[png] [eps] [pdf] Mass χ² distribution for the two signal regions for this analysis (tagged and antitagged) as well as for the control region. We show the data along with the best fit of signal and background templates to the data. Overlaid are the fit uncertainties and the expected signal from top FCNC decays at the measured 95% C.L. upper limit of 3.7%.  Contents: 
Feynman Diagram for Top FCNC Decay
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In the standard model, top quark flavor changing neutral current (FCNC) decays are highly suppressed; they do not occur at tree level and are only allowed at the level of quantum loop corrections, but at very small branching fractions on the order of 10^{–14}. Some exotic physics models including SUSY and two Higgs doublet models predict higher branching fractions, up to 10^{–4}. Any signal of this rare decay at the Tevatron or the LHC would be an indication of new physics. Previous searches for the top FCNC decay t→Zq have been performed in CDF Run I and by the LEP experiments. The Run I analysis yielded an upper limit on the branching fraction B(t→Zq) of 33% at 95% C.L. The current best published 95% C.L. upper limit on the t→Zq branching fraction is 13.7%, inferred from the L3 experiment's nonobservation of e^{+}e^{–}→ tq 
We have presented preliminary results of the first Tevatron Run II top FCNC search for the summer conferences 2007. Based on 1.1 fb^{–1} of data, we derived a limit of B(t→Zq)<10.4% at 95% C.L. We have updated the top FCNC search with 1.9 fb^{–1} of data and with an improved analysis technique. We have enhanced the sensitivity of the analysis by introducing a template fit technique that takes into account systematic shape uncertainties by linear interpolation between templates ("morphing"). Using a FeldmanCousins construction we set a 95% C.L. upper limit on B(t→Zq) of 3.7%; the expected upper limit in the absence of a signal is (5.0 ± 2.2)%. This is currently the world's best limit on B(t→Zq) and improves upon the best published limit by more than a factor of 3.5.
Our search for top FCNC is based on a template fit to a mass χ² variable constructed from kinematic constraints present in top FCNC events. We construct templates for the signal expected from the top FCNC decay t→Zq and for all significant standard model (SM) background contributions. We take the signal acceptances and trigger efficiencies from a Monte Carlo simulation with appropriate corrections for the simulation's deficiencies applied. We normalize the expected event yield to the measured top pair production cross section in the lepton+jets channel. We perform a simultaneous template fit to two signal regions and one control region. The control region enables us to constrain uncertainties in the normalization and the shape of the templates. With the help of a FeldmanCousins construction that takes into account systematic uncertainties we derive an upper limit on the branching fraction B(t→Zq).
We search for the decay tt→Zq Wb in events
with a Z boson and four or more jets. For the Z reconstruction, we
require exactly one lepton pair of the same flavor and opposite charge
(e^{+}e^{–} or
μ^{+}μ^{–}) with an invariant mass in the
range of 76–106 GeV/
Improved electron coverage using track leptons. The black points show the coverage with tight electrons only, the red points show the additional coverage gained by using track leptons. 
Improved muon coverage using track leptons. The black points show the coverage with tight muons only, the red points show the additional coverage gained by using track leptons. 
In addition to the Z candidate we require four or more jets. We correct the energies of reconstructed jets to the parton level and initially require jets to have corrected E_{T} ≥ 15 GeV and to fall into the pseudorapidity range of η<2.4.
We have optimized the event selection for the previous version of this analysis, a blind counting experiment, and keep the selection for the current version (removing the cut on the mass χ² present in the counting experiment and performing a fit to mass χ² templates instead). The optimized event selection includes additional cuts, on the transverse mass of the events, and on the transverse energies of the four leading jets, as listed in the following table:
The two most powerful kinematic variables to separate signal from background are mass χ², which will be used in the template fit, and transverse mass. The mass χ² exploits our ability to fully reconstruct the event kinematics in the absence of neutrinos in the final state. In a signal event, there is one decay of the type t→Wb. Two jets in the event form a W boson, which in turn forms a top quark together with a third jet. There is also one decay of the type t→Zq in which the Z has to be paired with the fourth jet to form the second top. The mass χ² is thus defined as
where we assume a top quark mass of 175 GeV/c². The widths used in the χ² construction were measured in the Monte Carlo simulation: 15 GeV/c² for W→qq, 21 GeV/c² for t→Zq, and 24 GeV/c² for t→Wb. We calculate χ² for all 12 combinations of the leading four jets in an event and pick the combination with the lowest value. We do not make use of btagging information in resolving the combinatorics.
We expect the top decays to be more central than the forward decaying Z+jets. The transverse mass of the event is sensitive to this difference. We define transverse mass as
where the sums include the four leading jets and the reconstructed Z boson.
The key element of this analysis is a template fit to the measured mass χ² distribution. The template fit is more sensitive than the previous counting experiment because it explores the full χ² shape information to measure B(t→Zq). The fit also reduces the dependence on absolute predictions of the background contributions by making the background normalization a free fit parameter. On the other hand, the template fit requires good control of the template shapes. We found that the largest uncertainties in the mass χ² shape are induced by uncertainties in the choice of the jet energy scale (JES).
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DataMC comparison of the mass χ² distribution for base selection ("pretag") for nominal jet energy scale (left) and for a –1σ jet energy scale shift (right). The standard model (SM) top and diboson backgrounds are fixed to their absolute predictions, and the Z+jets backgrounds are scaled such that the total background integral matches the number of observed data events. The dashed line shows the shape of the expected FCNC signal, normalized to the number of observed data events. 
The influence of all other shape uncertainties is much smaller than the JES shape uncertainty; therefore we take the JES shift as representative for all sources of shape uncertainties. We have introduced "horizontal template morphing" to the template fit (see illustration below), so that the fit treats shifts in the JES as a continuous fit parameter by interpolating between templates at discrete values of the JES shift.
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Illustration of horizontal template morphing. A 75% morphed histogram is obtained by (a) constructing cumulative distribution functions (C.D.F.s) of the two source histograms, (b) constructing a new C.D.F. as the 75% interpolation between the C.D.F.s of the source histograms, and (c) taking the derivative of the resulting C.D.F. 
The template fit is implemented as a simultaneous fit to two signal regions and one control region. The first signal region ("tagged") requires at least one bjet identified by the loose flavor of CDF's standard btagging algorithm SECVTX. The second complementary signal region ("antitagged") requires exactly zero bjets. In order to control uncertainties in the background shape, we also introduce a control region with large background acceptance and small signal contamination. The control region contains all events that pass the base selection (reconstructed Z and four or more jets) but fail at least one of the optimized selection criteria. Additionally we use the fitted number of events in the control region to apply a loose (20%) constraint on the number of events expected in the two signal regions, where the uncertainty is derived from systematic variations of internal parameters of the ALPGEN Monte Carlo generation. In summary, the following five parameters are used the template fit:
There are several physics processes that have signatures consistent with our event selection. The dominant background contribution for this analysis comes from Z bosons produced in association with jets (Z+jets). The template fit technique relies on the shape of the mass χ² distribution for Z+jets events but not on absolute predictions of the amount of Z+jets events. This is in contrast to the blind counting experiment performed in the summer 2007 analysis, which required absolute predictions for all background contributions.
A much smaller background contribution comes from SM top pair decays, tt→WbWb, in which the invariant mass of two leptons in the dilepton decay mode or a lepton and a jet misidentified as a lepton in the lepton+jets decay mode fall within the Z mass window. A contribution similar in size comes from diboson events which contain a real Z boson (WZ and ZZ). The SM top and diboson backgrounds are estimated using Monte Carlo simulations. We found background contributions from WW diboson and W+jets production negligible; these processes do not contain a real Z in the final state. The following table shows the expected number events in the two signal regions and the control region in 1.9 fb^{–1} of data:
To derive a limit on the branching fraction B(t→Zq) we employ a FeldmanCousins method including systematic uncertainties. The FeldmanCousins method is ideal for analyses with very small signal expectations like this top FCNC search in that it ensures a physical limit even for unphysical measured values, in our case negative values of B(t→Zq).
The FeldmanCousins construction is based on pseudoexperiments for true values of B(t→Zq) between 0% and 16%. A single pseudoexperiment consists of (Poisson) random mass χ² distributions in the signal regions and the control region, generated from the signal and background templates and taking into account all known systematic effects and their correlations among the signal and control regions. We extract a measured value of B(t→Zq) from a template fit to the pseudoexperiment.
From the FeldmanCousins construction, we derive an expected limit in the absence of signal of 5.0%. The figures below show the resulting FeldmanCousins band, the expected limit, and the coverage of the FeldmanCousins intervals.
[png] [eps] [pdf] FeldmanCousins band. We construct the FeldmanCousins band from pseudoexperiments for true branching fractions B(t→Zq) between 0% and 16%. 
[png] [eps] [pdf] Expected limit. The expected limit distribution is the convolution of the FeldmanCousins band with the distribution of pseudoexperiments at a true branching fraction of B(t→Zq) = 0%. 
[png] [eps] [pdf] Coverage of FeldmanCousins intervals. The horizontal line indicates 95% coverage. 
[png] [eps] [pdf] Distribution of pseudoexperiments at a true branching fraction of B(t→Zq) = 0%. 
We apply the template fit to the 202 candidate events we found in the 1.9 fb^{–1} CDF Run II dataset. The best fit to the data is shown below:
The parameters of the best fit to the data are given in the table below. The measured branching fraction is B(t→Zq)=–1.49%, consistent with background only. From pseudoexperiments assuming B(t→Zq)=0% we derive a pvalue of 26.6% for this outcome, which corresponds to a 0.62σ downward fluctuation from the expectation. The central value of the ratio R_{sig} of events in the signal over the control region can be derived from σ_{Rsig} and the shift in the jet energy scale: R_{sig} = 52.2%. Using the fitted tagging fraction, the fit corresponds to 13.5 tagged and 53.9 antitagged Z+jet events.
From the measured branching fraction B(t→Zq) = –1.49%, we determine an upper limit of B(t→Zq)<3.7% at 95% C.L. from the FeldmanCousins band, as shown below:
The limit of B(t→Zq)<3.7% at 95% C.L. is in good agreement with the expected limit of (5.0 ± 2.2)%. This analysis improves the world's best published limit, 13.7% set by L3, by more than a factor of 3.5 and improves the CDF Run I limit of 33% by an order of magnitude.
The search for the top FCNC decay t→Zq is based on a template fit to the mass χ² distribution. As a consequence, we take into account systematic uncertainties in both the event rate and the mass χ² shape.
As the event yield is normalized to the measured lepton+jets top production cross section, we attribute systematic uncertainties to the ratio of the FCNC acceptance to the acceptance used in the cross section analysis, distinguishing between correlated and anticorrelated uncertainties. Uncertainties which we label as correlated are those which shift the number of events in both the antitagged and the tagged signal regions in the same direction.
We attribute correlated systematic uncertainties to Monte Carlo corrections factors (lepton scale factors for lepton identification efficiencies and separate trigger efficiencies), and estimations on initial state radiation (ISR) and final state radiation (FSR) from the event. Since our signal Monte Carlo sample is generated flat in cos(θ*), the angle between the top boost and the positive lepton in the Z rest frame, we chose to reweight it to the handedness expected from a standard model like Higgs mechanism: 65% longitudinal and 35% lefthanded. We apply a systematic uncertainty on this helicity reweighting of the signal FCNC Monte Carlo sample. We also include a correlated systematic uncertainty on the parton distribution functions. The jet energy scale uncertainty is not considered here as the shift in the jet energy scale is a free parameter in the template fit. As the measurement is normalized to the lepton+jets top production cross section, luminosity uncertainties cancel in the ratio.
Systematic uncertainties that are anticorrelated shift the number of events in the antitagged and tagged signal regions in opposite directions. We attribute an anticorrelated systematic uncertainty on the btagging scale factors and the mistag parameterization applied to the Monte Carlo simulation. We also include an anticorrelated systematic uncertainty for the difference in event tagging rate between tt → Zu Wb and tt → Zc Wb decays. The following table contains a summary of all systematic rate uncertainties:
The number of Z+jets events in the control region is a free parameter in the template fit; therefore uncertainties of the background rate affect only the smaller backgrounds from standard model top pair and diboson decays. The background rate uncertainty is dominated by the 6% uncertainty on the luminosity. The full table of correlated and anticorrelated uncertainties is shown below:
We have carefully examined all known sources of shape uncertainties both for the FCNC signal and for the main background from Z+jets events. Jet energy scale (JES) uncertainties show by far the largest overall effect. The mean value of the √χ² distribution is shifted by approximately ±5% for a ±1σ JES shift in the Z+jets background and by approximately ±1% for ±1σ JES shift in the FCNC signal. The uncertainty due to JES shifts is taken into account in the template fit via "template morphing."
Smaller but still sizable effects come from the variation of internal parameters in the ALPGEN Monte Carlo generator used to determine the Z+jets background shape. We have simultaneously varied the parameter qfac, related to the renormalization and factorization scale, and the parameter ktfac, which determines the energy scale at each internal vertex, between 0.5 and 2.0. We observe a variation of up to 17% in the ratio R_{sig} of events in the signal regions to events in the control region. As a result, we conservatively assign a 20% constraint on R_{sig} in the template fit. We have also verified with pseudoexperiments that we can use JES uncertainties as a "placeholder" for ALPGEN uncertainties. We observe a small bias in the average measured value of B(t→Zq), which we take into account by "smearing" all pseudoexperiments accordingly.
The three distributions below show the best fit to the data in four different representations. We show two different choices of binning for the antitagged and the control region. Note that the result has been derived for the original binning. We also show the templates including the expected FCNC signal at the measured upper limit of 3.7%.
The mass χ² variable is defined as follows:
We compare the mass χ² distributions in data and the Monte Carlo (MC) simulation for the nominal jet energy scale choice and for ±1σ shifts of the jet energy scale. Each set of distributions includes the tagged and the antitagged signal regions, the control region, and the base selection ("pretag"). The standard model (SM) top and diboson backgrounds are fixed to their absolute predictions, and the Z+jets backgrounds are scaled such that the total background integral matches the number of observed data events. The dashed line shows the shape of the expected FCNC signal, normalized to the number of observed data events.
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The mass χ² is composed of three mass constraints, on the W→qq mass, the standard model t→Wb mass, and the FCNC t→Zq mass. The distributions below show a dataMC comparison of these masses for the combination of jets in an event that results in the lowest χ² for the nominal jet energy scale. The SM top and diboson backgrounds are fixed to their absolute predictions, and the Z+jets backgrounds are scaled such that the total background integral matches the number of observed data events. The dashed line shows the shape of the expected FCNC signal, normalized to the number of observed data events.
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DataMC comparison of the mass χ² distribution for a jet energy scale shift of –1σ. The standard model (SM) top and diboson backgrounds are fixed to their absolute predictions, and the Z+jets backgrounds are scaled such that the total background integral matches the number of observed data events. The dashed line shows the shape of the expected FCNC signal, normalized to the number of observed data events.
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DataMC comparison of the mass χ² components for the for the combination of jets in an event that results in the lowest χ² for a jet energy scale shift of –1σ. The SM top and diboson backgrounds are fixed to their absolute predictions, and the Z+jets backgrounds are scaled such that the total background integral matches the number of observed data events. The dashed line shows the shape of the expected FCNC signal, normalized to the number of observed data events.
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DataMC comparison of the mass χ² distribution for a jet energy scale shift of +1σ. The standard model (SM) top and diboson backgrounds are fixed to their absolute predictions, and the Z+jets backgrounds are scaled such that the total background integral matches the number of observed data events. The dashed line shows the shape of the expected FCNC signal, normalized to the number of observed data events.
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DataMC comparison of the mass χ² components for the for the combination of jets in an event that results in the lowest χ² for a jet energy scale shift of +1σ. The SM top and diboson backgrounds are fixed to their absolute predictions, and the Z+jets backgrounds are scaled such that the total background integral matches the number of observed data events. The dashed line shows the shape of the expected FCNC signal, normalized to the number of observed data events.
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The transverse mass is defined as
where the sums include the four leading jets and the reconstructed Z boson. We show distributions for the tagged and the antitagged signal regions, the control region, and the base selection ("pretag"). The SM top and diboson backgrounds are fixed to their absolute predictions, and the Z+jets backgrounds are scaled such that the total background integral matches the number of observed data events. The dashed line shows the shape of the expected FCNC signal, normalized to the number of observed data events. All distributions are N1 distributions, i.e. all selection cuts are applied except for the kinematic variable shown.
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We show distributions of the leading jet transverse momentum for the tagged and the antitagged signal regions, the control region, and the base selection ("pretag"). The SM top and diboson backgrounds are fixed to their absolute predictions, and the Z+jets backgrounds are scaled such that the total background integral matches the number of observed data events. The dashed line shows the shape of the expected FCNC signal, normalized to the number of observed data events. All distributions are N1 distributions, i.e. all selection cuts are applied except for the kinematic variable shown.
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We show distributions of the second jet transverse momentum for the tagged and the antitagged signal regions, the control region, and the base selection ("pretag"). The SM top and diboson backgrounds are fixed to their absolute predictions, and the Z+jets backgrounds are scaled such that the total background integral matches the number of observed data events. The dashed line shows the shape of the expected FCNC signal, normalized to the number of observed data events. All distributions are N1 distributions, i.e. all selection cuts are applied except for the kinematic variable shown.
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We show distributions of the third jet transverse momentum for the tagged and the antitagged signal regions, the control region, and the base selection ("pretag"). The SM top and diboson backgrounds are fixed to their absolute predictions, and the Z+jets backgrounds are scaled such that the total background integral matches the number of observed data events. The dashed line shows the shape of the expected FCNC signal, normalized to the number of observed data events. All distributions are N1 distributions, i.e. all selection cuts are applied except for the kinematic variable shown.
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We show distributions of the fourth jet transverse momentum for the tagged and the antitagged signal regions, the control region, and the base selection ("pretag"). The SM top and diboson backgrounds are fixed to their absolute predictions, and the Z+jets backgrounds are scaled such that the total background integral matches the number of observed data events. The dashed line shows the shape of the expected FCNC signal, normalized to the number of observed data events. All distributions are N1 distributions, i.e. all selection cuts are applied except for the kinematic variable shown.
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We show distributions of the Z boson mass reconstructed from a lepton pair for the tagged and the antitagged signal regions, the control region, and the base selection ("pretag"). The SM top and diboson backgrounds are fixed to their absolute predictions, and the Z+jets backgrounds are scaled such that the total background integral matches the number of observed data events. The dashed line shows the shape of the expected FCNC signal, normalized to the number of observed data events.
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We normalize our measurement of the branching fraction B(t→Zq) to a measurement of the top pair production cross section in the lepton+jets channel in events with at least two btags obtained from the "loose" flavor of CDF's standard SECVTX btagging algorithm. Using a mixture of data driven and Monte Carlo driven methods to estimate contributions from standard model background processes, we observe a top pair production cross section of 8.8 pb in 1.9 fb^{–1} of data. This is consistent with an earlier measurement with 1.1 fb^{–1} of data, see CDF Note 8795. The plot and the table below show the number of events expected from tt signal compared to background expectations.
In the left column, we show distributions of the number of reconstructed jets in events with a Z boson for the base selection ("pretag") without a cut on the number of jets. In the right column we show the corresponding ratios of data versus the Monte Carlo prediction. The njet spectra are shown for the nominal ALPGEN settings as well as for Q² scale variations of 0.5 and 2.0 times the nominal value. The SM top and diboson backgrounds are fixed to their absolute predictions, and the Z+jets backgrounds are scaled such that the total background for events with zero jets matches the number of observed data events with zero jets. Note that we do not derive the expected total number of Z+jets events from these distributions.
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Public documentation for top FCNC search: