Neural Network Variables
The neural network uses the 8 kinematic variables to distinguish
gluon-fusion produced ttbar events and quark annihilation produced events.
Kinematic Variables
The top quarks are reconstructed using a kinematic fitter[1].
This provides us with the fully reconstructed kinematics of the ttbar system.
The top mass is constrained to 175 GeV. All permutations
of jet to partons, which are consistent to b-tag information, are
tried. No requirement is made of the &chi2 of the fit.
The permutation with the lowest &chi2 is used to extract the
kinematic variables of the event. A total of 8 variables, two
of which describe the production and six of which describe the decay
of a given ttbar event, are calculated.
The two kinematic variables we use that describe the production of the event
are evaluated in the ttbar rest frame[2]:
- cos&theta*: the angle between the top quark and the right incoming parton.
- &beta: the top quark velocity relative to c.
The remaining six variables describe the decay and contain information
about the spin correlations. These variables are angles with respect to the
``off-diagonal'' spin basis in the
top (or anti-top) rest frame. The ``off-diagonal'' basis is defined
using the zero momentum frame of the ttbar system, and is designed such
that the like spin components,
up-up, or down-down, vanishes on average over large number of events.
For this choice of spin basis the top pairs are, on average, in a
state of unlike spins independent of their production angle and
rest frame speed. For a further description of this basis,
see[3]. The decay variables we use are as follows:
- cos&thetaLep: angle between lepton and the ``off-diagonal'' basis.
- cos&thetaNeu: angle between neutrino and the ``off-diagonal'' basis.
- cos&thetaWlep: angle between leptonically decaying W and the ``off-diagonal'' basis.
- cos&thetaWhad: angle between hadronically decaying W and the ``off-diagonal'' basis.
- cos&thetaDown: angle between down quark and the ``off-diagonal'' basis.
- cos&thetaUp: angle between up quark and the ``off-diagonal'' basis.
Variable Plots
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Neural Network: Fit to the Data (left 1 tag, right 2 tag).
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&beta: Fractions set from the neural network fit to the Data (left 1 tag, right 2 tag).
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cos&theta*: Fractions set from the neural network fit to the Data (left 1 tag, right 2 tag).
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cos&thetaLep: Fractions set from the neural network fit to the Data (left 1 tag, right 2 tag).
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cos&thetaNeu: Fractions set from the neural network fit to the Data (left 1 tag, right 2 tag).
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cos&thetaUp: Fractions set from the neural network fit to the Data (left 1 tag, right 2 tag).
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cos&thetaDown: Fractions set from the neural network fit to the Data (left 1 tag, right 2 tag).
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cos&thetaWhad: Fractions set from the neural network fit to the Data (left 1 tag, right 2 tag).
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cos&thetaWlep: Fractions set from the neural network fit to the Data (left 1 tag, right 2 tag).
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References
1. A. Abulencia, et al (CDF Collaboration),
Phys. Rev. D 73,032003 (2006).
2. G. Mahlon, S. Parke,
Phys. Rev. D 53, 4886 (1996).
3. S. Parke and Y. Shadmi, Phys Lett. B 387, 199 (1996);
G. Mahlon and S. Parke, Phys Lett. B 411, 173 (1997);
G. Mahlon, hep-ph/9811281.
Jared Yamaoka
Last modified: Thurs May 17 11:31:56 CST 2007