CERN-THESIS-2012-153 26/07/2012 - CERN Document Server

computed from Equation 8.12 replacing Xd with the median statistical test for the background hypothesis,
Xb.
8.2.1 Uncertainties
The confidence level is by itself an expression of uncertainty. Thus, instead of quoting an uncertainty on the
confidence limit, the confidence limit is modified to allow for the experimental uncertainties. The approach
is to create a new set of “smeared” background rates and signal efficiencies, and from these, background
and signal events are generated to form the input to the likelihood ratio for each pseudo-experiment. The
consequence of this smearing procedure is that the likelihood ratio distributions get widened. In particular,
the background tail under the signal+background distribution and the signal+background tail under the
background are enhanced. This means the overlap of the distributions is increased, reducing both the
exclusion and the discovery potential of the search, and weakening both the discovery-like and exclusion-like
observations [106]. In this analysis, both statistical and experimental uncertainties of the signal efficiency
and expected background are taken into account, and are implemented assuming Gaussian distributions,
with the lower tail cut off at zero, so that negative signal or background are not allowed. In addition,
the statistical fluctuations of the pseudo-experiments are performed using Poisson distributions. Poisson
statistics are required given that expected signal and background levels are small. For the combination of
the 2ID+TL and 3ID channels the systematic uncertainty of the MC-based backgrounds (WZ, ZZ and
t¯t + W/Z) and signal acceptance are considered to be fully correlated, while other sources of uncertainties
(statistical or systematic) are considered uncorrelated.
8.3 Results
The limits on number of signal events expected are then converted into upper limit on the corresponding BRs
using the approximate NNLO calculation, and its uncertainty, for the t¯t cross section (σt¯t = 165 +11
−16 pb) [108].
This is simply achieved with the use of the cross section definition:
σt¯t = Nt¯t , (8.13)
Ldt
where N t¯t is the number of collision events that produce t¯t events, and constraining BR(t → Zq) by:
BR(t → Zq) + BR(t → Wq) = 1. (8.14)
96