Production of Single W bosons at LEP

We report on the observation of single W boson production in a data sample collected by the L3 detector at LEP2. The signal consists of large missing energy final states with a single energetic lepton or two hadronic jets. The cross-section is measured to be 0.61(-0.33)(+0.43) +/- 0.05 pb at the centre of mass energy root s = 172 GeV, consistent with the Standard Model expectation. From this measurement the following limits on the anomalous gamma WW gauge couplings are derived at 95% CL: -3.6 < Delta kappa gamma < 1.5 and -3.6 < lambda gamma < 3.6. (C) 1997 Published by Elsevier Science B.V.

J.M. You ak, An. Zalite"", Yu. Zalite"", P. Zemp az, Y. Zeng a, Z. Zhang h, Z.P. Zhang   A specific feature of this reaction is a final state positron (electron) produced at very low polar angle and therefore not detected. Thus the signature of this process is large transverse missing energy and either a single energetic lepton, if the W boson decays into lepton and neutrino, or two hadronic jets in case of hadronic W decays. This process constitutes a background to missing energy searches for new physics beyond the Standard Model. No measurement of single W production has so far been reported at LEP In this paper we present a measurement of the cross section for the process efe-+ e+v,W-using both leptonic and hadronic decays of W bosons. From this observation we derive limits on the anomalous yWW couplings. The Monte Carlo events are simulated in the L3 detector using the GEANT 3.15 program [ 201, which takes into account the effects of energy loss, muItiple scattering and showering in the detector. The GHEISHA program [ 2 11 is used to simulate hadronic interactions in the detector.

Analysis
In the analysis described below, the signal is defined as e+e-+ e+v, ff events that satisfy the following phase space requirements: lcos f&1 ) > 0.997 min (Ef,E,,) > 15 GeV lcos e,-1 < 0.75, fore+v,e-fi, events only (2) where tJ,i (8,-) is the polar angle of the outgoing positron (electron), and Ef and E? are the fermion energies. The final states e+e---f e+v, f?' that do not satisfy these conditions are considered as a background; they consist mostly of the reaction e+e-+ w+w-. Inside the region of phase space (2) the single W production (process I ) dominates since it peaks strongly at 1 cos Be 4 1 -1. On average it accounts for 90% of all events in this region, the remaining 10% being mostly non-resonant final states. The purity depends slightly on the flavour of the f? pair from Wdecays.
The above is illustrated in Fig. 2 using a Monte Carlo sample of e+e-+ efv,pu-p, final states. The cosine of the polar angle distribution, cos B,t , is shown in Fig. 2a. The invariant mass distributions MpLfi, and M,+ ,+ for events satisfying phase space conditions (2) are presented in Figs. 2b and 2c. Only the MppYp spectrum shows resonant behaviour at the W mass; the M,I + spectrum is clearly non-resonant since the positron does not originate from a W.
Due to the small data samples at the two centre of mass energies, the data are combined and the crosssection is quoted at ,,& = 172 GeV. The cross-section increases by a factor 1.20 from 4 = 161 GeV to fi = 172 GeV according to the GRC4F predictions. The relative contribution of each final state to the signal is given by the corresponding cross-section and experimental selection efficiency. The selection efficiencies depend slightly on the amount of non-resonant contribution and thus on the anomalous couplings AK, and A,. In the following measurement this dependence is neglected. This leads to an additional systematic uncertainty which is estimated to be smaller than 5% of the measured cross-section.

Leptonic Jinal states
A distinct feature of the process e'e-+ e+v,W-, W-+ e-fil is a high energy lepton from W decay with no other significant activity in the detector.
Events with one charged lepton (electron, muon or tau) with an energy of at least 15 GeV are selected. The lepton identification is based on the energy distribution in the electromagnetic and hadron calorimeters with respect to the trajectory of charged tracks. Events containing tracks that do not belong to the lepton are rejected. The visible energy, Evis, is calculated as the sum of the lepton energy, Et, and the energies of all neutral clusters in the event. The ratio Ep/'E,is for events preselected as described above is shown in Fig. 3a. The requirement Ee/E,is > 0.9 suppresses background from two fermion production e+e----f C+C-(y). In addition, the energy in the 0.44 rad azimuthal angle sector along the missing en- ergy direction must be below 1 GeV. For the single electron final states, the polar angle is required to be ( cos 8,1 < 0.72. This requirement reduces the contribution from Bhabha scattering and from the process e+e-+ e+e-vti where the e+e-pair originates from a low-mass virtual photon. A high energy lepton from the two fermion processes efe--+ PC(y) which matches the above selection criteria is usually produced along with a high energy electron or photon detected in the forwardbackward luminosity calorimeters. This correlation is a direct consequence of momentum conservation in the transverse plane. Therefore it is required that the energy deposition in the forward calorimeters, Em, does not exceed 15 GeV (Fig. 3b). Two events satisfy all selection criteria: a 40.5 GeV electron candidate from the fi = 161 GeV data sample (shown in Fig. 4) and To reject events from the two fermion production process e'e-+ qq(r) the transverse missing energy is required to exceed 10 GeV. The missing momentum vector must be at least 0.30 rad away from the beam axis and the energy in the 0.44 rad sector along its direction must be below 10 GeV. In addition, the opening angle between the two jets in the plane perpendicular to the beam direction must not exceed 3.0 rad and the energy in the 0.70 rad sector along the direction opposite to the two jets must be below I5 GeV. The final lepton energy spectrum for the selected Events containing identified leptons with energy events is presented in Fig. 5 together with the Monte greater than 15 GeV are rejected in order to suppress Carlo expectations for the signal and background. The the remaining background from e+e-+ W+Wsignal selection efficiencies at 4 = 161 GeV are where one of the W bosons decays into leptons. In found to be (80*4)%, (S&2)% and (30&2)% for W-i e-v,, W---f p"-fiK and W--+ r-V, decays, respectively. Each efficiency decrease slightly at fi= 172GeV b y approximately 4% absolute. The background in the fi = 161 GeV data sample is estimated to be 0.23 f 0.08 events of which 0.11 & 0.0 1 are from efe-4 ,LL+,.Y (y) and e+e-+ r+r-(y) events, 0.07 f 0.07 are from e+e----f e+e-(y) scattering and 0.05 + 0.03 are from four-fermion processes. The background from two-photon interactions is found to be negligible. For the fi = 172 GeV data sample the background contamination is calculated to be 0.26 f 0.07 events. The total error on the background is mostly due to the large uncertainty in the number of expected e+e-+ e+e-(y) events.

Hadronicjnal states
The selection of candidates for the process e+e-+ eiveW-, W---t qq' is based on the following requirements: two acoplanar hadronic jets, no leptons, and large missing transverse energy.
High multiplicity hadronic events with more than four charged tracks are selected with large energy deposition in the electromagnetic calorimeter (EEcA~_ > 15 GeV). All energy clusters in the event are combined to form two hadronic jets using the DURHAM algorithm [ 22). The energy in the forward luminosity calorimeters is required to be smaller than 50 GeV. These cuts reduce contributions from the pure leptonic final states e+e-+ e+e-(y), p+p-(y), 7-+7-(y) and two-photon interactions efe-+ e+e-qq while keeping a significant fraction of hadronic events from e+e-+ Z(y), e+e--+ W+W-and eie-+ ZZ.

Run # 667611
Event # 920 b-----', Fig. 6. A candidate event for single W boson hadronic decay. The event consist of two acoplanar hadronic jets seen as groups of topologically connected tracks (TJZC) and energy clusters (ECAL and HCAL) The pulse heights in the ECAL and size of squares in the HCAL are proportional to the energy deposition. The opening angle between the jets is 2.82 rad in the plane transverse to the beam direction. The jet-jet invariant mass is measured to be 9 I GeV and the missing energy is 35 GeV in the transverse plane.
addition, three jets are formed for every remaining event using the DURHAM algorithm. The stereo angle defined by the directions of these jets is required to be smaller than 3.0 rad. Four candidate events are selected in the ,/? = 161 GeV data sample and seven in the fi = 172 GeV data sample. A typical candidate event satisfying all selection criteria is shown in Fig. 6. The jet-jet invariant mass spectrum of the selected candidates, Minv, is shown in Fig. 7 together with the fitted signal and the Monte Carlo background predictions.
Events with invariant mass smaller than 100 GeV are used for the cross-section determination. This requirement rejects one candidate from the fi = 172 GeV data sample and reduces significantly the background contamination.
The signal efficiency is then found to be (41 III 2)%, independent of the centre of mass energy. The background is estimated to be 2.1 i 0.1 events for the fi = 161 GeV data and 4. I * 0.2 events for the fi = 172 GeV data sample.

Results
The total cross-section of all signal processes is determined from a binned likelihood fit to the distributions presented in Figs. 5 and 7. The background shapes and normalisations are fixed to the Monte Carlo prediction. The fitted signal cross-section, g( e+e-+ ev,W), corresponds to that of the process e+e-4 ev,f ?', where f f' denotes a sum of cut and q q' final states satisfying the phase space conditions (2). The measured values of the W branching fractions [23] are assumed in the fit. The relative contribution of the non-resonant eu,f? final states to the signal is fixed to the GRC4F prediction. The total cross-section is found to be a(e+e----f ev,W) = 0.61?:,:; * 0.05 pb (3) at fi = 172 GeV. The first error represents statistics and the second one accounts for the experimental systematics due to the uncertainties in the efficiency and the background contamination. The measured crosssection value is consistent with the Standard Model prediction of 0.35 pb calculated with GRC4F. This is the first experimental measurement of the process e+e-+ e+v,W-.
The total cross-section for the leptonic final states (2)  at fi = 172 GeV using the same fitting technique. The total cross-section for the hadronic final states (2) is found to be v( e+e-+ eveq q') = 0.4510,$ It 0.04 pb.
The signal cross-section as a function of anomalous couplings is calculated with GRC4F. Using the same fitting technique as for the cross-section measurement, the following limits on AK, and A, are obtained: -3.6 < A, < 3.6 at 95% CL -3.6 < AK, < 1.5 at 95% CL.
The 63% and 95% contours are presented in Fig.  8. These limits are comparable to similar limits on anomalous couplings reported at hadron colliders [ 4-61.