Measuring the sign of the top charge in L+J channel
using the top decay products


Jaroslav Antos1, Pavol Bartos2
Andy Beretvas3, Veronique Boisvert4,a
Yen-Chu Chen5, Kevin McFarland4, Veronica Sorin6
Stanislav Tokar2, Kirsten Tollesfson7

1Institute of experimental physics Kosice, 2Comenius University Bratislava, 3FNAL,
4University of Rochester, 5Institute of Physics Academia Sinica,
6Institute de Fisica d'Altes Energies Barcelona, 7Michigan State University
acurrently at Royal Holloway, University of London

Public Note

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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 anti-top quark decays to a W- and an anti-bottom 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 b-jet 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.

The gif version of the plots can be obtained with a right-click and "save image as",the eps version by clicking on the eps link beside the plot.

Pairing: To find the right association between the lepton and b jet, we use top mass &chi2 fitter. See the public note for the details. How often the method gives the right pairing is the purity of pairing, ppairing.
ppairing      83%
Efficiency      53%
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 Pt environment. How often this algorithm gives the right flavor in MC is the purity of Jet charge, pJQ.
pJQ       61%
Efficiency       98%

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 b-bbar 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 b-bbar events present in the sample, secondary decays and mixing.


Scale Factor between the data corrected purity and the JQ purity calculated on b-jets selected from MC (Pythia) samples (combination of a Heavy Flavor enriched MC and dijet MC). The constant fit is shown.
SFJQ = 0.99 ± 0.01 (stat.) ± 0.03 (sys.)


Systematic Uncertainties on SF.

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).

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 anti-top.
Getting Signal Purity

Ps = fnonb SFnonb pnonb + (1-fnonbSFnonb)(ppair pJQ SFJQ + (1-ppair)(1-pJQSFJQ))
Above is the definition of Signal Purity, Ps.The measured jet charge purity in MC is corrected by the SFJQ. The measured fraction of nonb in MC,fnonb, is corrected by the mistag rate, SFnonb, between data and MC.


Summary of Systematic Uncertainties.


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.



f+ = fraction of pairs with top charge +2/3

Using a Profile Likelihood and the above nuisance parameters (Ns,Nb,ps,pb) we got the Log Likelihood curve for the observed N+ and N- .

The minimum of this curve is at a value of 0.83.

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:
p-value under SM of 0.134
p-value under XM of 1.4 x 10-4
We calculate p-value under XM (p_XM) and p-value under SM (p_SM).

To obtain final conclusions we use a-priori criteria:
if p_SM < 0.0013 => 3&sigma evidence of non-SM effect
if p_SM < 2.87 x 10-7 => 5&sigma observation of non-SM effect
if p_SM > 0.0013 => do not exclude SM
if p_XM < 1% => would exclude XM with 99% CL

Four outcomes are possible from above:
Reject XM and fail to reject SM
Reject SM at the 3&sigma or 5&sigma significant level, fail to reject XM
Fail to reject either XM and SM
Reject both - XM and SM
Bayes Factor = P(N+ | SM) / P(N+ | XM) = odds of SM versus XM
2.Ln(BF) Evidence Against H0
0-2 Not worth than a bare mention
2-6 Positive
6-10 Strong
>10 Very Strong

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 a-priori 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 p-values based on f+ as test statistic: pSM, the lower tail area under the SM distribution, and pXM, the upper tail area under the XM distribution. To reject the SM we require pSM &le αSM, where αSM is the standard 5-sigma discovery threshold of 2.87x10-7. To exclude the XM we similarly require pXM &le αXM. The choice of αXM requires care as it should reflect the high sensitivity of our measurement. The XM exclusion confidence level is 1-αXM, and the probability of not excluding the XM when the SM is true is the Type-II error βXM of the test. As shown on the plot on the right, low αXM values can only be achieved at the price of high βXM. One way to choose αXM based on standard HEP values while taken the measurement sensitivity into account, is to set αXM to the lowest standard value that is still higher than the associated value of βXM. We found that the desired value of αXM is 1%, and corresponds to βXM=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 p-value under the SM hypothesis is 0.134, we do not exclude SM. But since p-value 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.

Cross-check on lepton type



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.





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.



Bacause using only the electron or muon channels reduces the statistics of the sample and thus the sensitivity of the analysis, the chosen a-priori criteria for αXM 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.


Pairing Related Plots

The plot shows the &chi2 distribution after L+J cuts and double tagging.
  • "Alternative Interpretation of the Tevatron Top Events", D. Chang et, al., hep-ph/9810531.

  • Last Update on 2011