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 of the 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 5.6fb^{1} of Lepton+Jets channel (L+J) data, we found the result to be consistent with the SM, while excluding the Exotic quark hypothesis (XM) with 99% confidence. 
Method 

Pairing: To find the right association between the lepton and b jet, we use top mass &chi^{2} fitter. See the public note for the details. How often the 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} environment. 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  
Performance of the Jet Charge (JQ) algorithm is calibrated using dijet data on selected bbbar events where one of b's decay semileptonically to a muon. We calculate the observed purity as the fraction of the total events for which the muon and the JQ of the away jet have opposite sign. We correct the purity by taking into account the amount of non bbbar events present in the sample, secondary decays and mixing.


eps Scale Factor between the data corrected purity and the JQ purity calculated on bjets selected from MC (Pythia) samples (combination of a Heavy Flavor enriched MC and dijet MC). The constant fit is shown. 
Result:
epsSF_{JQ} = 0.99 ± 0.01 (stat.) ± 0.03 (sys.) Systematic Uncertainties on SF.


Expectation  
eps 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 7.4pb) by the corresponding efficiencies (pairing efficiency and jet Q efficiency).

eps 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.


eps 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  
eps 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.

eps Summary of Systematic Uncertainties.


Results 

eps 416 SM like pairs and 358 XM like pairs have been observed in data.

Product of the W charge and the associated jet charge for Data and MC ("+2/3 Q" corresponds to the SM signal MC distribution for WQ*JQ). A negative value corresponds to a SM like pair. 

WQ*JetQ PLOT HAVE THE MC NORMALIZED TO THE DATA AREA.


eps f_{+} = fraction of pairs with top charge +2/3
Using a Profile Likelihood and the above nuisance parameters (N_{s},N_{b},p_{s},p_{b}) we got the Log Likelihood curve for the observed N+ and N .
The minimum of this curve is at a value of 0.83. 
eps Distribution of the fraction of SM like pairs (f_{+}) assuming either the Exotic or the Standard Model. Indicated is the measured f_{+} value of 0.83 which corresponds to:
pvalue under SM of 0.134 pvalue under XM of 1.4 x 10^{4}  
We calculate pvalue under XM (p_XM) and pvalue under SM (p_SM). To obtain final conclusions we use apriori criteria:
Four outcomes are possible from above:

Bayes Factor = P(N_{+}  SM) / P(N_{+}  XM) = odds of SM versus XM
Observed 2*Ln(BF) = 19.6. Based on Bayes Scale, 19.6 means "data favors very strongly SM over XM". 
A note on the statistical treatmente: the apriori Type I and II error criteria  
Shown above is the plot of the distributions of f_{+} under the SM and XM hypotheses. We compute two pvalues based on f_{+} as test statistic: p_{SM}, the lower tail area under the SM distribution, and p_{XM}, the upper tail area under the XM distribution. To reject the SM we require p_{SM} &le α_{SM}, where α_{SM} is the standard 5sigma discovery threshold of 2.87x10^{7}. To exclude the XM we similarly require p_{XM} &le α_{XM}. The choice of α_{XM} requires care as it should reflect the high sensitivity of our measurement. The XM exclusion confidence level is 1α_{XM}, and the probability of not excluding the XM when the SM is true is the TypeII error β_{XM} of the test. As shown on the plot on the right, low α_{XM} values can only be achieved at the price of high β_{XM}. One way to choose α_{XM} based on standard HEP values while taken the measurement sensitivity into account, is to set α_{XM} to the lowest standard value that is still higher than the associated value of β_{XM}. We found that the desired value of α_{XM} is 1%, and corresponds to β_{XM}=0.16% (green triangle on the plot). 
Results in 5.6fb^{1}  
Observed f+ = 0.83 p_SM = 0.134 p_XM = 1.4 x 10^{4} 
Since the pvalue under the SM hypothesis is 0.134, we do not exclude SM. But since pvalue under the XM hypothesis is lower than the a priori chosen value of 1%, we exclude the exotic quark model with 99% CL. confidence.  Based on the Bayes Factor value, we conclude that the data favors very strongly the standard model top quark hypothesis over the exotic quark hypothesis. 
Crosscheck on lepton type 

Electrons eps Distribution of the fraction of SM like pairs (f_{+}) assuming either the Exotic or the Standard Model.
The measured f_{+} value of 1.11 is indicated. 
eps 
Muons eps Distribution of the fraction of SM like pairs (f_{+}) assuming either the Exotic or the Standard Model.
The measured f_{+} value of 0.57 is indicated. 
eps 
Bacause using only the electron or muon channels reduces the statistics of the sample and thus the sensitivity of the analysis, the chosen apriori criteria for α_{XM} is 5%. Based on the results we can conclude that neither the electrons nor the muons channels can exclude the SM, and that both exclude XM with 95% CL. The Bayes Factor for electrons favors very strongly SM over XM, while muons favors positively SM over XM. 
eps 
The plot shows the &chi^{2} distribution after L+J cuts and double tagging.

References 
