1. All-hadronic channel
A reevaluation of the systematic uncertainties on the mea-surement of the top quark mass in the all-hadronic channel as reported in Ref.关12兴has shown that some of those estimates were overly conservative. Since that publication further stud-ies of the systematic uncertaintstud-ies have led to better proce-dures, which we now apply to all channels. The systematic uncertainties which have been revised include: initial and final state radiation, fitting procedure, and jet energy scale.
These revisions are discussed below.
The contribution due to uncertainty in modeling initial and final state hard radiation was 8.0 GeV/c2. To evaluate this uncertainty, standard HERWIGt t¯ events were compared to samples which were constructed to have smaller and larger fractions of events in which one or more of the final state jets did not match any of the daughter quarks from the t t¯ decay. The most evident difference between the samples was that the width of the reconstructed mass distribution broadened as this fraction increased. On the other hand, simulated experiments showed only a very small shift in the fitted top quark mass. The systematic uncertainty was evalu-ated as follows. We generevalu-ated two samples of simulevalu-ated ex-periments: 共a兲one using the defaultHERWIGtemplates and 共b兲one using templates which were constructed to have 90%
of events containing one or more jets that were not matched to the daughter quarks from the t t¯ decay. For the default
HERWIG sample, approximately 60% of events have one or more jets not matched to a quark from the t t¯ decay. In both cases, we evaluated the median and the rms width of fitted top quark masses from the simulated experiments. The sys-tematic uncertainty was taken to be the quadrature difference of the widths between samples共a兲and共b兲. This number was then added in quadrature with the small shift in the median mass which was observed between sample 共a兲 and 共b兲. Es-sentially all of the 8.0 GeV/c2 uncertainty was from the in-crease in the width of the distribution of sample共b兲. Further studies show that the change in width of the reconstructed mass distribution with increased radiation is reflected in the statistical uncertainties returned by the fits for simulated ex-periments; thus the statistical uncertainty obtained from our fitting procedure for the data sample already takes into ac-count this effect. A reevaluation, using the same procedure as described in Sec. IX B, results in a contribution from this source of 1.8 GeV/c2 关65兴.
Another large source of systematic uncertainty (5.2 GeV/c2) came from the effect of selecting the second-best rather than the second-best kinematic fit to each event. A smaller contribution came from considering different ways
of interpolating between likelihood values at discrete top quark mass values in order to find the maximum likelihood point. A third contribution came from the finite Monte Carlo statistics that provided the expected reconstructed mass dis-tributions at different top quark mass values. The first two contributions are no longer identified as sources of signifi-cant systematic uncertainty since they concern the robustness of the chosen method. The contribution from Monte Carlo statistics, of 0.3 GeV/c2, remains.
The jet energy scale uncertainty was determined to be 5.4 GeV/c2. Part of that (3.7 GeV/c2), was due to differ-ences in the calorimeter energy scale between two versions of the detector simulation. The source of this uncertainty was later corrected. As a result, the 3.7 GeV/c2 contribution to the uncertainty was eliminated.
A small reorganization of the contributions has occurred, which we mention in order to avoid any confusion in a com-parison with Ref. 关12兴. The soft gluon uncertainty (3.0 GeV/c2) has been moved from the ‘‘gluon radiation and fragmentation effects’’ to the ‘‘jet energy scale’’ category.
The Monte Carlo generator uncertainty (0.8 GeV/c2) has been assigned its own category. The result is a new system-atic uncertainty of 5.7 GeV/c2, with a breakdown into dif-ferent contributions as listed in Table XVIII.
2. Dilepton channel
The top quark mass measurement in the dilepton channel uses eight observed events that pass the standard selection criteria used for the dilepton channel 关14,65兴. The criteria require that the leptons have opposite charges, that there be at least two jets per event, and include cuts on the missing transverse energy and the lepton transverse energies.
This measurement involves two steps: a top quark mass estimate is obtained for each event, and then a likelihood fit, which allows for the presence of background, gives an over-all best estimate of the top quark mass. The second step is similar to that in the lepton⫹jets topology, but the first step is appreciably different.
In order to get a mass estimate for an individual event, we determine a weight distribution as a function of an assumed top quark mass, mt. First, we assume that the event origi-nates from t t¯ production and decay, that the leading two jets are b jets from top decay, and that the leptons 共e or兲are from associated W-boson decays. Next, we assume a value for the top quark mass, mt, assume pseudorapidity values,
1 and 2, for the two neutrinos, and solve for the two neutrino momenta. In general there are eight solutions be-cause of a quadratic ambiguity in each neutrino’s longitudi-nal momentum and a choice of pairing leptons with jets. For each solution, we denote as E”T
p the vector sum of the solu-tion’s neutrino transverse momenta. Then we assign a weight to each solution according to how well E”T
p agrees with the event’s measured missing transverse energy, E”T
m, as follows:
g共mt,1,2兲⫽exp
冉
⫺共E”Tpx2⫺E”2Tmx兲2冊
⫻exp
冉
⫺共E”Tpy2⫺E”2Tmy兲2冊
, 共C1兲whereis the resolution in each component共x and y兲of the measured unclustered transverse energy共see below兲. The ex-perimental resolution in jets and leptons is taken into account by sampling the measured quantities many times according to their resolutions. That is, for each set of assumed mt,1, and 2 values a weight is calculated many times, and the sum is accumulated. For each assumed mtvalue, 100 pairs of
1 and 2 values are assumed in turn, and the summed weights are again summed, to give a final summed weight, f (mt), at any mt value. The 1 and 2 values are drawn independently from a Gaussian distribution with unit width and centered at 0.0, as predicted by HERWIG Monte Carlo simulations. Thus all the uncertainties on the E”T measure-ment are taken into account, except for the resolution of the unclustered energy. We use ⫽4
冑
n GeV, where n is the number of interactions in the event and comes from studies of low-luminosity minimum-bias events.For each event, mtvalues in the range 90 to 290 GeV/c2, in 2.5 GeV/c2 steps, were assumed in order to give a f (mt) distribution. This distribution is used to determine a top quark mass estimate, as follows. The position of the maxi-mum value, f (mt)max, is denoted by Mmax. The first points on either side of Mmaxthat have f (mt)⭐f (mt)max/2 are de-noted by M1and M2. The average of M1and M2is taken as the top mass estimate.
The f (mt) distributions, normalized to unity, for the eight events are shown in Fig. 39. The eight events, with their lepton identifications, numbers of jets 共with uncorrected transverse energy greater than 10 GeV and pseudorapidity in the range ⫺2.0 to ⫹2.0 units兲, and estimated top quark masses are given in Table XXVII.
It is useful to define a variable, Pev, as the sum of f (mt) over all assumed mt values, divided by the number of reso-lution samplings used. The latter number is 1500 for data and
30 for Monte Carlo events. This variable gives an indication of how easily an event can be fit to the t t¯ decay hypothesis.
The log(Pev) distribution of simulated t t¯ plus background events is shown in Fig. 40. The t t¯ events are from the
HERWIG simulation with a top quark mass of 175 GeV/c2. The log(Pev) values for the eight observed events are listed in Table XXVII and are indicated by arrows in Fig. 40. The data points all lie within the range spanned by the simulated distribution. In the simulated events, 0.7% have log(Pev)
⬍⫺5.2, the value for the lowest data point, so the probability for an eight-event sample to have at least one event at⫺5.2 or lower is 5%.
In Ref. 关65兴it was noted that the same method could be applied to events in the lepton⫹jets topology that had two FIG. 39. Weight distribution f (mt), normalized to unity, for the
eight observed dilepton events.
FIG. 40. Predicted distribution of log(Pev), the total weight sum per resolution sampling, for the expected t t¯ and background event mix in the dilepton sample. The arrows indicate the values for the eight observed events.
TABLE XXVII. Information on the eight candidate dilepton events used in the dilepton mass analysis. Shown are the run and event numbers, the types of leptons in each event, the number of reconstructed jets 共with uncorrected PT⬎10 GeV/c and 兩兩⬍2), and the top quark mass estimates for each event. Also listed is log(Pev), where Pev is the sum of all the weights for the event divided by the number of resolution samplings used.
Run Event leptons Njet Top quark mass log(Pev)
41540 127085 e⫺⫹ 2 158.8 0.47
45047 104393 e⫹⫺ 2 180.0 1.82
47122 38382 e⫹⫺ 2 176.3 1.40
57621 45230 e⫹⫺ 2 156.3 2.20
66046 380045 e⫹⫺ 4 172.5 ⫺5.20
67581 129896 e⫹⫺ 2 143.8 0.44
68185 174611 e⫹⫺ 2 161.3 4.10
69808 639398 e⫺⫹ 3 170.0 3.50
SVX-tagged jets. In such events the two untagged jets共of the four highest ET jets兲 are assumed to result from W-boson decay, and in order to mimic a W-boson leptonic decay one of those jets is treated as a lepton共electron or muon兲and the other as a neutrino. In the following we took the jet with
lower ETas an unobserved neutrino and recalculated E”Tmfor the event. Then the above dilepton method was applied.
The five events in the SVX double sample were fit with this method. A top quark mass value of 181.5
⫾12.6 GeV/c2was obtained. This value has to be compared with the value shown in Table XV of 170.0⫺⫹8.99.4GeV/c2, a difference of 11.5 GeV/c2. In order to understand the differ-ence between the two methods a comparison was made in a Monte Carlo study that used a sample of approximately 1300 simulated lepton⫹jets t t¯ events with Mto p⫽175 GeV/c2and with two jets having SVX tags. The distribution of the re-constructed mass from the standard lepton⫹jets kinematic fit is shown in Fig. 41共a兲. Also shown is the top mass estimate per event with the pseudodilepton method described above.
The two distributions are similar. The medians are 170.5 GeV/c2 and 170.9 GeV/c2, and the widths are 21.4 GeV/
c2 and 23.4 GeV/c2, respectively for the kinematic fit and the dilepton methods. Here the widths are one-half the sepa-ration of the 16th and 84th percentiles in the distributions. As expected, the dilepton method gives a slightly wider distri-bution. In Fig. 41共b兲 the mass difference between the two methods is plotted for each event. The width of this distribu-tion is 24.3 GeV/c2. This shows that the shift of 11.5 GeV/c2found for the five SVX double events using the two methods is well within expectation.
This study shows that fitting the dilepton events, which are underconstrained, using the technique described here is just as valid and precise as the completely constrained 2C fit used for the lepton⫹jets sample. In addition, if we calculate the statistical correlation between the two methods, we ob-tain a correlation coefficient of 0.36, i.e., fitting the SVX double events with this technique could improve the statisti-cal uncertainty on the mass determination from this channel.
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