Measurement of the ttbar Cross Section in the Lepton + Jets Channel Using Event Kinematics

Authors:

R. Hughes, R. Marginean, E. Thomson, B. Winer

The Ohio State University

R. Erbacher, R. Roser
Fermi National Accelerator Laboratory

J. Conway
Rutgers University

Blessed Plots and Tables, Summer 2003:

Final Results with 126 /pb:

Table showing number of events, ttbar fraction, and resulting cross section with statistical errors only. (EPS)

Cross section results including systematic errors. (EPS)

DeltaPhi Cut:

For this shape analysis we needed to remove as much of the QCD/fake background as possible since it is difficult to model such events. On examining the delta phi between the MET and the leading jet, there was an excess of events in the data between 0.5 < dPhi < 2.5 for events with MET between 20 < MET < 30. These events are thought to be background, and so are removed.

Shown is dPhi between MET and lead
jet for lepton+1 jet data. We remove
events with MET between 20 and 30 GeV
and dPhi between 0.5 and 2.5. (EPS)

Shown is dPhi between MET and lead
jet for ttbar and W+3p MC. There is no
excess where we make our dPhi cut,
resulting in very little signal reduction. (EPS)

The utility of the delta phi cut is shown in the below table: note that it does not affect the statistical precision of the measurement, but reduces the systematic uncertainty due to modeling this background by a factor of two. (EPS)

Observed/Expected Event Yield:

Shown is the number of events accepted in each jet bin, along with the predicted ttbar fraction in that bin. (EPS)

QCD Background Fraction:

Below is our estimate of the fraction of QCD/fake events that enter our sample for each jet bin and for electrons and muons separately. We used the traditional MET v. Isolation method and the non-isolated lepton sample to determine the contamination. For our fit, the QCD shape normalization was fixed to 6.3% and we applied a systematic error to account for our (lack of) knowledge of the exact contamination. (EPS)

Shape Differences Between W+3p and ttbar MC Events for Various Kinematic Quantities:

Event Ht (EPS)	Et Lead Jet (EPS)
Et Jet 2 (EPS)	Et Jet 3 (EPS)
Et Jet 1 + Et Jet 2 (EPS)	Et Jet 2 + Et Jet 3 (EPS)
Sum Et of Selected Jets (EPS)	Missing Et (EPS)
Aplanarity (EPS)	Maximum Eta, 3 Lead Jets (EPS)
Average Eta², 3 Lead Jets (EPS)	Minimum DeltaR Between Two Jets (EPS)

Expected Sensitivity to Various Event Kinematic Variables:

The points in the charts below are the mean returned uncertainties from fitting ~5k pseudo-experiments. Error bars represent the 1-sigma range of possible returned uncertainties from the fit.

Predicted sensitivities, determined by fitting pseudo experiments, from a range of kinematic variables. (EPS)

Predicted ttbar content in W+NJets:

This plot shows the W + N Jets distribution in data (red) along with a prediction of the amount of top in the sample (blue) from MC.

WNjets plot here

Predicted ratio of top to background as a function of jet multiplicity. The ratio is about 1:1 in the 4 and 5 jet bins, but only about 12% in the 3 jet bin. We can use the 3 jet bin to help validate the MC as agreeing with data (along with the 1, 2 jet bins).

Ratio plot here

Data/MC Comparisons:

Use the W + 1, 2, 3 jet bins to compare data to MC so as to demonstrate that our MC shapes are modeling the data well. We model the background using AlpGen W+ n parton MC (for the nth jet bin) plus non-isolated leptons. In the 3 jet bin we add a ttbar component. We summarize the goodness of fit using a modified (not ROOT default) KS test in which we flatten the KS distribution.

Data/MC Comparisons in the 1-Jet Bin:

Total Event Energy Ht, 1 Jet Bin (EPS)

Put in Lead Jet Et plot

Data/MC Comparisons in the 2-Jet Bin:

Total Event Energy Ht, 2 Jet Bin (EPS)

Lead Jet Et, 2 Jet Bin (EPS)

Data/MC Comparisons in the 3-Jet Bin:

Total Event Energy Ht, 3 Jet Bin (EPS)

Lepton Et, 3 Jet Bin (EPS)

Results of the modified KS test for a subset of kinematic variables:

Conclusions: While the 1-jet bin agreement is not so good, we find
that for the 2 and 3 jet bin, a mixture of W+np MC, non-isol.
leptons, and ttbar MC models the data well. This table was
not blessed, but is included for completeness. (EPS)

Final Fits to the Signal Region:

Our fits to the signal region follow below. The W-like shapes include the contribution from W+3p, Wbbar+1p, Z->ll (3 flavors), W->tau nu+2p, WW+1p, WZ, single top. Electrons and muons have been combined for the fits. The QCD shape is taken from the non-isolated leptons and fixed to 6.3% from our MET v. Isolation calculations. The ttbar and W-like shapes float in the fits. Our primary result is using Ht and our a priori selection is the result for the 3 or more jet bin.

W + 3 or More Jet Sample	W + 4 or More Jet Sample
Fit to Ht for at least 3 jets, showing shapes of contributing components (EPS)	Fit to Ht for at least 4 jets, showing shapes of contributing components (EPS)
Fit to Ht for at least 3 jets, showing stacked contribution of each component (EPS)	Fit to Ht for at least 4 jets, showing stacked contribution of each component (EPS)
Fit to Sum Et of 2nd and 3rd jet for 3 or more jets (EPS)	Fit to Sum Et of 2nd and 3rd jet for 4 or more jets (EPS)
Fit to the Minimum DeltaR between two jets, for events with 3 or more jets (EPS)	Fit to the Minimum DeltaR between two jets, for events with 4 or more jets (EPS)
Fit to the Minimum DeltaR between two jets, for events with 3 or more jets (EPS)	Fit to the Minimum DeltaR between two jets, for events with 4 or more jets (EPS)
Fit results are fairly stable across a range of kinematic variables for events with 3 or more jets. (EPS)	Fit results are fairly stable across a range of kinematic variables for events with 4 or more jets. (EPS)