gauge invariant theory, with minimal particle content, includes the term W R [2,3]: where λ ijk , λ ′ ijk and λ ′′ ijk denote the Yukawa couplings and i, j and k the generation indices; L i and Q i are the left-handed lepton-and quark-doublet superfields, E i , D i and U i are the right-handed singlet superfields for charged leptons, down-and up-type quarks, respectively.The L i L j E k and L i Q j D k terms violate the leptonic quantum number L, while the U i D j D k terms violate the baryonic quantum number B.
R-parity is a multiplicative quantum number defined as: where S is the spin.For ordinary particles R is +1, while it is −1 for their supersymmetric partners.R-parity conservation implies that supersymmetric particles can only be produced in pairs and then decay in cascade to the lightest supersymmetric particle (LSP), which is stable [4].This hypothesis is formulated in order to prevent a fast proton decay [5], disfavoured by present limits [6].However, the absence of either the B-or the L-violating terms is enough to prevent such a decay, and the hypothesis of R-parity conservation can be relaxed.As a consequence, two new kinds of processes are allowed: single production of supersymmetric particles [7,8], or LSP decays into Standard Model particles via scalar lepton or scalar quark exchange.For these decays, the MSSM production mechanisms are unaltered by the operators in Equation 1.In this letter, the cases in which either a neutralino or a scalar lepton is the LSP are considered.
In this paper, we describe the search for pair-produced neutralinos (e + e − → χ0 m χ0 n, with m = 1, 2 and n = 1, .., 4), charginos (e + e − → χ+ 1 χ− 1 ), scalar leptons (e + e − → l+ R l− R , where l± R represents scalar electrons, muons or tau and e + e − → ν ν) and scalar quarks (e + e − → qq) with subsequent R-parity violating decays, assuming that only one of the coupling constants λ ijk or λ ′′ ijk is non-negligible.Only the supersymmetric partners of the right-handed charged leptons, lR , are considered, as they are expected to be lighter than the corresponding left-handed ones.
Supersymmetric particles can either decay directly into two or three fermions according to the dominant interaction term, or indirectly via the LSP.The different decay modes are detailed in Table 1.Four-body decays of the lightest scalar lepton are also taken into account in the case of λ ′′ ijk .In the present analysis, the dominant coupling is assumed to be greater than 10 −5 [9], which corresponds to decay lengths below 1 cm.
Previous L3 results at centre-of-mass energies ( √ s) up to 189 GeV are reported in References 10 and 11, where also λ ′ ijk couplings are discussed.Two new analyses are presented in this letter: e + e − → ν ν and e + e − → qq in the case of λ ′′ ijk couplings.New interpretations for scalar leptons and scalar quarks in the MSSM framework are also performed.
Searches for R-parity violating decays of supersymmetric particles were also reported by other LEP experiments [8,12].

Direct decays
Indirect decays

Data and Monte Carlo Samples
The data used correspond to an integrated luminosity of 450.6 pb −1 collected with the L3 detector [13] at √ s = 192 − 208 GeV.For the search for scalar quarks and scalar neutrinos decaying via λ ′′ ijk couplings, also the data sample collected at √ s = 189 GeV is used.This corresponds to an additional integrated luminosity of 176.4 pb −1 .The signal events are generated with the program SUSYGEN [14] for different mass values and for all possible choices of the generation indices.
The detector response is simulated using the GEANT package [22].It takes into account effects of energy loss, multiple scattering and showering in the detector materials.Hadronic interactions are simulated with the GHEISHA program [23].Time dependent detector inefficiencies are also taken into account in the simulation procedure.
Data and Monte Carlo samples are reconstructed with the same program.Isolated leptons (ℓ = e, µ, τ ) are identified as described in Reference 11.Remaining clusters and tracks are classified as hadrons.Jets are reconstructed with the DURHAM algorithm [24].The jet resolution parameter y mn is defined as the y cut value at which the event configuration changes from n to m jets.At least one time of flight measurement has to be consistent with the beam crossing to reject cosmic rays.

λ ijk Analysis
The different topologies arising when λ ijk couplings dominate are shown in Table 2 and can be classified into four categories: 2ℓ + E /, 4ℓ + E /, 6ℓ, ≥ 4 ℓ plus possible jets and E /.The missing energy E / indicates final state neutrinos escaping detection.After a common preselection [11], based on the visible energy, the event multiplicity and the number of identified leptons, a dedicated selection is developed for each group, taking into account lepton flavours, particle boosts and virtual W and Z decay products.
Figure 1 shows the distributions of the number of leptons, thrust, normalised visible energy and ln(y 34 ) after the preselection.The data are in good agreement with the Monte Carlo expectations.
The final selection criteria are discussed in Reference 11 and yield the efficiencies for direct and indirect decays of the supersymmetric particles summarized in Tables 3 and 4, respectively.Here and in the following sections we discuss only the results obtained for those choices of the generation indices which give the lowest selection efficiencies.The quoted results will thus be conservatively valid for any ijk combination.In the case of direct R-parity violating decays, the efficiencies are estimated for different mass values of the pair-produced supersymmetric particles.In the case of indirect decays, the efficiencies are estimated for different masses and ∆M ranges.∆M is defined as the mass difference M susy − M χ0 1 , where M susy is the mass of the supersymmetric particle under investigation.
For direct neutralino or chargino decays, as well as for all indirect decays studied, the lowest efficiencies are found for λ ijk = λ 133 , due to the presence in the final state of taus, whose detection is more difficult.3: Efficiency values (ǫ, in %) and 95% C.L. cross section upper limits (σ, in pb) for direct decays of the supersymmetric particles, as a function of their mass (M, in GeV).As an example the efficiencies at √ s = 206 GeV are shown, for the most conservative choice of the couplings.At the other centre-of-mass energies they are compatible within the uncertainties.Typical relative errors on the signal efficiencies, due to Monte Carlo statistics, are between 2% and 5%.χ0 m χ0 n indicates neutralino pair-production with m = 1, 2 and n = 1, .., 4. For direct neutralino decays we quote the χ0 1 χ0 1 efficiencies.The upper limits on the pair-production cross sections are calculated using the full data sample, with a total luminosity of 627 pb −1 , except for the last mass point, where only the data collected at √ s ≥ 204 GeV are used, corresponding to a luminosity of 216 pb −1 .Chargino and scalar lepton pair-production via λ ijk couplings are not investigated for mass values excluded in Reference 11.For the processes marked with * we refer to four-body decays, as described in Section 4.  In the case of pair-production of scalar charged leptons, followed by direct decays via λ ijk , the final state contains two leptons plus missing energy.The lepton flavours are given by the indices i and j, independently of the value of k.The lowest selection efficiency is found for λ ijk = λ 12k , i.e. for events with electrons and muons in the final state, since these low multiplicity events require a tight selection to suppress the large background from lepton pair-production.

Indirect decays
Direct decays of scalar neutrinos yield four leptons in the final state.The 4ℓ+E / selections are used as they provide a good analysis sensitivity comparable to that of the dedicated selections for scalar electrons, muons and taus.Scalar neutrino decays into electrons and muons are selected with lower efficiency than decays into taus, due to the missing energy requirements.In particular, the lowest efficiency is obtained for λ 121 , which can give rise to the decays νe → µ − e + and νµ → e − e + .

λ ′′ ijk Analysis
When the λ ′′ ijk couplings dominate, the flavour composition depends on the generation indices.In the case of neutralino and chargino pair-production, the different topologies can be classified into two groups: multijets and multijets with leptons and/or missing energy, as shown in Table 5.After a common preselection [11], dedicated selections are developed for each group, depending on the particle boosts, the ∆M values and the virtual W decay products.[11].For masses below 50 GeV or small ∆M values not all jets in the event can be resolved.χ0 m χ0

Direct decays
n indicates neutralino pair-production with m = 1, 2 and n = 1, .., 4. For final states with neutrinos we use selections with no explicit missing energy requirement, because for those topologies E / is small, except for the scalar neutrino dacays.
In the case of neutralino, chargino, scalar charged lepton and scalar quark pair-production, the preselection aims at selecting well balanced hadronic events and yields 11770 events in the data sample to be compared with 11719 ± 31 expected from Standard Model processes, of which 62.0% are from qq and 32.8% W + W − .Figure 2 shows the distributions of thrust, ln(y 34 ), ln(y 45 ) and width of the most energetic jet after the preselection.The width of a jet is defined as p jet T /E jet , where the event is clustered into exactly two jets, and p jet T is the sum of the projections of the particle momenta on to a plane perpendicular to the jet axis, and E jet is the jet energy.There is good agreement between data and Monte Carlo expectations.The efficiencies for direct and indirect decays of the supersymmetric particles after the selections discussed in Reference 11 are summarized in Tables 3 and 4, respectively.
Scalar quarks and scalar neutrinos, not studied in our previous papers, are searched for as follows.Scalar quark pairs can decay directly into 4 or indirectly into 8 quarks, as shown in Table 1.In the first case, the main background sources are qq events and W + W − decays.For low masses of the primary scalar quarks, the signal configuration is more similar to two backto-back jets, due to the large jet boost.In this case we use the least energetic jet width to reject the qq background, which is the dominant one at low masses.For larger scalar quark masses (M q > 50 GeV), the signal events are better described by a 4-jet configuration and selection criteria are applied on y 34 and the χ 2 of a kinematical fit, which imposes four-momentum conservation and equal mass constraints.In the case of indirect decays into 8 quarks, the same selections as for χ0 1 χ0 1 decays into 6 quarks are used [11].For scalar neutrino pair-production, a different preselection is performed, to take into account the missing momentum in the final state.Low multiplicity events, such as leptonic Z and W decays, are rejected by requiring at least 13 calorimetric clusters.At least one charged track has to be present.The visible energy has to be greater than 0.2 √ s.In order to remove background contributions from two-photon interactions, the energy in a cone of 12 • half-opening angle around the beam axis has to be below 20% of the total visible energy.Furthermore, the thrust axis is required to be well contained in the detector.Unbalanced events with an initial state radiation photon in the beam pipe are removed.Semileptonic W + W − decays are rejected by the requirement that neither the di-jet invariant mass nor that of any identified lepton and the missing four-momentum should be in a 5 GeV interval around the W mass.This preselection yields 13950 events in the data at √ s = 189 − 208 GeV where 13662 ± 45 are expected from Standard Model processes and the main contributions are 50.6%from qq, 32.8% from W + W − , 9.2% from e + e − qq and 4.0% from qq ′ eν.The difference in the number of found and expected data appears in the region where the visible energy is below 0.5 √ s, where an important contribution from two-photon interactions and ℓνℓ ′ ν events is expected.Such events are afterwards rejected by the optimization procedure, which requires a high visible energy.
In the case of indirect decays of scalar neutrinos, the only visible decay products are the jets coming from neutralino decays.Therefore we have derived five selections according to the neutralino mass value, reflecting the different boost and jet broadening configurations.The final selection criteria are optimized [11] by taking into account the following variables: jet widths, ln(y 34 ) and ln(y 45 ), visible energy and polar angles of the missing momentum vector and of the thrust axis.
Supersymmetric partners of the right-handed leptons have no direct two-body decays via λ ′′ ijk couplings.However, when scalar leptons are lighter than χ0 1, the four-body decay lR → ℓqqq can occur [3] providing the same final state as that resulting from indirect decays, but with virtual χ0 1 production.The non-resonant four-body decay is not implemented in the generator.For this reason, we use the results of the indirect decay analysis, performing a scan over all neutralino mass values up to M lR .The resulting lowest efficiency is conservatively quoted in the following for four-body decays.It is found in most cases for M χ0 1 ≃ M lR , as the resulting low energy lepton can not be resolved from the nearby jet.For scalar taus with masses above 70 GeV, the lowest efficiency is found for high ∆M values, as in the case of indirect decays.

Model Independent Results
Table 6 shows the overall numbers of candidates and expected background events for the different processes.No significant excess of events is observed.Therefore upper limits are set on the neutralino, chargino and scalar lepton pair-production cross sections assuming direct or indirect R-parity violating decays.
In the case of λ ijk couplings, upper limits are set for each process, independently of the mass value of the supersymmetric particle considered.For λ ′′ ijk couplings, upper limits are derived for each process depending on the mass range of the supersymmetric particles, since this procedure improves the sensitivity of analyses with high background level.
These limits take into account the estimated background contamination.Systematic uncertainties on the signal efficiency are dominated by Monte Carlo statistics.The typical relative error is between 2% and 5% and it is included in the calculations of the signal upper limits [26].
Tables 3 and 4 show the 95% confidence level (C.L.) upper limits on supersymmetric particle pair-production cross sections.For each mass point, all data collected at centre-of-mass energies above the production threshold are combined.For low mass values, the data at √ s = 189 GeV are also used.Therefore these upper limits should be interpreted as a limit on the luminosityweighted average cross section.
Coupling Process 4.9 ± 0.5 6 Table 6: Number of observed data (N data ) and expected background (N back ) events for the different processes.The uncertainty on the expected background is due to Monte Carlo statistics.The deficit in the number of observed data in the neutralino, chargino and slepton analyses is correlated among the channels.

Interpretation in the MSSM
In the MSSM framework, neutralino and chargino masses, couplings and cross sections depend on the gaugino mass parameter, M 2 , the higgsino mass mixing parameter, µ, the ratio of the vacuum expectation values of the two Higgs doublets, tan β, and the common mass of the scalar particles at the GUT scale, m 0 .The results presented in this section are obtained by performing a scan in the ranges: 0 ≤ M 2 ≤ 1000 GeV, −500 GeV ≤ µ ≤ 500 GeV, 0 ≤ m 0 ≤ 500 GeV and 0.7 ≤ tan β ≤ 40.They do not depend on the value of the trilinear coupling in the Higgs sector, A.
6.1 Mass Limits from Scalar Lepton and Scalar Quark Searches For scalar lepton and scalar quark pair-production, mass limits are derived by direct comparison of the 95% C.L. cross section upper limits with the scalar particle pair-production cross sections, which depend on the scalar particle mass.
We assume no mixing in the scalar lepton sector.Scalar electron and scalar electron neutrino pair-production have an additional contribution from the t-channel exchange of a neutralino or chargino, whose mass spectrum depends on the MSSM parameters.In this case the mass limits are derived at a given value of tan β and µ, here chosen to be tan β = √ 2 and µ = −200 GeV.For scalar quarks, mixing is taken into account for the third generation.The cross section depends on the scalar quark mass and on the mixing angle θ LR .For √ s = 189 − 208 GeV the production cross section for scalar top pairs is minimal for cos θ LR ∼ 0.51 and for scalar bottom pairs for cos θ LR ∼ 0.36.These values are conservatively used in this analysis.Figures 3 and 4 show the excluded 95% C.L. contour for different scalar lepton and scalar quark masses, as a function of the neutralino mass.Indirect decays of the scalar leptons dominate over direct ones in the region with ∆M > 2 GeV.For 0 ≤ ∆M < 2 GeV, 100% branching ratio either into direct or indirect decays is assumed and the worst result is shown.In the negative ∆M region only direct decays contribute.For λ ′′ ijk direct decays of the scalar leptons we quote the results from four-body processes.The 95% C.L. lower mass limits are shown in Table 7, for both direct and indirect decays.7: Lower limits at 95% C.L. on the masses of the scalar leptons and scalar quarks.The limits result from direct comparison of the 95% C.L. cross section upper limits with the scalar particle pair-production cross sections.ũR , ũL , dR and dL refer to any type of up and down supersymmetric partners of the right-handed and lefthanded quarks.t1 and b1 limits are quoted in the case of minimal production cross section.For λ ′′ ijk direct decays of scalar leptons we refer to four-body processes.

Mass Limits from Combined Analyses
A point in the MSSM parameter space is excluded if the total number of expected events is greater than the combined upper limit at 95% C.L. on the number of signal events.Neutralino, chargino, scalar lepton and scalar quark analyses are combined since several processes can occur at a given point.Gaugino and scalar mass unification at the GUT scale is assumed.
The constraints from the L3 lineshape measurements at the Z pole [25] are also taken into account [11].We derive lower limits at 95% C.L. on the neutralino, chargino and scalar lepton masses, as detailed in Table 8.  8: Lower limits at 95% C.L. on the masses of the supersymmetric particles considered in this analysis.The limits result from combined analysis at each MSSM point and from a global scan in the parameter space, as detailed in section 6.The limits on M lR hold for ẽR , μR and τR .
Figure 5 shows the 95% C.L. lower limits on neutralino and scalar lepton masses as a function of tan β.The χ0 1 and χ0 2 mass limits are shown for m 0 = 500 GeV and the lR ones for m 0 = 0.These values of m 0 correspond to the absolute minima from the complete scan on M 2 , µ, m 0 and tan β.The chargino mass limit is almost independent of tan β, and is close to the kinematic limit for any value of tan β and m 0 .For high m 0 values, neutralino and scalar lepton pair-production contributions are suppressed and the mass limits are given mainly by the chargino exclusion.
For 0 ≤ m 0 < 50 GeV and 1 ≤ tan β < 2, the lightest scalar lepton, the supersymmetric partner of the right-handed electron, can be the LSP.Therefore in this region only the scalar lepton analysis contributes to the limit on the scalar lepton mass.For higher values of tan β, χ0 1 is the LSP and the lower limit on the scalar lepton mass is mainly given by the χ0 1 χ0 1 exclusion contours.The absolute limit on M lR is found at tan β = 0.8 in the case of λ ijk and at tan β = 0.7 for λ ′′ ijk .The difference in the limits is due to the lower cross section upper limit of λ ′′ ijk for scalar lepton direct decays, since the limit on M lR is found when the lR is the LSP.The same limits are obtained without the assumption of a common scalar mass at the GUT scale.For λ ijk the bounds on the scalar lepton masses are found in the case in which the lR is the LSP.For λ ′′ ijk the limits are found when the lR and χ0 1 are nearly degenerate in mass.In both cases, the neutralino analyses give the main contribution to the exclusion in the regions of the parameter space around the limit.The remaining sensitivity is due to searches for direct slepton decays via λ ijk .As these searches are equally sensitive to scalar electron, muon or tau signals, as shown in Table 3, the limits are unchanged.The scalar neutrino mass limit is also mainly due to neutralino exclusions, resulting in a 95% C.L. lower limit on the scalar neutrino mass above the kinematic limit.
The search for R-parity violating decays of supersymmetric particles reaches at least the same sensitivity as in the R-parity conserving case [27].Therefore, the supersymmetry limits obtained at LEP are independent of R-parity conservation assumptions.
pair-production with m = 1, 2 and n = 2, .., 4. The efficiencies correspond to M χ0 m + M χ0 n = 206 GeV.For indirect decays of charginos, scalar leptons and scalar quarks, the selection efficiencies correspond to a mass of 102 GeV.The upper limits on the pair-production cross sections are calculated using the data at √ s ≥ 204 GeV, with an integrated luminosity of 216 pb −1 .

Figure 1 :
Figure 1: Data and Monte Carlo distributions of a) the number of leptons, b) thrust, c) the normalised visible energy and d) ln(y 34 ) after the λ ijk preselection.The solid histograms show the expectations for Standard Model processes.The dotted and dashed histograms show two examples of signal, with dominant coupling λ 133 .The dotted histograms represent the process e + e − → χ0 1 χ0 1, for M χ0 1 = 42 GeV, corresponding to two hundred times the luminosity of the data.The dashed ones represent e + e − → χ+ 1 χ− 1 , with M χ± 1 = 92 GeV and ∆M = M χ± 1 − M χ0 1 = 50 GeV, corresponding to twenty times this luminosity.

Figure 2 :Figure 3 :Figure 4 :Figure 5 :
Figure 2: Data and Monte Carlo distributions of a) thrust, b) ln(y 34 ), c) ln(y 45 ) and d) width of the most energetic jet after the λ ′′ ijk preselection.The solid histograms show the expectations for Standard Model processes.The dashed and dotted histograms show two examples of signal, with dominant coupling λ ′′ 212 , corresponding to decays into c, d and s quarks.The dotted histograms represent the process e + e − → χ0 1 χ0 1, with M χ0 1 = 40 GeV, corresponding to one hundred times the luminosity of the data.The dashed ones represent e + e − → χ+ 1 χ− 1 , with M χ± 1 = 90 GeV and ∆M = M χ± 1 − M χ0 1 = 60 GeV, corresponding to fifteen times this luminosity.

Table 1 :
R-parity violating decays of the supersymmetric particles considered in this analysis.Charged conjugate states are implied.Indirect decays via scalar leptons are relevant only for neutralinos when the scalar lepton is the LSP.Only supersymmetric partners of the right-handed charged leptons are taken into account.Decays to more than three fermions are not listed.Z * and W * indicate virtual Z and W bosons.

Table 4 :
Efficiency values (ǫ, in %) and 95% C.L. cross section upper limits (σ, in pb) for indirect decays of the supersymmetric particles, as a function of ∆M (in GeV).As an example the efficiencies at √ s = 206 GeV are shown, for the most conservative choice of the couplings.At the other centre-of-mass energies they are compatible within the uncertainties.Typical relative errors on the signal efficiencies, due to Monte Carlo statistics, are between 2% and 5%.χ0

Table 5 :
Processes considered in the λ ′′ ijk analysis and corresponding selections