Abstract: Since the discovery of the top quark, CDF has measured several properties of those events to confirm that the top quark has the properties expected in the standard model (SM) , as yet undone is measuring the top charge. Determining whether the top decays into a W^{+} and a bottom quark while the antitop quark decays to a W^{} and an antibottom quark would ensure indirectly that the charge of the top quark is indeed +2/3 as is the charge of the top quark in the standard model. If these events were found to have an object decaying to a W^{} and a bottom quark, the charge of this object would be 4/3 and would not correspond to the standard model top quark. Such a proposal has been put forward by D.Chang, W. Chang and E. Ma (see references). . We measured the sign of the top charge using the products of the top decay in t > Wb. Three are three main components to this measurement: determining the charge of the W (using the charge pf lepton), getting the flavor of the bjet and finally pairing the W with the b jet to ensure W and the b jet come from the same top decay branch. Using close to 1fb^{1} of data ( Dilepton(DIL) and Lepton_Jets channel (L+J) ) and defining the probability of incorrectly rejecting the SM to be 1%, we found the result to be consistent with the SM, while excluding the Exotic quark hypothesis (XM) with 81% confidence. 
Method 

Pairing: To find the right association between the lepton and b jet, we make use of the invariant mass of the lepton bjet pair, M_{lb} ^{2} in Dilepton channel and we use top mass &chi^{2} fitter in Lepton+Jets channel.See the public note for the details. How often each method gives the right pairing is the purity of pairing,p_{pairing}. 


Jet Charge: On the right is the Weighted jet charge algorithm which uses the charge of the tracks associated to the jet weighted by their momentum projection on the jet axis.This algorithm has been optimized to determine the flavor of b jets in high P_{t} enviroment.How often this algorithm gives the right flavor in MC is the purity of Jet charge, p_{JQ}.
MC performance can not be relied on therefore purity of jet charge was calibrated in data as explained below. 

Combining right pairing with the Jet charge information, we get N_{+} = number of SM like events with top charge +2/3
N_{} = number of XM like events with top charge 4/3


Calibration of Jet Charge Algorithm in Data  
eps Performance of the Jet Charge (JQ) algorithm is calibrated using dijet data. Event choice is to pick bbbar events where one of b's decay semileptonically to a muon. The plot shows the observed purity calculated as number of events where the muon and the jet charge applied to the away jet have opposite sign over the total number of events. Red points corresponds to the corrected purity which takes into account the amount of non bbbar events, secondary decays and mixing.
 eps Scale Factor between the corrected purity and the Jet Charge algorithm purity in bjets in a HF enriched MC (Pythia). Shown are the constant and linear fit
 
Systematic Uncertainties on SF.

SF_{JQ} = 1.03 ± 0.02 (stat.) ± 0.04 (sys.)
 
Expectation  
The
expected number of background and signal events after event selection and pairing requirements. The numbers are obtained by multiplying the predictions (using a top cross section of 6.7pb) by the corresponding total efficiency (pairing efficiency times jet Q efficiency).
 The
expected SM like and Exotic Model (XM) like events for background and signal. These numbers are obtained as the product of the expected number of events shown in previous table and their corresponding purities.


Expected number of signal and background pairs and their purities.There are two pairs per event for each event containing a top and and antitop.  
Getting Signal Purity  
P_{s} = f_{nonb} SF_{nonb} p_{nonb} + (1f_{nonb}SF_{nonb})(p_{pair} p_{JQ} SF_{JQ} + (1p_{pair})(1p_{JQ}SF_{JQ}))
Above is the definition of Signal Purity, P_{s}.The measured jet charge purity in MC is corrected by the SF_{JQ}. The measured fraction of nonb in MC,f_{nonb}, is corrected by the mistag rate, SF_{nonb}, between data and MC.
 Summary of Systematic Uncertainties.
 
Results  
62 SM like pairs and 48 XM like pairs have been observed in data.
 f_{+} = fraction of pairs with top charge +2/3 Using a Profile Likelihood, and the above nuisance parameters, the Log Likelihood curve for the observed N+ and N . The minimum of this curve is at a value of 0.88.


Distribution of the fraction of SM like pairs (f_{+}) assuming either the Exotic or the Standard Model. Indicated is the observed pvalue of 0.35 .

pvalue distribution for the SM assuming the XM is true. Indicated is the a priori alpha value of 1% (probability of incorrectly rejecting the SM if SM is true) and its corresponding beta value or Power of Test (probability of rejecting the SM if XM is true).


Bayes Factor = P(N_{+}  SM) / P(N_{+}  XM) = odds of SM versus XM
Based on Bayes Scale, 8.54 means "data favors strongly SM over XM". 

eps 
On the left is the plot showing the probability for both SM and XM with given total number of 110 (62 SM + 48 XM) events. P_{comb} is the combined purity taking the background into account. Given that the probability of XM and SM with respect to the total number of events can be calculated. If we present &alpha = 0.01 then the boundary for us to claim SM is true is shown by the green vertical line. One can read from the plot that it is 59 or so. Since we observe 62 SM Top pairs in data ( that exceeds 59), the CDF data supports SM strongly based on the 2.Ln(BF) = 8.54.  
eps eps Product of the W charge and the associated jet charge for Data and MC for Lepton+Jets pairs. A negative value correspond to a SM like event.

Product of the W charge and the associated jet charge for Data and MC for Dilepton events . A negative value corresponds to a SM like pair.


BOTH WQ*JetQ PLOTS HAVE THE MC NORMALIZED TO THE DATA AREA.  
For speakers who are likely to mention also the D0 result if they are covering Tevatron results  
Since CDF and D0 do not calculate the confidence limits in the same way a direct comparison of their results is not possible. What can be compared is their sensitivity. On the left is the &beta versus &alpha plot. The first two blue points are the &beta at 1% corresponding to CDF's limit and &beta at 5%. The third is the value of &beta (99.8%) at &alpha of 50% which approximately corresponds to the D0 quoted sensitivity of 91.2%.
The following number CAN NOT appear on an official conference slide, it is just provided as extra information in case the speaker gets a questionD0 reports a pvalue under the exotic quark model hypothesis, this value is 7.8%. They turn this pvalue into a confidence limit of 92.2% of excluding the exotic quark hypothesis. CDF computes their confidence limit in a different way and use the SM as their null hypothesis, but nonetheless their pvalue under the exotic quark model hypothesis is 0.2%. " 
Results in ~ 1fb^{1}  
Observed f+=0.88 pvalue =0.35 
Since the pvalue under the SM hypothesis is 0.35, this is greater than the a priori chosen value of &alpha 0.01, so we exclude the exotic quark model with 81%. confidence.  Based on the Bayes Factor value, we conclude that the data favors strongly the standard model top quark hypothesis over the exotic quark hypothesis. 
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The above four plots show the distributions of the four posibble M_{lb} ^{2} values in DIL channel after DIL selection with one tight tagged jet. The above two correspond to the two M_{lb} ^{2} values for the lepton b pair we picked. The red line on the bottom left plot indicates the cut at 22000Gev/c^{2} we put on the maximum of the four M_{lb} ^{2}.
The left plot is the &chi^{2} distribution after L+J cuts and double tagging. 
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References 
