Final States with Four Leptons
6.7 Analysis Results
The expected SM background in the SR is shown with the number of observed events in Table 6.6.
A total of 1.7±0.8 events is expected and 2 events are observed in the signal region, which yields a p-value for the background-only hypothesis ofp0 = 0.29, reflecting a good agreement between the SM expectation and the observed data. The data driven estimate for the reducible background is negative due to underfluctuations in data and is therefore set to 0. The estimation of the irreducible background is done via MC simulations, where reconstructed objects are matched (in terms of ∆R) to generator level objects, such that the contribution with fake leptons from these samples can be subtracted. This is done in order to avoid double counting of such backgrounds, because the fake background is estimated from data; it is also the reason why some numbers differ from the expectations as shown in Table 6.3.
In Figure 6.19, some of the most important distributions for the signal region are shown, such as the leptonpT distributions, the distribution of the missing transverse energy and a splitting of the signal events into different lepton flavour channels. There is no evidence for physics beyond the SM in that signal region.
Process Signal Region
ZZ 0.6+0.5−0.5
ZWW 0.12+0.12−0.12
ZZZ <0.01+0.00−0.00 Higgs 0.26+0.07−0.07
ttZ 0.73+0.34−0.34
ttWW <0.01+0.01−0.01 Irreducible SM 1.7+0.8−0.8 Reducible SM 0.00+0.16−0.00 Total SM 1.7+0.8−0.8
Data 2
p0 0.29
Table 6.6: Results in the signal region. The observed number of events is in good agreement with the expected number of events from the SM. For the estimation of the irreducible back-ground, MC has been used, where reconstructed objects have been matched to generator level objects in order to remove events where only three of the prompt leptons, and an additional fake lepton, were reconstructed. These contributions are estimated with the weighting method.
0 50 100 150 200 250 300 350 400 450 500
eeee eeem eemm emmm mmmm
Events
all eeee eeem eemm emmm mmmm
Data / SM
Figure 6.19: Distributions in the signal region. The agreement between the SM expectation and the observed data is reasonable [147].
6.7.1 Statistical Interpretation of the Results
The results of the analysis are interpreted using a profile log likelihood ratio test. The likelihood is defined using the expected number of background events and the expected number of signal events for a point in parameter space. Systematic uncertainties are included by adding nuisance parameters, where correlations between different samples are taken into account. In the case of asymmetric uncertainties, these are symmetrised for the calculation of the log likelihood ratio.
Let nS be the number of observed events in the signal region,b the background expectation, θ the nuisance parameters for the systematic uncertainties and µ the signal strength, which is used to scale the expected number of signal events in a provided signal grid. The likelihood is
then given by
L(nS|µ,b,θ) =P(nS|λS(µ,b,θ))·Psyst(θ0,θ), (6.25) where Psyst is a product of unit Gaussian probability distribution functions, by which the sys-tematic uncertainties are considered. λS is the expected number of events in the signal region, which is a function of the expected number of background and signal events as well as the nuisance parameters θ.
The calculation of p-values and CLs values is performed using the ATLASHistFitter pack-age, which is heavily based on the RooStats framework [179]. A FrequentistCalculator is used to run pseudo experiments. The number of pseudo experiments that are used varies be-tween 30,000 and 150,000 - the calculation is done in steps of 10,000 toys and continued until the p-value is stable at the permille level for three steps.
Two different fits are considered here. First, to assess the comparability of the SM with the observed number of events in the signal region, the signal strength is set to 0, and the probability value for the SM hypothesis is calculated. In a second step, the signal strength is set to 1, and limits are placed in the defined simplified models for ˜χ02−χ˜03 production.
Compatibility with the Standard Model
The SM provides a good description of the observation in the signal region. The probability to get the observed result, or one that is in worse agreement with the SM is given by p0 = 0.29.
There is no need to extend the SM in order to explain the observation.
Limits in the Simplified Model
For certain parameter combinations in the studied simplified models for ˜χ02 −χ˜03 production the predicted number of events (signal plus background) in the signal region is in significant disagreement with the observation. These models can therefore be excluded with a confidence level of 95%, or higher.
Limits are placed in both generations of the models, and the results are shown in Figures 6.20 and 6.21. The theory uncertainty on the signal prediction is taken into account for the observed limit, while all other uncertainties are considered to calculate the expected limit and the uncertainties on the expected limit.
For a fixed mass differencemχ˜0
3−mχ˜0
1 = 80 GeV andmχ˜0
2−mχ˜0
1 = 75, Higgsino-like interme-diate neutralinos with a mass of mχ˜0
3 .270−340 GeV are excluded, if the masses of the first and second generation right chiral sleptons are not too close to the masses of the neutralinos.
For varying mass differencemχ˜0 3−mχ˜0
1 = 20−80 GeV, Bino-like LSPs with a mass ofmχ˜0 1 . 100−250 GeV are excluded, where for small mass differences the limit on the LSP mass gets worse.
[GeV]
0
χ∼3
200 250 300 350 400 450 500 m550 600
[GeV] Rl~ - m0 3χ∼m
20 30 40 50 60
70
ATLAS
Internal=8 TeV s
-1, L dt = 20.7 fb
∫
theory) σSUSY
±1 Observed limit (
exp) σ
±1 Expected limit ( All limits at 95% CL
Figure 6.20: The observed and expected 95% CL limit contours for the signal modelv2A. The signal cross section uncertainty is taken into account in the observed limit. The yellow band is the ±1σ experimental uncertainty on the expected limit. The red dashed lines are the±1σ signal theory uncertainties on the observed limit. In order to account for the discreteness of points for which MC has been produced, a bilinear interpolation is used to calculate the CLs values for intermediate points.
[GeV]
0
χ∼1
m
100 150 200 250 300 350 400 450 500
[GeV]0 1χ∼ - m0 3χ∼m
20 30 40 50 60 70 80
ATLAS
Internal=8 TeV s
-1, L dt = 20.7 fb
∫
theory) σSUSY
±1 Observed limit (
exp) σ
±1 Expected limit ( All limits at 95% CL
Figure 6.21: The observed and expected 95% CL limit contours for the signal modelv2B. The signal cross section uncertainty is taken into account in the observed limit. The yellow band is the ±1σ experimental uncertainty on the expected limit. The red dashed lines are the±1σ signal theory uncertainties on the observed limit. In order to account for the discreteness of points for which MC has been produced, a bilinear interpolation is used to calculate the CLs values for intermediate points.