Similarly to the strategy depicted in Section6.5.3, this analysis employs the pruning and smoothing of certain systematic uncertainties. This is because some of the nuisance pa-rameters would otherwise behave in an uncontrolled way during the profile likelihood fit and lead to an unstable result or even preventing the fit from converging. Furthermore, statistical fluctuations in the parameters can lead to non-physical constraints on the uncertainties. Another motivation is that the pruning and smoothing of the systematic uncertainties proves essential in order to reduce the CPU time required to perform the fit.
10.4 Pruning and smoothing of systematic uncertainties The normalisation and shape effects of systematic uncertainties are pruned separately through bin-by-bin variations relative to each sample in each region. The smoothing is then done in an analogous way to the b-tagging calibration analysis in that the his-tograms are rebinned meaning the bins are merged and then smoothed, constrained by the maximum number of shape variations allowed which is configurable for each sys-tematic uncertainty. Here, the pruning thresholds are set to 1%. This means that a systematic uncertainty is pruned if its impact on the normalisation of a sample or if the difference of each individual bin variation with respect to the average bin variation in the discriminant distributions is less than 1%. The pruning is done separately for each systematic uncertainty and each region. This threshold value is a result found to signif-icantly speed up the fit procedure without any observable changes to the uncertainty on µor to constraints or pulls on any of the nuisance parameters.
CHAPTER 11
Results of the t ¯ tH (H → b ¯ b) analysis
In this chapter, the results of the search for the presence of a t¯tH(H → b¯b) signal are presented. They are based on the combined profile likelihood fit described in Section9.2.
The fit method as well as the results presented throughout this chapter are subject to consistency checks in Section 11.1. The plots presented in Section 11.2 show the pre-fit and post-pre-fit modelling of the discriminant distributions and the event yields in all considered analysis regions, split up into the different signal and background categories introduced in Section7.3. The signal strength parameter is extracted twice, once for the single lepton and dilepton channels individually and once for the combination of both channels. Along with the signal strength parameter, the most dominant uncertainties limiting the measurement are listed and the behaviour of the nuisance parameters during the fit is highlighted. Finally, upper limits on the expected and observedt¯tH(H→ b¯b) cross-sections are set. The analysis results are combined with those of other t¯tH search channels in the Atlascollaboration and compared to those of the Cms experiment in AppendixF. Studies that aim to reduce the most dominant systematic uncertainties i.e.
those associated to the signal and main background modelling are presented in the next chapter.
11.1 Consistency checks of the fit result
As will be highlighted in the following section, the simulation of the t¯t+ ≥ 1b pro-cess is subject to large uncertainties. One aspect of this evaluation involves comparing t¯t+ ≥1b events modelled by different MC generators and this comparison reveals sig-nificant differences in the normalisation and shape of relevant distributions. With the generators that employ the five flavour scheme PDF in the ME, thett¯+b¯bprocess, which is the actual background of interest, is only accessible via the PS simulation, not the ME generation. Therefore, the nominal generator setups currently available in Atlas
are only able to model the t¯t+b¯b process with a sub-optimal precision in QCD. As a consequence, the systematic uncertainties associated to the modelling of this process are dominant and limit the sensitivity of this search. Thus, it is reasonable to explore possibly false evaluations of these systematic uncertainties and their sources.
Firstly, the choice of nuisance parameters which encode the systematic uncertainties associated to the t¯t+≥ 1b background is studied. For this background, thirteen inde-pendent nuisance parameters are included in the fit. The profile likelihood fit should have the capability to correct any potential mis-modellings of this background without introducing any bias in the fitted signal strength parameter. This capability to correct for mis-modellings, aside from those shown in the distributions in the following section, is tested by evaluating the agreement between data and the simulation of all input variables to the classification BDT post-fit. The result is positive as no significant disagreement between data and prediction is observed [4]. On the contrary, the agreement is improved post-fit. Alternative strategies have been considered and tested for this background, namely regarding its modelling or the definition of corresponding uncertainties and their correlations. The respective results are found to be compatible with the nominal result quoted in the following section [4].
Some of the employed nuisance parameters are shifted away from their nominal values by the fit which can be seen in Figure11.10in the following section. It shows the twenty nuisance parameters from independent sources of systematic uncertainty that have the largest impact on the total uncertainty onµ, ranked by decreasing impact. In order to find the cause of these shifts, those nuisance parameters are set as uncorrelated between all analysis categories and samples and the fit procedure is repeated. This reveals that the fit uses these nuisance parameters mostly to correct thet¯t+jets background to match the observed data in multiple regions [4]. When the fit employs the background-only hypothesis and the most signal-enriched bins are taken out of the distributions, a similar trend can be observed when repeating the fit. The impact of these shifts on the signal strength can be tested and quantified by fixing the nuisance parameters individually to their pre-fit values throughout the fit and then comparing the new result with the nom-inal fit result. Using this approach, the contribution of these parameter shifts are found to be smaller than the uncertainty onµ[4]. In addition to this, a strategy is followed in which independent signal strength parameters are fitted using different sets of analysis categories in the dilepton and single lepton channels. The parameter values of this test are also compatible with the nominal results [4].
It should be noted that some of the systematic uncertainties are decreased by the fit.
This is because the fit strongly constrains the corresponding nuisance parameters if their variation would affect the distributions of the discriminants in such a way that they would lead to a significant discrepancy between prediction and data. To test this hypothesis, the capability of the profile likelihood fit to constrain systematic uncertainties is vali-dated through a fit to a so-called Asimov dataset [133] which is a pseudo-dataset based on all nominal simulated samples [4].