Feldman-Cousins Limit Setting

Measured Top Width Distributions

This is the output of the Likelihood fit with quadratic dependency on the top width.

Likelihood Ratio (lambda) distribution

Likelihood ratio = p(# PE | width) / p(# PE | best)

parameterization fit to the width distribution

We characterize the shapes of the top width distributions to use the Feldman-Cousins construction in a continuous manner.

difference between fit and the width distribution

Likelihood ratio function

likelihood ratio function. The red line is the 95% CL region in width distribution.

95% CL interval in the width function

Shaded region is the 95%CL region in the top width function (and not in the top width distribution)

Confidence Band!!

95% CL band.
The left plot is the confidence bands drawn only for the true width that we have MC samples. The right plot is the confidence bands drawn for every 1 GeV true top width. Red bands corresponds to the bands on the left plots (i.e. for our MC samples' top width).

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PE for the top width limits without systematics

This plot is PE from using lots of CL bands. The x-axis is the measured top width (output of the likelihood) and the y-axis is the upper and lower limit given that measured top width.

Lower and Upper limits for the input top width of 1.5 GeV
Projection on Y axis to see the number of entries in each limit.
For the input top width of 30 GeV


Coverage vs input top width from 3000 PEs (at 95% CL)

Top Width limits with systematics included

Measured Top width distribution with systematics (after convolution). On the right is the fit to this distribution.

Likelihood Ratio Function

Confidence Band with Systematics

PE results for 1.5 GeV with systematics at &Gamma_top^input = 1.5 GeV and M_top = 175 GeV

PE results for 1.5 GeV with x10 statistics and systematics at &Gamma_top^input = 1.5 GeV and M_top = 175 GeV

PE results for 30 GeV with systematics at &Gamma_top^input = 1.5 GeV and M_top = 175 GeV

Comparison of 90%CL and 95% CL bands