7 Results
impact. The effect of the JES component related to the flavour composition is slightly lower. The fit constrains this uncertainty. An overestimation of it could be caused by the assumption that is made when calculating its pre-fit uncertainty. In this, the fraction of quark and gluon jets is assumed to be 0.5±0.5. This could be improved by deriving the quark-gluon profile individually for each process in the selected region of phase space and reducing the assigned uncertainty. However, the effect of this NP on the final result is already very small, suggesting that with the current data sample no significant gain would be achieved by this approach.
For thettbackground normalisation, a pre-fit uncertainty of 40 % is assigned for thetttemplate. This is slightly constrained by the fit and has an impact onµSIGof less than 4 %. This is also the case for the luminosity, that is set as a constant 2.1 % uncertainty for all signal and background predictions.
The last three uncertainties in the plot are related to the scale factors for b-tagging efficiency and electron and muon identification. All three NPs are unconstrained and have a very low impact on the signal strength.
Templates comparing the nominal and the up and down systematic variations of all the uncertainties discussed above, for the signal and background processes are included in appendixB.
Expected significance
The expected significance quantifies the compatibility of the background-only hypothesis with the ob-servation (that in this case is set to be the SM signal plus background prediction). The significance obtained from the likelihood fit yields 5.2σ. This means that, if the observed data would perfectly match the predictions, it would be possible to discovertZqproduction with the current analysis.
7.2 Observed fit results
10 20 30 40 50
Entries / 0.1
= 13 TeV, 36.1 fb-1
s
Data tZq
+tW t t Z+jets Diboson
H t V+t t t Uncertainty
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 ONN
0 1 2
Data / Pred.
Channel Nevents
tZq 35± 9
tt+tW 18± 7
Z+jets 37±11
Diboson 53±13
ttV+ttH+tWZ 20± 3
Total 163±12
Data 141
Figure 7.3: Pre-fit NN output distribution (left) and event yields (right) in the SR. The quoted errors include the pre-fit statistical and systematic uncertainties.
coming from the signal dominated bins. The uncertainties in some of the bins, for example the 5th bin in the distribution (labelled "Bin 4" on the plot), are large. This can be traced to the larger fraction of events coming from thett background. This sample has very low statistics (45 unweighted events total) and thus will yield a large statistical uncertainty.
Figure7.6shows the correlation matrix of all parameters included in the likelihood fit. Only uncer-tainties that have at least one correlation above 10 % are included. As it is shown in the plot, the diboson andZ+jets normalisation uncertainties show the largest correlation among all NPs. These have a neg-ative correlation of−0.54. This is understood because the two backgrounds combined account for over 70 % of the total number of background events and the two templates also have very similar shapes for the NN output distribution. Hence, if the fit would enhance one of them, the number of events from the other background would have to go down. Another NP pair that has a correlation higher than±0.3 is thett normalisation and the MC statisticsγ parameter in the fifth bin of theONN distribution (labelled as “MC statONN (bin 4)” in the plot). As mentioned before, the sample driving the MC statistical un-certainty is thett sample and the largest fraction oftt events is found in this particular bin. Hence, an anti-correlation between thett normalisation and the MC stat. uncertainty in that bin is expected.
The tZqradiation uncertainty and µSIG also have a large correlation of −0.41. Since changing the signal scale and radiation directly modifies the number of selected tZqevents, it is expected that this NP will have minor correlations to all other NPs but will have a strong effect on the signal strength parameter.
Another NP that is correlated with the signal strength is the diboson normalisation. These show a correlation of−0.23. Events coming from diboson production represent the dominating background in the signal region. Additionally, it is also the background with the largest number of events in each of the signal dominated bins of the NN discriminant. This means that in order to better fit the data, if the number of signal events is increased, the diboson contribution must be reduced, hence explaining the anti-correlation.
A summary of the effect of each systematic uncertainty on the number of fittedtZqevents is given in table7.1. All uncertainties related to a single physics object are added together (e.g. “Jets” includes all JES related NPs and the JER uncertainty). Even with this merging of some uncertainties, the tZq radiation is dominant, changing the number of signal events by up to 10 %.
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−0.1 0 0.1
µ µ /
∆ resolution soft term
miss
ET
Muon identification -tagging scale factor b
Luminosity JES flavour composition normalisation t
t
Jet energy resolution tZq theory Diboson normalisation tZq radiation
−2 0 2
θ
∆
0)/
θ θ - (
ATLAS
= 13 TeV, 36.1 fb-1
s
signal
µ Pre-fit impact on
signal
µ Post-fit impact on
Figure 7.4: The pulls of the fitted NPs (black circles) along with their post-fit uncertainties (black lines), as obtained from the data fit, can be read on the topx-axis. The expected pre-fit (in yellow) and post-fit (as hatched blue boxes) impact of the systematic uncertainties on the signal-strength parameterµSIGis also shown can be read on the bottomx-axis. On they-axis, the uncertainties are ranked according to their pre-fit impact onµSIG; only the largest ten uncertainties are included in the plot.
Source Uncertainty [%]
tZqradiation ±10.8
Jets ±4.6
b-tagging ±2.9
MC statistics ±2.8
tZqPDF ±2.2
Luminosity ±2.1
Leptons ±2.1
EmissT ±0.3
Table 7.1: Breakdown of the impact of the systematic uncertainties on the number oftZqsignal events in order of decreasing effect.
7.2 Observed fit results
Figure 7.5: Ranked impact plots with pulls for the Monte Carlo simulation statistics NPs in each bin of the final discriminant when performing a fit to data. The expected pre-fit (in yellow) and post-fit (as hatched blue boxes) impact of the systematic uncertainties on the signal-strength parameterµSIGis shown can be read on the bottom x-axis. The pulls of the fitted NPs (black circles) along with their post-fit uncertainties (black lines) can be read on the topx-axis. On they-axis, the uncertainties are ranked according to their pre-fit impact onµSIG.
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1
− 0.8
− 0.6
− 0.4
− 0.2
− 0 0.2 0.4 0.6 0.8 1
Diboson norm.Luminosity Z+jets norm.
NC 1
JESη Jet energy resolutiontZq radiation norm.tt
(bin 0) NN MC stat. O
(bin 4) NN MC stat. O
(bin 9) NN MC stat. O µ µ
(bin 9) MC stat. ONN
(bin 4) MC stat. ONN
(bin 0) MC stat. ONN
norm.
tt tZq radiation Jet energy resolution NC 1 JESη Z+jets norm.
Luminosity Diboson norm.
-0.23 -0.13 0.04 -0.02 0.18 -0.41 -0.09 0.04 0.00 -0.12 1.00
0.03 0.00 -0.01 0.00 0.01 0.00 0.02 -0.00 0.00 1.00 -0.12
-0.03 -0.02 0.02 -0.12 0.01 -0.01 -0.30 0.02 1.00 0.00 0.00
-0.05 -0.00 -0.14 0.01 0.01 -0.00 -0.01 1.00 0.02 -0.00 0.04
-0.16 -0.03 -0.13 -0.04 -0.05 0.01 1.00 -0.01 -0.30 0.02 -0.09
0.04 0.01 0.02 0.00 -0.03 1.00 0.01 -0.00 -0.01 0.00 -0.41
-0.07 -0.01 0.03 -0.01 1.00 -0.03 -0.05 0.01 0.01 0.01 0.18
0.06 -0.00 0.03 1.00 -0.01 0.00 -0.04 0.01 -0.12 0.00 -0.02
-0.54 -0.06 1.00 0.03 0.03 0.02 -0.13 -0.14 0.02 -0.01 0.04
-0.06 1.00 -0.06 -0.00 -0.01 0.01 -0.03 -0.00 -0.02 0.00 -0.13
1.00 -0.06 -0.54 0.06 -0.07 0.04 -0.16 -0.05 -0.03 0.03 -0.23
ATLAS s= 13 TeV, 36.1 fb-1
Figure 7.6: Correlation matrix of the parameters included in the likelihood fit for the data. Only those uncertainties that are correlated by more than 10 % with another uncertainty are included.