All selections are mutually exclusive.
A first preselection step aims at removing events with a large undetected ISR photon from radiative returns to the Z by requiring that the absolute value of the total longitudinal momentum of all objects be less than 1.5(Mvis-MZ) where Mvis is the observed visible mass. All accepted particles are then forced to form four jets using the DURHAM-PE algorithm [] for the following STANDARD analysis. Only events where the transition in the jet resolution parameter, y34, is larger than 0.001 are kept. To reject q[`q] events with a visible ISR photon, none of the four jets can have more than 95% of electromagnetic energy in a 1° cone around any particle included in the jet. Four-fermion final states in which one of the fermions is a charged lepton are rejected by requiring that the leading charged particle of each jet carries less than 90% of the jet energy.
A neural network trained at five CM energies (189, 196, 200, 205 and 207 GeV) on Monte Carlo CC03 and background events is used to tag the preselected events. There are 14 input variables based on global event properties, heavy quark flavour tagging, reconstructed jet properties and WW kinematics. The neural net output ranges from 0 to 1. The signal is well separated from the q[`q](g) background with 90% efficiency and 80% purity by requiring a neural net output ³ 0.3.
According to the Monte Carlo a significant fraction ( ~ 6%) of the accepted events are accompanied by an initial state radiation (ISR) photon that can be detected in the calorimeters separately from the hadronic jets. Such photons can be removed from the jet clustering process, thus improving the invariant mass resolution for W pairs. Studies at 189 GeV show that such photons with energies above 3 GeV are identified in SiCAL or LCAL and above 5 GeV in ECAL with an overall efficiency of 63% and purity of 72% if an isolation criterion based on a minimum angular separation from the closest energy flow object is applied. The minimum separation applied is 8° in SiCAL or LCAL and 18° in ECAL for CM energies. These events are treated differently in the subsequent kinematic fit.
Only one of the three possible jet pairings per event is chosen, by selecting the combination with the largest value of the matrix element |M(pf1,p[`(f2)],pf3,p[`(f4)],mWref)|2, where the pfj's denote the fitted four-momenta of the respective jets and mWref the reference W mass, taken to be 80.35 GeV/c2. However, if the selected combination has the smallest sum of the two di-jet opening angles, it is replaced by the combination with the second largest value of |M|2.
The invariant mass of each chosen di-jet combination are determined using the kinematically fitted jet four-momenta. Both masses for the selected combination must lie within the mass window 60 to 110 GeV/c2. If this condition is not satisfied, the combination with the second largest value of |M|2 is accepted instead, provided its two masses satisfy the di-jet opening angle and window criteria; otherwise the event is rejected. The combinations with the largest and second largest value of |M|2 are chosen in 90% and 10% of the cases, respectively. The combination with the smallest value of |M|2 is never considered.
The fraction of kinematically fitted signal events surviving these criteria is 80% (??) at 189 (207) GeV. Of these events, 90% (??) are found to have the correct combination of di-jets when comparing their directions to those of the original W di-quarks. The bias from the choice of reference mass is found to be negligible. In addition, the combinatorial and physical backgrounds are flat over a wide mass range, reducing the background contamination systematic uncertainty on mW.
A preselection common to the three lepton topologies requires at least seven tracks in the event. Background from q[`q] events is reduced by requiring the estimated sum of missing energy and missing momentum to be greater than 35 . The Zg events in which the photon is undetected are rejected by requiring the missing longitudinal momentum to be smaller than Max((s-MZ2)/(2ECM)-27.5 GeV, (Ös-MZ)2/ECM-Ö(\notE2-\notpT2)-6 GeV) where \notpT is the transverse missing momentum and \notE is the missing energy.
Following the identification of the lepton and associated objects, the remaining particles are clustered into two jets using the DURHAM-PE algorithm as in the q[`q]q[`q] channel.
In addition to the common preselection, a tighter cut is used on the total visible energy and visible longitudinal momentum to further reject Zg events: Evis (s-MZ2)/(s+Mz2) - Pzvis > 5 GeV where Evis and Pzvis are the visible energy and longitudinal momentum, respectively.
The lepton candidate is chosen as the good track with the largest P sin(qlj/2) where P is the track momentum and qlj is the angle from the track to the closest jet clustered from the remaining tracks using the Durham-PE [] algorithm (ycut = 0.0003). Events are further considered if this lepton candidate satisfies either the electron or muon criteria defined in [] and if the sum of the lepton and missing energy is greater than 30 . Identified electrons are corrected for energy losses due to bremstrahlung in the detector material by combining their four-momenta with those of any detected photons that are consistent with this hypothesis. These photons can appear either as an excess of energy in the ECAL electron cluster or as a separate deposit within 2.5° of the electron track impact point on ECAL. This correction is not applied when the electron is accompanied with other charged particles with summed momenta greater than 5 GeV/c within 6° of the electron track. In addition, for muons and electrons, a search is made for isolated final state (FSR) photons associated with the lepton. Such a photon must have an energy above 0.5 GeV, be closer to the charged lepton track than to any other object or the beam axis and at least 40° away from any other good charged track. Their four-momenta are then combined.
More detailed studies of neutral objects not already classified as bremsstrahlung within 2.5° of the electron track impact point on ECAL show a higher multiplicity than expected even after the removal of single stack objects. Fig. shows the extra activity from these objects as a function of angle to the electron extrapolated to the front face of ECAL. The reference simulation fails to reproduce the data for cone angles up to 8°. Further studies show that a smaller but still significant excess of neutral and also charged objects is present in the data for both enq[`q] and mnq[`q] events. Although the summed energy of these objects near the isolated lepton is small, their impact on the closest jet is significant, especially for the enq[`q] channel. Therefore, all these objects up to 8° from the lepton are removed from the jet reconstruction. Also, they are not included in the calculation of the lepton four-momentum.
Two different neural networks (NN) have been trained to select and classify e nqq and mnqq signal events. Both use three discriminant variables, the event transverse momentum, the lepton energy and the lepton isolation. The last variable is defined as log(tanqC/2)+log(tanqF/2) where qC and qF are, respectively, the maximum angle of a cone around the lepton candidate which includes less than 200 MeV of good charged track energy, and the opening angle of the largest cone centred on the lepton direction with less than 5 of total energy.
The event is classified as e nqq or mnqq if the corresponding NN output value is larger than 0.60.
A new selection has been designed, based on an improved reconstruction [] of the tau.
Leptonic t decays are searched for by examining those events with e or m candidates which fail the e nqq or mnqq NN cuts. These events are subjected to a similar three variable neural network but trained on leptonic tau decays. Events with the NN output greater than 0.4 are kept.
After removing the events which have satisfied any of the three variable NN selections for e nqq, mnqq or tnqq the remaining events are further examined for additional tnqq final states. Use is made of the fact that one-prong tau decays are characterized by a low visible mass with mean about 0.75 \GEVcc. The first step is to perform a jet clustering using the JADE [] algorithm with a low ycut = (0.75 / Evis)2. The tau candidate is defined as the jet which maximizes p (1-cosqj), where qj is the smallest angle with respect to other jets and p is the jet momentum. The event is then subjected to additional cuts, in particular the invariant mass of the hadronic recoil system to the tau candidate be in the range 60 to 105 . For those events which fail, the procedure is repeated with increasingly higher values of ycut in an attempt to find a suitable candidate.
If a tau-jet candidate is found, the event is subjected to further cuts to remove the main backgrounds. Most of the gg interactions are rejected by requiring the visible mass of the event to be larger than 50 and the missing transverse momentum greater than 10 GeV/c. The event is divided into two hemispheres with respect to a plane perpendicular to the thrust axis. The acollinearity angle between the two hemispheres is required to be less than 175° to reject most of the q[`q] background. About 80% of the events with a tau candidate satisfy these cuts but significant background remains, mainly from q[`q] events. These events are then subjected to a 15 variable neural network. The event is selected if the result is greater than 0.4.
W pair events are treated as four body final states with either four jets or two jets and a lepton and neutrino to which the missing momentum is assigned. The effect of ISR radiation is taken into account in the simulation. For each selected event, invariant masses are computed from the visible W decay products. In order to improve resolution a kinematic fit employing Lagrange multipliers, with the constraint of event four momentum conservation, keeps the velocities (p/E) of the jets fixed to their measured values. Imposing energy and momentum conservation alone corresponds to a four-constraint (4C) fit in the case of fully hadronic events, and a one-constraint (1C) fit in the case of semileptonic events, giving two different masses. An equal mass constraint for the two bosons corresponds respectively to a five (5C) or two-constraint (2C) fit. In the tnqq channel, since the t energy is largely unknown due to neutrinos in the t decay, only the hadronic side of the event is used with its 1C energy constraint set by the beam energy.
The measured jet momenta and directions are corrected during the fit to take into account the effect of particle losses in the detector. The expectation values of these corrections and their resolutions are determined using the independent CC03 Monte Carlo sample by comparing the fully simulated jets in the detector with those built from the generated particles directly. They are parametrised by Gaussian functions in bins of jet energy and jet polar angle qjet.
The raw resolution of 12% on average on the total jet momentum improves by a factor two, and by a factor up to 5 for polar angles down to 20 degrees.
For all classes of events the fits converge successfully (is this true?), producing flat c2 probability distributions for P(c2) > 0.05, as shown for example in Fig. for the enq[`q] channel. The peak below P(c2) = 0.05 is populated by events that do not fully satisfy the fitting hypothesis. Monte Carlo studies show that approximately half of these events have ISR energies greater than 0.5 GeV, leading to a significant positive bias in the reconstructed di-jet masses. However, these events are not removed since the Monte Carlo adequately describes the observed c2 probability distributions in all channels. Furthermore, the event-by-event mass error distributions compare well with Monte Carlo predictions in each lnq[`q] channel.
In the q[`q]q[`q] channel and for those events with an identified ISR photon in the detector, the procedure of event clustering and fitting is modified. In this case, the remaining energy flow objects are forced into four jets. The fit is performed taking into account the modified constraints
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