Search for Heavy Isosinglet Neutrino in e+e- Annihilation at LEP

We report on a search for the first generation heavy neutrino that is an isosinglet under the standard SU(2)_L gauge group. The data collected with the L3 detector at center-of-mass energies between 130 GeV and 208 GeV are used.The decay channel N_e -->eW is investigated and no evidence is found for a heavy neutrino, N_e, in a mass range between 80 GeV and 205 GeV. Upper limits on the mixing parameter between the heavy and light neutrino are derived.


Introduction
In the Standard Model of electroweak interactions [1], neutrinos are the only fundamental fermions which do not have a right-handed component that transforms as an isosinglet under the SU(2) L gauge group.However, additional heavy isosinglet neutrinos occur in various models that attempt to unify the presently known interactions into a single gauge scheme, such as Grand Unified Theories or Superstring inspired models [2].Several extended electroweak models, including left-right symmetric and see-saw models [3] also predict the existence of such neutrinos.
Heavy isosinglet neutrinos can couple to the W and Z bosons through their mixing with the light neutrinos.Constraints on isosinglet neutrino mixing were set by several experiments [4][5][6].Heavy neutrinos were searched for in leptonic decays of mesons and in neutrino beam experiments [4], resulting in stringent upper limits on the square of their mixing amplitude to ordinary neutrinos, |U ℓ | 2 , down to 10 −7 in the mass region below 3 GeV.LEP experiments [5] set limits on |U ℓ | 2 of the order of 10 −3 to 10 −5 for the neutrino mass range from 3 GeV up to 80 GeV, and the L3 experiment derived the first limits on |U ℓ | 2 for neutrino masses above the W mass [6].
The data used in this analysis were collected with the L3 detector [7] at LEP at center-ofmass energies, √ s, between 192 GeV and 208 GeV corresponding to an integrated luminosity of 450 pb −1 , out of which ∼115 pb −1 were collected at √ s = 206.5 GeV and ∼8 pb −1 at √ s = 208 GeV.Final results also include our earlier data recorded at √ s = 133 − 189 GeV [6].

Production and decay
This search is performed under the assumption that one heavy isosinglet neutrino N ℓ is associated with each generation of light neutrinos with the mixing amplitude U ℓ .Neither the mixing between light neutrinos and higher isodoublet states nor the mixing among light neutrinos are considered [8].
In e + e − annihilation, single production of heavy neutrinos occurs via the mixing between the heavy neutrino and its associated isodoublet neutrino, as presented in Figure 1: e + e − → N ℓ ν ℓ .
The corresponding heavy neutrino pair production cross section is suppressed with respect to the single production cross section by an additional |U ℓ | 2 factor, which is expected to be below 0.1 for a heavy neutrino mass, m N , larger than 80 GeV [9].The single production proceeds through s-channel Z exchange for all generations.In addition, the first generation heavy neutrinos, N e , which couple to electrons, are also produced through t-channel W exchange. Figure 2 shows that the t-channel contributions to the total production cross section are dominant and the production cross section for N e can be as high as 0.7 pb.The production cross section for N µ and N τ is below the sensitivity of LEP and these heavy neutrinos are not considered in the following.
Heavy isosinglet neutrinos decay via the neutral or charged weak currents: The decay into the Z boson is suppressed by the limited phase space for heavy neutrinos with masses close to the the W and Z masses.For masses above 150 GeV the branching ratios reach the asymptotic values Br(N e → eW) = 2/3 and Br(N e → Zν e ) = 1/3 [10].

Event simulation
Using the full differential cross section [11], a dedicated Monte Carlo generator is constructed to simulate the production and decay of the heavy isosinglet neutrinos.Subsequent hadronic fragmentation and decays are simulated by the JETSET Monte Carlo program [12].The effects of the finite width of the produced W and Z bosons as well as initial and final state radiation are taken into account.This Monte Carlo program is used to generate several samples of signal events with heavy neutrino masses ranging from 80 GeV up to the kinematic limit.For the simulation of background from Standard Model processes, the following Monte Carlo programs are used: KK2f [13] (e + e − → qq(γ)), PYTHIA [12] (e + e − → Ze + e − , ZZ), KORALZ [14] (e + e − → τ + τ − (γ)), KORALW [15] (e + e − → W + W − ), PHOJET [16] (e + e − → e + e − qq), DIAG36 [17] (e + e − → e + e − τ + τ − ), and EXCALIBUR [18] for other four-fermion final states.
The Monte Carlo events are simulated in the L3 detector using the GEANT [19] and GHEISHA [20] programs, which take into account the effects of energy loss, multiple scattering and showering in the materials.Time dependent detector inefficiencies, as monitored during the data taking, are also reproduced.

Event signatures and selection
The present analysis concentrates on the decay channel N e → eW with W → jets.The signature of these events is one isolated electron plus hadronic jets.Since there is only one neutrino in the final state, it is possible to reconstruct the invariant mass of the heavy neutrino, that will manifest itself as a peak in the invariant mass distribution.Moreover, this decay channel has the largest branching ratio varying between 68% and 45% depending on the heavy neutrino mass.The dominant backgrounds come from W + W − production with one hadronic and one leptonic W decay (92%), qq(γ) (5%) and ZZ production (2%).
The electron identification and jet reconstruction procedures follow the criteria described in Reference 6.The event selection requires at least two hadronic jets plus one isolated electron.The visible energy must exceed 70 GeV and the number of reconstructed tracks must be greater than 6.The polar angle θ of the missing momentum has to be in the range 25 • < θ < 155 • .The visible mass of the event, m vis , is reconstructed and, to improve the resolution, it is rescaled as: where p ν is the missing momentum of the event, and E vis is the visible energy.Figure 3 presents the distribution of the rescaled invariant mass, m resc , after the application of the previous cuts.Good agreement is found between data and Monte Carlo expectation.This spectrum is divided in two regions of m resc , below and above 100 GeV.In the first, "region 1", the heavy neutrino mass is close to the W mass and a significant fraction of W's produced in N e decays are offshell.For m resc > 100 GeV, "region 2", the W's are produced mostly on-shell.In this case a kinematic fit improves the resolution on the mass measurement, the determination of jet energies and angles, and the missing momentum direction for both the signal and the W + W − background.Four-momentum conservation and the constraint that the invariant mass of the hadronic jets is equal to the W mass, are imposed in the fit.In region 1 we select 27 data events with 23.6 ± 0.6 events expected from the Standard Model processes.The corresponding numbers for region 2 are 794 and 776.2 ± 3.5.Figure 4 displays the distribution of the invariant mass of the electron and the missing momentum, m eν , for events in region 2 after the application of the kinematic fit.A clear peak coming from the W + W − background is observed at the W mass.
Finally, the W + W − background is reduced by requiring the invariant mass of the electron and missing momentum to be outside the W mass region, m eν < 70 GeV or m eν > 90 GeV, which rejects 70% of the background events.Figure 5 shows the invariant mass of the events accepted after this cut.We observe a good agreement between the data and expected Standard Model background: 233 data events pass the selection with 226.5 ± 1.8 events expected from the background, out of which 88% are from W + W − production, 9% from qq(γ) production and 3% from ZZ production.

Results
As no signal is observed, the 95% confidence level upper limits on the square of the mixing amplitude, |U e | 2 , are calculated from the number of the data and background events [22].In region 1, the total number of selected and expected events is used.In region 2, the number of events in data and background for a given heavy neutrino mass m N is defined as the number of events with a reconstructed mass in the interval m N ± 2σ.The mass resolution σ varies from 2 to 2.5 GeV over the investigated mass range.The overall selection efficiency for heavy neutrino events varies smoothly from 20% up to 45% depending on the values of m N and √ s.The systematic uncertainty on the signal selection efficiency is mainly due to the uncertainty in the simulation and reconstruction of the heavy neutrinos (∼3%), the signal Monte Carlo statistics (∼3%), and the energy calibration (∼2%).It is estimated to be 5% relative and is taken into account in the limit calculation by reducing the selection efficiency by 5%.
Figure 6 shows the measured upper limits on the mixing amplitude |U e | 2 as a function of the heavy neutrino mass, along with the expected limits as calculated from a large number of Monte Carlo experiments.These results are obtained using the whole data sample collected by L3 at LEP, and improve upon and supersede our previously published results [6].

Figure 1 :Figure 2 :Figure 3 :Figure 4 :Figure 5 :
Figure 1: Feynman diagrams showing the production of isosinglet neutrinos via a) s-channel and b) t-channel.Here ℓ denotes e, µ or τ for the s-channel production.

Figure 6 :
Figure 6: Observed and expected upper limits at the 95% confidence level on the mixing amplitude |U e | 2 as a function of the heavy isosinglet neutrino mass m N .