Abstract

We present a measurement of the top pair production cross section  in ppbar collisions at 1.96 TeV, with an integrated luminosity of  4.6 fb^-1 at the CDF experiment on the Fermilab Tevatron. We use a neural network technique to discriminate between top pair production and background processes in a sample of events with an isolated, energetic lepton, large missing transverse energy and three or more energetic jets. We then significantly reduce the dependence on the luminosity measurement and its associated large systematic uncertainty. We compute the ratio of the ttbar to Z cross section, measured using the same triggers and dataset, and then multiply this ratio by the theoretical Z cross section. In essence we replace the luminosity uncertainty with the uncertainty on the theoretical Z cross section.
We measure a top pair production cross section of 
σ_ttbar =  7.63 ± 0.37 (stat) ± 0.35 (sys) ± 0.15 (Z theory) pb for a top mass of 172.5 GeV/c². 
The total uncertainty is 7.0%, greatly surpassing the Tevatron Run II goal of 10%, and now more precise than the best theoretical calculations.

The top cross section was measured for 2 additional assumed top masses: 170 and 175 GeV/c².
The systematics were not re-computed but were scaled from the 172.5 GeV/c² measurement

σ_ttbar (M_ttbar = 170 GeV/c²) =  8.33 ± 0.40 (stat) ± 0.39 (sys) ± 0.17 (Z theory) pb  
σ_ttbar (M_ttbar = 175 GeV/c²) =  7.29 ± 0.35 (stat) ± 0.34 (sys) ± 0.14 (Z theory) pb.

Note that for this analysis, the central value is quoted after re-weighting to the CTEQ6.6 central PDF.

Event Selection

We use the standard CDF lepton + jets selection

• Central Lepton (electron or muon) p_T >= 20 GeV/c;
• Missing transverse energy >= 20 GeV;
• At least 3 jets with E_T >= 20 GeV. 

 We apply additional cuts

• Tighter missing transverse energy cut at 35 GeV;
• Tighter leading jet E_T cut at 35 GeV.

The tighter cuts were optimised to remove the most QCD background while maintaining reasonable efficiency for the ttbar signal. As the statistical uncertainty is not our dominant uncertainty, we can afford to cut quite hard. These cuts remove ~85% of the QCD, ~40% of the W+jets while maintaining ~80% efficiency for the ttbar signal.

Both central electrons and muons have been used for the final fit.
 
Note: We do not require any b-tagging.

Signal and Background Modeling

• The ttbar signal is modeled from PYTHIA Monte Carlo with an assumed mass of 172.5 GeV/c².
• The W+jets background is used to model all EWK backgrounds; the previous analysis showed that the effect of including all backgrounds was very small and such a difference is included as a source of systematic uncertainty.
• The W+jets background is modeled from ALPGEN+PYTHA MC. The W+jets sample is obtained from a combination of W+0p, W+1p, W+2p, W+3p exclusive as well as W+4p inclusive.
• The QCD shape is modeled from a sample of di-jet events which pass our event selection criteria. These events are dominated by jets that fake electrons. The QCD contamination in the electron sample is significantly larger than in the muon sample

Neural Network Input Variables

The Neural Network uses 7 kinematic distributions as inputs, with 1 hidden node.
The NN is trained to separate W+4p from ttbar Monte Carlo. It was not retrained for this iteration of the analysis.
The input variables are
Global event variables

• Σ_jets E_T of all jets excluding two leading jets
• H_T of the event (sum of transverse energy of all reconstructed objects)
• Aplanarity of the event

Variables related to the 3 leading jets

• Σ_jets p_z / Σ_jets E_T
• Minimum di-jet mass
• Minimum di-jet separation
• Maximum jet E_T

Ratio over the Z Cross Section

The dominant systematic uncertainty of the direct measurement of the ttbar cross section is in the luminosity measurement, 5.8%. 
We can almost entirely cancel this uncertainty by considering the ratio of the ttbar to the Z cross sections.
The Z cross section is measured using the same triggers ( central electron and central muon) and the same data sample as for the ttbar cross section.
For this measurement, the signal MC for ttbar and Z is re-weighted to the CTEQ6.6 PDF (with its associated uncertainties).
The measured ttbar cross section, from the NN fit, is found to be
σ_ttbar = 7.52) ± 0.36 (stat) ) ± 0.34 (sys) ± 0.44 (lumi) pb.
The Z cross section is measured to be
σ_z =  247.79 ± 0.79 (stat) ± 4.38 (sys) ± 14.59 (lumi) pb.
The ratio of the ttbar to Z cross section is computed, taking into account the correlations between the systematics
We multiply the ratio by the theoretical Z cross section
σ_Z^theory = 251.3 ± 5.0 (sys) pb. The dominant uncertainties on the theoretical Z cross section are the scale and the PDFs.
We get a final result for the measured top pair production cross section of
The total uncertainty is 7.0%, a significant reduction on the 8.6% uncertainty obtained using the NN kinematic fit only.

Final Fits to NN Output Distribution

Fits for the 4.6 fb^-1 data sample follow bellow.

The input QCD normalisation is obtained from a fit to the missing E_T distribution before the missing E_T cut is applied.
The uncertainty on the constraint is set to 50% in the final fit.
The ttbar and W+jets shapes float freely in the fit.  

Plots of NN Input Variable

These plots are shown using the signal and background normalisations obtained from the final fit.
Note that for these plots the overflow and underflow bins are not shown, hence the slightly different number of events)

	Σ ET of jets excluding 2 leading jets
	HT of the event
	Σ pz / Σ ET of 3 leading jets
	Aplanarity of the Event
	Minimum dijet separation of 3 leading jets
	Minimum dijet mass of 3 leading jets
	Maximum jet eta of 3 leading jets