Neutral-Current Four-Fermion Production in e+e- Interactions at LEP

Neutral-current four-fermion production, e+e- ->ffff is studied in 0.7/fb of data collected with the L3 detector at LEP at centre-of-mass energies root(s)=183-209GeV. Four final states are considered: qqvv, qqll, llll and llvv, where l denotes either an electron or a muon. Their cross sections are measured and found to agree with the Standard Model predictions. In addition, the e+e- ->Zgamma* ->ffff process is studied and its total cross section at the average centre-of-mass energy 196.6GeV is found to be 0.29 +/- 0.05 +/- 0.03 pb, where the first uncertainty is statistical and the second systematic, in agreement with the Standard Model prediction of 0.22 pb. Finally, the mass spectra of the qqll final states are analysed to search for the possible production of a new neutral heavy particle, for which no evidence is found.


Introduction
The centre-of-mass energy, √ s, of the LEP e + e − collider reached 209 GeV, allowing the study of four-fermion production mediated by the exchange of real and virtual gauge-bosons. Fourfermion events are classified as charged-current processes or neutral-current processes [1,2]. The former proceed through the exchange of W bosons, while the latter comprise the exchange of both Z bosons and off-mass-shell photons.
The L3 collaboration has investigated both charged-current processes, in particular Wboson pair production [3] and single W-boson production [4], and neutral-current processes, with Z-boson pair production [5] and single Z-boson production [6]. Reference 7 provides a comprehensive bibliography of these studies at LEP. This Letter extends previous studies, focused on the signature of boson pairs or a single boson and missing energy, to a general analysis of neutral-current processes, e + e − → ff f ′f ′ , with either high-mass or low-mass fermion pairs. The special case of events with a Z boson and an off-mass-shell photon, e + e − → Zγ * → ff f ′f ′ , is also considered. Figure 1 presents some of the Feynman diagrams responsible for neutralcurrent four-fermion production. In the following, four processes with different combinations of quarks, leptons and neutrinos in the final state are considered: e + e − → qqνν, e + e − → qqℓ + ℓ − , e + e − → ℓ + ℓ − νν and e + e − → ℓ + ℓ − ℓ ′+ ℓ ′− , where ℓ denotes either an electron 1) or a muon. Events with tau leptons are considered as background.
High-resolution studies of four-fermion events are also sensitive to manifestations of new physics, and the mass spectra of events from the e + e − → qqℓ + ℓ − process are investigated to search for new neutral heavy particles decaying into hadrons.
L3 results on neutral-current four-fermion production in a smaller data sample obtained at lower values of √ s are discussed in References 8 and 9. A study of the e + e − → qqℓ + ℓ − process by the OPAL collaboration is described in Reference 10.
Two additional phase-space criteria, also listed in Table 1, are applied to increase the relative contribution from the e + e − → Zγ * → ff f ′f ′ process. The mass of one of the fermionantifermion pairs is required to be in the range m Z ± 2Γ Z , while the mass of the other pair is required to be outside this range, where m Z = 91.19 GeV [11] and Γ Z = 2.49 GeV [11] are the Z-boson mass and width, respectively.

Data and Monte Carlo samples
The full data-sample collected at high centre-of-mass energies with the L3 detector [12]  in Reference 9, are re-analysed within the signal definitions discussed above. In order to optimise the event selection and calculate the signal efficiencies, four-fermion events are generated with the EXCALIBUR [13] Monte Carlo program in a phase space larger than that of the signal definition criteria of Table 1. These cuts are applied on generated quantities and the selected events are considered as signal, while the remaining ones are treated as background. EXCALIBUR is also used to model four-fermion background from the e + e − → τ + τ − ff and e + e − → Weν processes. Additional four-fermion background is due to Wboson pair production and subsequent decay into fully-hadronic or semi-leptonic final states. This process is modelled with the KORALW [14] Monte Carlo program. The background from fermion pair-production, e + e − → qq, e + e − → τ + τ − and e + e − → µ + µ − , is described by KK2f [15]. Bhabha scattering is described with BHAGENE [16] and BHWIDE [17]. The e + e − → e + e − γ process with high transverse-momentum photons and low polar-angle electrons is simulated with TEEGG [18]. Events with multiple hard-photon production are generated with GGG [19]. Hadron and lepton production in two-photon collisions are modelled with PHOJET [20] and DIAG36 [21], respectively.
The L3 detector response is simulated using the GEANT [22] program which takes into account the effects of energy loss, multiple scattering and showering in the detector. GHEISHA [23] is used for the simulation of hadronic interactions. Time-dependent detector efficiencies, as monitored during the data-taking period, are included in the simulations.
The signal cross sections are calculated with the GRC4F [24] Monte Carlo program which, unlike EXCALIBUR, includes fermion masses. About twenty thousand events are generated at each value of √ s for each possible flavour combination. The numbers of events satisfying the criteria in Table 1 and their weights are then used to calculate the signal cross sections, listed in Table 3. The cross sections for the e + e − → Zγ * → ff f ′f ′ processes are extracted for each final state by applying the additional cuts in Table 1, with the results listed in Table 4. Small differences between the GRC4F and the EXCALIBUR modelling of the e + e − → ff f ′f ′ process have a negligible impact on the measurements described in the following.

Event selection
The event selection [25] is similar to that devised for the study of Z-boson pair production [5]. Events which contain electrons, muons or hadronic jets are selected and these objects are then combined to construct kinematic variables to isolate the neutral-current four-fermion signal from the two-fermion, four-fermion and two-photon backgrounds.
Electrons are identified by requiring a well-isolated electromagnetic cluster in the electromagnetic calorimeter with an associated track in the tracking chamber. To increase efficiency, this track-matching requirement is relaxed by some selections.
Muons are reconstructed from correlated tracks in the muon spectrometer and the central tracker which are in time with the beam crossing. Calorimetric clusters compatible with a minimum ionising particle with an associated track in the central tracker are also accepted.
Quark fragmentation and hadronisation yield a high multiplicity of calorimetric clusters and charged tracks. These are grouped into jets by means of the DURHAM algorithm [26].
Fermion-antifermion pairs can originate from a Z boson or, for charged fermions, from an offmass-shell photon. In the first case, the pair is characterised by high mass, while in the second case it has most likely a low mass. Appropriate selections for these two cases are implemented.
Typical selection variables are: the visible energy of the event, E vis ; the transverse, p t , and longitudinal, p , components of the vectorial sum of the momenta of all objects in the event; the missing momentum, p mis , and the angles between two jets or two leptons in space, ∆ψ, or in the plane transverse to the beam axis, ∆φ.
The data sample spans a √ s range of about 25 GeV, which results in appreciable differences in the kinematics of the signals. The selection criteria are optimised to reflect these differences and change over the √ s range.
Some aspects of the different selections are described in the following, while their yields are summarised in Table 3.

The qqνν channel
The signature of the e + e − → qqνν process is two hadronic jets and missing energy mostly due to the production of a Z boson decaying into neutrinos. The most important background is W-boson pair production.
High-multiplicity events are selected and reconstructed as two jets. No electrons or muons with energies above 20 GeV are allowed in order to reduce the background from W-boson pair production and subsequent semi-leptonic decay. Events with photons with energy above 20 GeV are rejected so as to reduce background from the e + e − → qq process with a hard initial-state-radiation (ISR) photon. The background from hadron production in two-photon collisions is suppressed by limiting the energy deposition in the low-angle calorimeters and by rejecting events with a two-jet mass, m qq , below 10 GeV. A low-mass selection is applied for m qq < 50 GeV and a high-mass selection otherwise.
The low-mass selection removes background from hadron production in two-photon collision by requiring at least one jet to point more than 0.3 rad away from the beam axis. The e + e − → qq process results in two back-to-back jets in the plane transverse to the beams and, if no ISR occurred, in two jets which are also back-to-back in space. It is strongly suppressed by requiring ∆φ < 3 rad and ∆ψ < 3 rad. The requirements ∆φ > 1.8 rad and ∆ψ > 1.8 rad remove background from the e + e − → Weν process and semi-leptonic decays of W-boson pairs as the W-boson boost results in opening angles smaller than those for the signal. Large missing momentum is due to the production of a Z boson and is tagged by requiring p mis > 0.3 √ s and The high-mass selection accepts events with a higher multiplicity and a missing mass, m νν = ( √ s − E vis ) 2 − p 2 mis , compatible with m Z , 78 GeV < m νν < 115 GeV. Background from Wboson pair production and the e + e − → qq process is reduced by requiring 8 GeV < p t < 40 GeV. The normal to the plane of the two jets must not point more than 1.5 rad away from the beam axis. In addition, the event thrust must be greater than 0.78 − 0.88 and ∆ψ > 2 − 2.5 rad, depending on √ s. The e + e − → qq process with hard ISR photons is further reduced by requiring p < 30 − 42 GeV. Figure 2a shows the distribution of ∆φ for both the low-and high-mass selections. The residual background is mostly due to W-boson pair production and the e + e − → Weν process.

The qqℓ + ℓ − channel
The signature of the e + e − → qqℓ + ℓ − process is two hadronic jets and either an electron or a muon pair. This signature can also arise from four-fermion events outside the signal definition. Other sources of background are W-boson pair production and the e + e − → qq process with leptons coming from heavy-quark decays.
High-multiplicity events with two electrons or two muons are selected and the remaining calorimetric clusters are reconstructed as two jets. The measured energies and momenta of the two jets and the two leptons are varied within their resolutions to best fit the hypotheses of energy and momentum conservation. This kinematic fit improves the resolution of the jetenergy measurements.
Events with W-boson pair production and semi-leptonic decay have missing momentum due to the neutrinos and are suppressed by requiring p t /E vis < 0.35 and p /E vis < 0.35. A low-mass selection is applied if 500 GeV 2 < m qq ×m ℓℓ < 4000 GeV 2 , where m qq is the two-jet mass and m ℓℓ the mass of the lepton pair. A high-mass selection covers the range m qq × m ℓℓ > 4000 GeV 2 . Events with m qq × m ℓℓ < 500 GeV 2 exhibit a large background contamination and are not further considered. The selection criteria depend on the flavour of the leptons and on √ s.
In order to reduce the background from W-boson pair production, the low-mass analysis requires p t /E vis < 0.12 − 0.14 for electrons and p t /E vis < 0.22 − 0.30 for muons. The energy of the most energetic lepton, E 1 , is required to satisfy E 1 / √ s > 0.12 − 0.15 in order to remove leptons from heavy-quark decays. For electrons, the energy of the least energetic lepton, E 2 , must satisfy E 2 / √ s > 0.07 − 0.15. The high-mass analysis requires E 2 / √ s > 0.06 − 0.10 and p t /E vis < 0.11 − 0.14 for electrons and E 1 / √ s > 0.10 − 0.16 and E vis / √ s > 0.5 − 0.7 for muons. Figures 2b and 2c, show the distributions of p t /E vis and E 1 / √ s. The residual background in both channels is due to events from four-fermion production outside the signal definition, from W-boson pair production and from the e + e − → qq process.

The ℓ + ℓ − νν channel
The signature of the e + e − → ℓ + ℓ − νν process is an electron or muon pair and large missing energy, mostly due to a Z boson decaying into neutrinos. The most important backgrounds are lepton pair production with a hard ISR photon and W-boson pair production.
Events with just one or two tracks associated to two identified electrons or muons are selected. To reduce background from annihilation and two-photon lepton pair production, no large energy deposition is allowed in the low polar-angle calorimeters. Events with m ℓℓ < 10 GeV are removed from the sample. The remaining events are considered by three overlapping selections, according to the value of m ℓℓ . Background from lepton pair production results in low-p t events with back-to-back leptons and is reduced by requiring p t / √ s > 0.1 − 0.3 and ∆φ < 2.6 − 3.1 rad as shown in Figure 2d. The background is strongly suppressed by requiring the recoil mass to be compatible with m Z . Finally, the signal purity is enhanced by requiring The remaining background is almost entirely due to e + e − → ℓ + ℓ − νν events outside the signal definition criteria.

The
The signature of the e + e − → ℓ + ℓ − ℓ ′+ ℓ ′− process is four leptons of which at least one pair originates from a Z boson or a low-mass virtual photon. These configurations are found in background from four-fermion events outside the signal definition criteria and lepton pair production with additional radiative photons, which mimic electrons in the detector.
Events with three or four tracks and four identified leptons are selected if E vis / √ s > 0.4. All same-flavour lepton pairs are considered and their mass is calculated. If at least one pair has a mass above 40 GeV, the event is considered by a high-mass selection which starts from the lepton pair with mass closer to m Z . A low-mass selection, aimed to identify events with a lepton pair originating from a low-mass off-mass-shell photon, is applied if at least one lepton pair has a mass below 60 GeV. The low-mass selection starts from the lepton pair with the lowest mass. An event can be considered and selected by both selections.
The high-mass selection requires the lepton pair to have 1.55 rad < ∆ψ < 3.10 rad, where the upper cut removes non-radiative fermion-pair events. The other two leptons must satisfy 0.1 rad < ∆φ < 2.3 rad. Radiative lepton-pair production is further suppressed by requiring p / √ s < 0.4. Four-fermion background is reduced by requiring the masses of both pairs to be below 120 GeV. The low-mass selection requires the lepton pair to have 0.1 rad < ∆ψ < 2.8 rad, while the two other leptons must satisfy ∆φ < 1.0 rad and 1.45 rad < ∆ψ < 3.05 rad. Radiative lepton-pair production is suppressed by requiring p / √ s < 0.36, p t / √ s > 0.06 and by upper cuts on the lepton energies. Four-fermion events outside the signal definition are removed by requiring the mass of the second pair to be in the range 14 − 152 GeV. The residual background originates in equal parts from lepton pair production and fourfermion events outside the signal definition criteria. Some contribution from lepton production in two-photon collisions is observed for final states with electrons.

4.1
The e + e − → ff f ′f ′ process Figure 3 presents two-dimensional plots of the m νν and m qq masses for the qqνν final state and the m ℓℓ and m qq masses for the qqℓ + ℓ − final states. The data exhibit contributions from Z-boson pair production, final states with a Z boson and an off-mass-shell virtual photon and the continuum. A good agreement is observed with the Monte Carlo predictions, for the qqνν and qqe + e − final states, with some fluctuations for the qqµ + µ − final state.
The cross sections for neutral-current four-fermion production are derived from the m ℓℓ spectra for all channels with leptons and the m qq spectrum for the qqνν final state, shown in Figure 4. The background level and shape is fixed to the Monte Carlo predictions, and the e + e − → ff f ′f ′ normalisation is then derived from the data. Table 3 compares the measured and expected cross sections, determined as the luminosity-weighted average of the cross sections at each of the average centre-of-mass energies listed in Table 2. A good agreement is observed.
Several possible sources of systematic uncertainties are considered as summarised in Table 5. The jet and lepton identification and reconstruction are affected by the energy scale of the calorimeters and the accuracy of the track measurements. The analysis is repeated by varying the energy scale by ±2% and modifying the lepton selection criteria. The differences are considered as systematic uncertainties.
Monte Carlo modelling of the detector response is in general accurate. Possible systematic uncertainties could arise from distortions in the modelling of tails of distributions used in the event selection. These are addressed by varying the selection criteria on the variables susceptible to remove the largest part of the background by an amount compatible with their resolution. The measurements of the cross sections are repeated and largest variations are assigned as systematic uncertainties.
Small effects from the limited signal and background Monte Carlo statistics are also considered as systematic uncertainties.
Finally, the uncertainties of the background normalisations are propagated to the measured cross sections. A variation of ±10% is assumed for neutral-current four-fermion events generated with EXCALIBUR which fail the signal identification criteria and for the e + e − → Weν process, ±2% on fermion pair production, ±0.5% on W-boson pair production, and ±25% and ±50% on lepton and hadron production in two-photon collisions, respectively.

4.2
The e + e − → Zγ * → ff f ′f ′ process The cross sections of the e + e − → Zγ * → ff f ′f ′ process are determined with the same procedure as described above. Signal Monte Carlo events are subjected to the additional signal definition criteria for the e + e − → Zγ * → ff f ′f ′ process described in Table 1. The selected events are treated as the e + e − → Zγ * → ff f ′f ′ signal, illustrated in Figure 4. Events which fail these criteria are considered as an additional background and their cross section is fixed to the predictions. The cross sections measured for each channel are presented in Table 4. Systematic uncertainties are assessed as for neutral-current four-fermion production and listed in Table 5.
By combining the five different channels, the total e + e − → Zγ * → ff f ′f ′ cross section at √ s = 196.6 GeV is determined to be 0.29 ± 0.05 ± 0.03 pb, where the first uncertainty is statistical and the second systematic, to be compared with the GRC4F prediction of 0.22 pb.

Production of neutral heavy particles
Figures 5a and 5c present the spectra of the mass recoiling against the electron or muon pairs, respectively, while Figures 5e presents their sum. A new, neutral, heavy particle decaying into hadrons would manifest as a peak in these distributions. All distributions agree with the Monte Carlo predictions: apart from the Z-boson peak, no other significant structure is observed. The study is narrowed to the case in which the mass of the lepton pair is compatible with |m ℓℓ − m Z | < 2Γ Z . Again, no significant deviations from the Standard Model predictions are observed, as presented in Figures 5b, 5d and 5f.

Summary
The high energies and high luminosity achieved by LEP have allowed detailed studies of fourfermion production. Previous L3 studies involving single and pair production of W and Z bosons are complemented with a study of events from inclusive four-fermion neutral-current production, e + e − → ff f ′f ′ , and from the e + e − → Zγ * → ff f ′f ′ process. Four different final states are considered. Their cross sections are measured and found to agree with the Standard Model predictions, as shown in Table 3, Table 4 and Figure 6 for the e + e − → qqνν, e + e − → qqℓ + ℓ − and e + e − → Zγ * → ff f ′f ′ processes. The combined statistical and systematic accuracy of the e + e − → Zγ * → ff f ′f ′ cross section measurement is 15%. No evidence is found for a new neutral hadronic-decaying heavy particle produced in four-fermion events.
The L3 Collaboration: 7 188.6 191.6 195.5 199.5 201.7 205.1 206.8 196.6 L [pb −1 ] 55.4 176.8 29.7 83.7 82.7 37.1 69.1 138.9 673.4 Table 2: Centre-of-mass energies and integrated luminosities for the different data-taking periods. The last column gives the luminosity-averaged centre-of-mass energy and the total integrated luminosity.  Table 3: Numbers of events observed for the e + e − → ff f ′f ′ selections, N Data , compared to the Monte Carlo predictions for signal, N MC Sign , and background, N MC Back . The selection efficiencies, ε, are also given together with the measured cross sections, σ 4f and the expectations from the GRC4F Monte Carlo, σ Th 4f . They refer to the luminosity-weighted average of the cross sections for each value of √ s in Table 2, corresponding to an average centre-of-mass energy < √ s >= 196.6 GeV. The first uncertainty on σ 4f is statistical and the second systematic.  Table 4: Numbers of events observed for the e + e − → Zγ * → ff f ′f ′ selections, N Data , compared to the Monte Carlo predictions for signal, N MC Sign , and background, N MC Back . The selection efficiencies, ε, are also given together with the measured cross sections, σ Zγ * and the expectations from the GRC4F Monte Carlo, σ Th Zγ * . They refer to the luminosity-weighted average of the cross sections for each value of √ s in Table 2, corresponding to an average centre-of-mass energy < √ s >= 196.6 GeV. The first uncertainty on σ Zγ * is statistical and the second systematic.  Table 5: Sources and effects of systematic uncertainties. Values are given as the percentual variation on the measured cross sections of the e + e − → ff f ′f ′ (4f ) and e + e − → Zγ * → ff f ′f ′ (Zγ * ) processes. The last column refers to the combination of the channels used to measure the e + e − → Zγ * → ff f ′f ′ cross section. The total systematic uncertainty is the sum in quadrature of the different contributions. Figure 1: Dominant Feynman diagrams contributing to neutral-current four-fermion production. The wavy lines represent a Z boson or an off-mass-shell photon.
[rad] φ ∆  Figure 3: Distributions of the missing mass vs. the hadron mass for the qqνν channel, first row, and the lepton mass vs. the hadron mass for the qqe + e − channel, second row, and qqµ + µ − channel, third row. The left-hand side plots represent the data, the right-hand side ones the Monte Carlo predictions.  : Cross sections measured as a function of the centre-of-mass energies for the a) e + e − → qqνν, b) e + e − → qqℓ + ℓ − and c) e + e − → Zγ * → ff f ′f ′ processes. The expectations from the GRC4F Monte Carlo are also shown, with an uncertainty of ±5%. Both the data and the predictions for the e + e − → qqℓ + ℓ − process refer to the sum of the electron and muon final states.