1. CP Violating TGCs
Tim Barklow
July 2, 2003

2. Modified Log Likelihood Estimator
The standard log likelihood function that was used
in 1999 to fit CP violating TGCs in the
channels was augmented with a correction function
in to account for a variety of effects in
the more complicated
channels.
The correction function is properly reweighted so
that no TGC value is favored over another.
The correction function also makes it straightforward
to add new effects such as EW corrections.

3. Modified Log Likelihood Estimator
However, the correction function has a drawback
in that it disturbs the most important statistical
interpretation of the LL function:
in general
Because of these considerations, the LL estimator
with the correction function is not a true LL estimator,
and so I call it a Modified Log Likelihood Estimator,
or MLLE.

4. The MLLE function f(g) is given by
differential cross section using reconstructed variables
(sum over background MC events)

5. Fit for TGC g by solving where
Note that the function that forms the basis for the OO
method,
appears prominently here.

6. Statistical variance of TGC fit variable g
Including background the full expression for the statistical error is
(sum over bkgnd MC events)

7. Statistical variance of TGC fit variable g
can be calculated simultaneously using signal MC
while are calculated using background MC
Unlike the situation in , the statistical
variance of the TGC fit variable g can now be
calculated without trial MC runs.

8. Current Status Analysis with new error calculation software
has been performed on version ntuples.
Some pull distributions will be shown, as well
as initial results from data using v1.631 ntuples
The systematic error analysis is not yet completed. All results shown here include statistical errors only.

9. Pull distributions

10. Pull distributions

11. Oct 2001 Analysis: July 2003 Analysis:

12. Oct 2001 Analysis: July 2003 Analysis:

13. Oct 2001 Analysis: July 2003 Analysis:

14. from 2-d fit using Monte Carlo
Form Factor for Vector Resonance Enhancement of
95% C.L. contour for for
from 2-d fit using Monte Carlo
Our 1-d fit of using data:
@ 95% C.L. assuming stat errors only. Also assumes that WW scattering in J=1 channel
is dominated by lowest lying vector resonance

15. Summary
A formula for the variance of the Modified Log Likelihood Estimator (MLLE) method has been developed. This formula provides a means to calculate the statistical error without using trial MC runs.
Results were shown for CP violating TGCs and CP conserving TGCs without SU(2)XU(1) constraints using version 1.63 ntuples
The result of can be translated into a mass limit of at 95% CL for a techni-vector resonance.
Systematic error calculations are required before declaring the results final. However, this is a straightforward process and can be completed shortly.