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



R. Hughes, R. Marginean, E. Thomson, B. Winer
The Ohio State University

R. Erbacher, R. Roser
Fermi National Accelerator Laboratory

J. Conway
Rutgers University





Results for 195/pb:


Table showing number of events in data, ttbar fraction, and resulting cross section with statistical errors listed first, systematic errors listed second. Apriori our cross section result is for the 3 or more jet bin, the 4 or more jet bin result is intended to be a cross-check.  

Final Fits to the NN-output shape :

Fits for a 195^{-1} pb data sample follow bellow.  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.  Apriori, our primary result is for the 3 or more jet bin.

W + 3 or More Jet Sample

W + 4 or More Jet Sample


Fit to the NN-output shape for at least 3 jets, showing shapes of contributing components (EPS)

Fit to the NN-output shape for at least 4 jets, showing shapes of contributing components (EPS)

Predicted NN output shape for at least 3 jets, showing stacked contribution of each component (EPS)

Predicted NN output shape for at least 4 jets, showing stacked contribution of each component (EPS)

Choosing the NN:

Systematic/Statistical errors are studied as a function of the number of input variables. For a given number of input variables 3-4 different NN configuration are studied. The numbers corresponding to 1 variable werr obtained by fitting the HT shape alone. Number improve with adding more input variables. Based on the results shown bellow we choose a 7 input NN as a good compromise between simplicity and performance.

The average expected fractional error from pseudo-experiments when fitting the NN-output distribution for different NN configurations versus the number of input nodes. The average ttbar fraction in pseudo-experiments was 19% and the number of montecarlo events was estimated for ~195/pb. (EPS)

Estimated systematic error error when fitting the NN-output distribution for different NN configurations versus the number of input nodes. The average ttbar fraction in pseudo-experiments was 19% and the number of montecarlo events was estimated for ~195/pb. (EPS)

The NN-output shapes:

The NNs are trained to separate signal from background in the W+3 or More and respectively W+4 or More jet samples. In both cases we use feed forward NN with 7 input variables, 7 hidden nodes and 1 output in the [0,1] range. The input variables are: Aplanarity, Max-Jet-Rapidity, Ht, EtJ_{345}, SumPz/SumEt, Min-Dijet-Mass, Min-Dijet-Separation. The shapes of the NN output in a balanced set of PYTHIA ttbar and ALPGEN W+3(4)p events are shown bellow.

The output shape for a NN trained in the NJ>=3 mode. A balanced set of ttbar/W+3p MC events was used to fill these histograms.(EPS)

The output shape for a NN trained in the NJ>=4 mode. A balanced set of ttbar/W+4p MC events was used to fill these histograms.(EPS)

The NN-output for the SECVTX b-tagged sample:

The NN output for the b-tagged sample is shown bellow: blue histogram. The red line is the NN output shape of the tagged ttbar MC sample and is shown for comparison purposes (EPS). This is not a fit.


Fit Fractional-Error/Pull-Dist from pseudoexperiments:

The fit Fractional Error distribution and the fit Pull Distribution for 5000 pseudoexperiments is shown bellow. The red arrow indicates the fractional error obtained from fitting the data.

Distribution of Fit Fractional-Error for 5000 pseudo-experiments (EPS).

Distribution of Fit Fractional-Error for 5000 pseudo-experiments(EPS).

Fit Pull Distribution for 5000 pseudo-experiments (EPS).

Fit Pull Distribution for 5000 pseudo-experiments(EPS).

W+jets vs ttbar comparisions :

Pythia ttbar compared to Alpgen W3p MC for all the variables used in the NN input.

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