Combination of measurements of the relative fraction of ttbar events produced via gluon-gluon fusion
Authors
Ricardo Eusebi
(FNAL)
Eva Halkiadakis
Sunil Somalwar
Jared Yamaoka
(Rutgers)
Abstract
The relative fraction of ttbar events produced via gluon-fusion to the total number of
ttbar event was measured with two orthogonal techniques; the
NN kinematic analysis and the
track density
multiplicity analysis. With both analyses using a total integrated luminosity of 955 pb-1, we
find the total gluon fusion fraction in ttbar events to be 0.07+0.15-0.07. This web
page describes the combination of these two measurements.
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The Standard Model
predicts these to gg produced events and qq produced events to occur with relative
fractions of 85% and 15% respectively. The theory has large uncertainties.
For example, the contribution from gg fusion at the Tevatron can vary
up to a factor of 2 (from 10-20%).
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Analysis
The total production cross section of a given physical process can, in
general, be measured simply by counting events in specific final-state
channels. The contribution from different production processes to the
total production cross section is, however, very hard to
measure. CDF has made this measurement in two different ways. The first method
uses a neural network trained on the kinematics of the events to differentiate the gluon fusion
events. The
second method uses the fact that gluon fusion events tend to have more low pt
tracks caused by radiation from the gluons before the interaction.
The neural network analysis is well described
here, while a detailed description of the track analysis can be found
here.
Below you find a description on how we combine the two methods to achieve a more sensitive result.
Neural network for the three components of our sample. These are used to fit the data for
the correct fraction of gg produced top events. 1 Tag. Shapes are taken from Monte Carlo.
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Number of low pt for the gluon-rich events and for the no-gluon events. These are fit to the data to
find the gluon rich fraction. Shapes are taken from data.
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Combination
Overview
The track method originally used data to construct the templates because simulation is known not to correctly model the low pt
tracks the method is based on. However the method used in the combination depends on these simulations. To ensure we correctly model the
low pt tracks we morph our simulations to match the data.
Then to obtain our result, we created a large number of simulated data samples with the varying fractions of gg produce top events.
These simulated samples, or "pseudo-experiments" as we call them, are then fit to the neural network templates and to the track distributions independently. We then combine the results from the different methods and use
a statistical method called Feldaman-Cousins (FC) to create a map from the fitted value of our pseudo-experiments to the real gluon fusion
production fraction. More info on Feldman-Cousins Method can be found here.
Correlations
When combining two method like this we have to be careful to account for any correlation. These correlations fall into two
categories: correlations in the methods that lead to statistical correlations, and correlations in the systematic uncertainties
that are inherent in each method. To check the statistical correlations in
the methods, we ran a large set
of pseudo-experiments and plotted the results for each method, Figure 3. As you can see there are no statistical correlations.
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This plot shows the uncorrelated nature of the two analysis for a true gluon fraction of 50% (CF(true)=0.5),
which after acceptance corrections corresponds to a sample with a gluon fraction of 56% (CF(sample) of 0.56).
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Because the methods rely on very different variables, the correlation in the systematic uncertainties are,
for the most part, uncorrelated. For instance, uncertainties in the angular variable used in the neural network
method are independent of the uncertainties on the tracking efficiency. There are, however, a few small uncertainties
on the background measurement that are correlated. A full discussion of the systematic correlations can be found
here.
Combining
To each set of pseudo-experiments we fit a Gaussian to obtain a &sigma for each method (&sigmastatTK
and &sigmastatNN). Then for each individual pseudo-experiment we have value for each method
(CTKf and CNNf). We then apply the systematics to each pseudo-experiment:
Above Gauss(0,X) is a Gaussian random number between 0 and X and &Delta is the square root of the appropriate systematic
added in quadrature. We then weight each result (CTKf+sys and CNNf+sys) to
construct a value for the combined method (CCOMf+sys).
Results
We use the output of process described above to construct a FC band for the combination. We find the fitted gluon fraction
is 0.073. Applying this to the FC band we find the gluon fusion fraction in ttbar events is 0.07+0.15-0.07.
FC also allows use to quote an upper limit of 0.38 at a 95% confidence level.
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This is the final Feldman-Cousins plot of the combination. It shows the statistical+systematic
68% and 95% bands, the central value and its limits.
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More Information:
- A full set of plots from the combination can be found here.
- A paper with a complete description of the combination can be found here.
- A paper with a complete description of the low pt track analysis can be found
here.
- A paper with a complete description of the neural network analysis can be found
here.
Jared Yamaoka
Last modified: Mon Jan 14 00:24:52 CST 2008
