Future prospects
7.1 Low-mass range and correlation
As mentioned in Section 6.4, a large (anti)correlation is observed between µ and kt¯t + ≥1b (the t¯t + ≥1b normalisation), for the fits performed in the 250 − 300 GeV mass range. This
correlation is imputable to the very similar kinematics of the two processes, which are almost indistinguishable by the BDT. The parameters µ and kt¯t + ≥1b are unconstrained in the likeli- hood function, therefore their correlation can drive the signal strength to large pulls, reducing the meaningfulness of the result. Possible ways of addressing the issue are illustrated below. A first method to reduce the correlation between µ and kt¯t + ≥1b is to relax some of the con- straints on the most relevant t¯t + jets systematic uncertainties, making it preferable for the fit
to use such uncertainties rather than the floating parameters. In fact, the pre-fit uncertainties are large enough to cover for the differences between data and MC in all regions, but the correlation between uncertainties, and the correlation of each uncertainty with itself across regions, lead to constrained post-fit errors. The choice of keeping each nuisance parameter 100% correlated across regions is generally justified by the assumption that their behaviour should be consistent in various areas of the phase space. However, uncertainties like those related to the choice of the ME generator, or to the choice of the PS, embed multiple system- atic effects and can be of difficult physical interpretation. A dedicated decorrelation scheme
Future prospects
could be more effective for such nuisance parameters.
To better understand, one can consider the systematic variations depicted in Figure 7.1. The distributions correspond to the output of the BDT trained with the 300 GeV signal hypothe- sis, for the nominal t¯t + ≥1b background (in black) and the associated PS uncertainty (in red
and blue), in two signal regions 5j≥4b (a) and ≥6j≥4b (b). As explained in Section 6.3.2, the uncertainty on the PS is associated to the choice of the generator employed for the simulation of the showering and hadronisation of partons, and it is obtained by comparing the default Powheg + Pythia 8 sample to one produced with Powheg + Herwig 7. Such uncertainty affects both the shape and normalisation of t¯t + ≥1b events, however the +1σ variation in
5j≥4b corresponds to an overall positive (and small) variation in normalisation, while in the ≥6j≥4b region the difference in normalisation is much larger and negative. The impact of the uncertainty on the shape of the t¯t + ≥1b distribution is visible from the ratio plot. It is almost
negligible in the 5j≥4b region, where the variation is flat within statistical uncertainties, and stronger in the ≥6j≥4b region, where the ratio rises with the BDT output.
Similar differences have the potential of producing unexpected constraints. This is particu- larly true when the agreement between data and MC is improved by the pull of a NP in some regions, but not in others, or if the change in shape predicted by the systematic variation is in good agreement with data, but not the change in normalisation (and vice-versa). A possible solution is to decorrelate the corresponding systematic uncertainties between regions, and/or between shape and normalisation, allowing the fit to only exploit the "useful" part of the un- certainty and leave the rest unchanged. Promising results were obtained by decorrelating the PS, ME generator, radiation and 4vs5 flavour-scheme systematic uncertainties of the t¯t + jets
sample among the number of jets, i.e. between 5-jets and ≥ 6-jets regions, and the 4vs5 FS, PS and ME systematic uncertainties of the t¯t + ≥1b category between shape and normali-
sation. The net result is a considerably lower correlation between µ and kt¯t + ≥1b with only a slightly decreased sensitivity. Table 7.1 provides a comparison between the values of the signal strength and the (µ vs kt¯t + ≥1b) correlations, obtained by performing Asimov fits with the default model or implementing the new decorrelation scheme. The tests were performed using BDTs trained over the set of 12 variables described in Section 6.2.1, without exploiting the likelihood discriminant. The results are presented for mH+ ≤ 350 GeV, which is the most
sensitive region to such correlations. The fact that the result is more conservative, together with the reduced risk of an unwanted pull of the signal strength, make this decorrelation scheme preferable to the default model.
Low-mass range and correlation
(a) SR 5j≥4b.
(b) SR ≥6j≥4b.
Figure 7.1: The t¯t + ≥1b PS and hadronisation systematic uncertainty for the distribution of
the BDT trained with the 200 GeV signal hypothesis, in (a) the 5j≥4b region and (b) the ≥6j≥4b region. The red and blue lines represent the +1σ and −1σ systematic variations (after smoothing and symmetrisation). The bottom panel corresponds to the ratio between the systematic variations and the nominal distribution. Given the symmetry between the two sides of the systematic uncertainty, the statistical error is only reported for the +1σ variation.
Future prospects
default model new model
mass signal strength µ vs kt¯t + ≥1b
correlation signal strength
µ vs kt¯t + ≥1b correlation 200 GeV 0 ± 2.10 -48 0 ± 2.16 -19 225 GeV 0 ± 1.91 -56 0 ± 1.96 -20 250 GeV 0 ± 1.36 -43 0 ± 1.39 -25 275 GeV 0 ± 1.22 -73 0 ± 1.29 -49 300 GeV 0 ± 1.12 -68 0 ± 1.20 -49 350 GeV 0 ± 0.74 -47 0 ± 0.81 -47
Table 7.1: Signal strengths and (µ vs kt¯t + ≥1b) correlations obtained with the default t¯t + jets
modelling and with a new model in which the PS, ME generator, 4vs5 flavour scheme and radiation t¯t + jets systematics are decorrelated among the number of jets and the 4vs5 FS,
PS and ME systematic uncertainties for the t¯t + ≥1b category are also decorrelated between
shape and normalisation.
Low-mass range and correlation
A second way of improving the ability of the fit to distinguish between the two processes is to modify the analysis selection in order to create regions that are heavily enriched in t¯t + ≥1b
events. The H+ and t¯t + ≥1b distributions are in fact similar but not identical, therefore
a high purity can enhance the control over both components. A large part of the 5j≥4b and ≥6j≥4b regions is already composed by t¯t + ≥1b events, however better results can be
achieved by modifying the b-tagging efficiency used for the region definition. Figure 7.2 shows the background composition of the six regions used in the analysis when they are tagged using the 60%, 70% or 77% b-tagging working point.
(a) 60% efficiency. (b) 70% efficiency.
(c) 77% efficiency.
Figure 7.2: Background composition of control and signal regions tagged with different effi- ciencies: (a) 60%, (b) 70% and (c) 77%.
Future prospects
The larger the b-tagging efficiency, the larger is the mistag probability. At 77% efficiency, there is a large amount of t¯t + light and t¯t + ≥ 1c events in the ≥ 4b regions, while they
are expected to be mainly composed by t¯t + ≥ 1b events. The t¯t + light and t¯t + ≥ 1c
categories are consistently reduced at 70% efficiency and they almost disappear at 60%. Table 7.2 provides a comparison between the values of the signal strength and the (µ vs
kt¯t + ≥1b) correlation obtained with Asimov fits performed on regions tagged at 60%, 70% or 77% efficiency (dedicated BDTs were trained for each of the different b-tagging working points). The results show how the increased purity of the 60% regions allows to further reduce the correlation between µ and kt¯t + ≥1b, with a positive impact on the sensitivity of the analysis. Using a stricter efficiency at higher masses is disadvantageous because of the reduced statistics. At 77% efficiency, the total amount of t¯t + ≥ 1b events in the ≥5j≥3b
region is approximately 27000, but only 12000 events pass the selection at 60%. This has a small impact at low masses, where the uncertainty on the signal strength is dominated by systematic errors, but it has a strong effect at high masses, where the most signal-like bins of the BDT distributions are populated by few background events and the statistical error plays a more relevant role.
60% efficiency 70% efficiency 77% efficiency
mass signal strength µ vs kt¯t + ≥1b
correlation signal strength
µ vs kt¯t + ≥1b
correlation signal strength
µ vs kt¯t + ≥1b correlation 200 GeV 0 ± 1.74 -14 0 ± 2.16 -19 0 ± 2.25 -29 225 GeV 0 ± 1.37 -21 0 ± 1.96 -20 0 ± 1.85 -34 250 GeV 0 ± 1.15 -27 0 ± 1.39 -25 0 ± 1.80 -40 275 GeV 0 ± 1.01 -40 0 ± 1.29 -49 0 ± 1.43 -45 300 GeV 0 ± 1.02 -39 0 ± 1.20 -49 0 ± 1.40 -60 350 GeV 0 ± 0.70 -37 0 ± 0.81 -47 0 ± 0.90 -50
Table 7.2: Signal strengths and (µ vs kt¯t + ≥1b) correlations obtained with control and signal regions tagged at 60%, 70% or 77% efficiency.