5.3 Optimization studies
5.3.2 Data-driven background estimation
In Figure 5.4(b) we observed that the shape of themb¯b distribution regarding thet¯t+jets process does not change when the number of requested b-tags is two, thee or four. Initially, this allows us to use the shape of themb¯b distribution where #btagged jets=2, scaling it to the number of events that the condition #btagged jets=4 yields. This will lead to a smoother background shape, with smaller statistical fluctuations, resulting to a more accurate signal over background significance estimation.
Apart from increasing the statistics of the MC background sample, this observation can give
Figure 5.6: Superimposed mb¯b distributions of the t¯t+jets process when considering two (magenta) and four (black) jets to be b-tagged. The distributions are normalized to area.
Figure 5.7: Ratio of themb¯bdistribution when considering two b-tags over the corresponding distribution when considering four b-tags for the t¯t+jetsprocess.
exactly 2 b-tags, we are able to form a control region, which is signal depleted and has large statistics. We previously showed that the shape of thet¯t+jetsbackground does not depend
on the number of b-tags. So, we will use this sample to predict the background shape of the t¯t+jets process when requesting four b-tagged jets. The normalization factor can be taken from the MC studies, but can also be extrapolated from the data, using the Tagging Rate Function (TRF) [35] in order to have a completely data-driven approach.
5.4 Final mass reconstruction
5.4.1 Estimated significance of t tH, H ¯ → b ¯ b dilepton channel
For the final Higgs mass reconstruction, we apply to the signal and background samples the event pre-selection discussed in section 5.2. The signal shape of the t¯tH, H →b¯b process corresponds to the shape of the four b-tag requirement, whereas the shape of the t¯t+jets background is extrapolated from the two b-tag condition, scaled to the number of events expected when requesting four b-tags. The scaling factor of the→b¯bbackground from two to four b-tags is taken from the MC studies and corresponds to 0.0044. The MC weights are calculated for a luminosity of 200f b−1.Finally, the significance is defined as:
Signif icance= s
X
bins
S2
Bkg (5.2)
where S corresponds to the number of signal events in the particular bin whileBkg corre- sponds to the number of background events in the same bin.
Figure 5.8: Signal (t¯tH, H →b¯b) + background (tt¯+jets)mb¯b distribution (blue) super- imposed with the t¯t+jetsbackground mb¯b distribution (magenta). The distributions are
−1
(a) (b)
Figure 5.9: Left: Signal (black) mb¯b distribution requiring exactly four b-tagged jets and background (magenta) mb¯b distribution shape when requesting exactly two b-tagged jets scaled to the number of events expected when requesting exactly four b-tagged jets, su- perimposed and normalized to area. Right: Ratio of the signal+background over scaled background distribution.
In Figure 5.9(b) the denominator of the ratio is multiplied by a scaling factor, a=0.0044.
As a result, the error bars are calculated according to the following equation:
Ratio= S+a×Bkg
a×Bkg (5.3)
dRatio= s
dS a×Bkg
2 +
S×dBkg a×Bkg2
2
(5.4) wheredS anddBkgare the statistical bin errors of the signal and background distributions respectively.
Finally, it is reasonable to calculate the significance in the close proximity of the peak. We choose the mb¯b window of [0,300] GeV with a 10 GeV bin size. This selection yields the below significance:
Signif icance ∼ 1.5standard deviations (5.5)
5.4.2 Kinematic variables
Apart from the mb¯b distribution, there is a variety of other kinematic variables that can be studied regarding the signal (t¯tH, H →b¯b) and background (tt¯+jets) processes. Due to the different topologies as well as final state particles of these two processes, we expect a majority of kinematic variable distributions to be as well different. In the following section we examine different variable distributions, in order to observe if there is any additional discriminating power between the signal and the dominant background, apart from themb¯b
distribution. This could give us the opportunity to create a maximum likelihood function,
using a number of discriminant variables having as a main goal to reduce the background enhance the signal and finally increase the overall significance.
(a)DR between the two b-jets that are assigned from the method to the Higgs mass reconstruction.
(b) DR between the b-jet and corresponding lepton (of the same t decay branch) that are assigned by the method to ei- ther branch of the ¯tsystem re- construction.
(c)DRbetween the lepton and corresponding neutrino (of the same W decay branch) that are assigned by the method to ei- ther branch of the ¯tsystem re- construction.
Figure 5.10: DR=p
Dφ2+Dη2 between the different objects that the analytical solution method yields when choosing the maximum weight solution per event, for the signal (black) and background (magenta) distributions, superimposed and normalized to area in order to observe any shape differences.
(a) Dφ between the two b-jets that are assigned from the method to the Higgs mass reconstruction.
(b) Dφ between the b-jet and corresponding lepton (of the same t decay branch) that are assigned by the method to ei- ther branch of the ¯tsystem re- construction.
(c)Dφ between the lepton and corresponding neutrino (of the same W decay branch) that are assigned by the method to ei- ther branch of the ¯tsystem re- construction.
Figure 5.11: Dφ between the different objects that the analytical solution method yields when choosing the maximum weight solution per event, for the signal (black) and background (magenta) distributions, superimposed and normalized to area in order to observe any shape differences.
to the neutrino four vectors do not, due to the large ambiguity that the measurement of the missing energy has. Furthermore, apart from themHiggs, there are differences between the signal and background processes for themt¯tandmt¯tH distributions as well. Finally, in Figure 5.15(c) the distributions of the quantity log10(x1x2) are as well different, fact that we expected due to the different final states of the signal and background processes.
(a) (b)
Figure 5.12: The mt¯t distribution (left) and the mt¯tH distribution (right) for the signal (black) and background (magenta) processes, superimposed and normalized to area in order to observe any shape differences.
(a) (b)
Figure 5.13: Two dimensional contour of mb¯b versus mttH¯ for the signal (left) and back- ground (right) processes.
(a)M ET distribution of the signal (black) and background (magenta).
(b)pT asymmetry distribution of the signal (black) and background (magenta).
Figure 5.14: M ET = q
M ETx2+M ETy2 (left) and pT assymetry = ppT1−pT2
T1+pT2 (right) distri- butions.
(a) Distribution of momentum fractionx1for the signal (black) and background (magenta).
(b) Distribution of momentum fractionx2for the signal (black) and background (magenta).
(c) Distribution of the quan- tity log10(x1x2) for the signal (black) and background (ma- genta).
Figure 5.15
6 Data and Simulation comparison
For the final chapter of this thesis, it is essential to study the methods performance using Data as well as compare the Data distributions with the corresponding ones resulting from the simulation.
6.1 Event yields and Higgs mass distribution
The data samples used for the analysis, which correspond to 35.9f b−1 luminosity are listed in Table 6.1. We apply the same event selection with the MC samples, described in section 5.2. For consistency, the weights are evaluated using the same LHAPDF version (6.1.2) and PDF set (CT10). The energy scale as well as themtopandmW limits are set to have the same value as in the simulation (Q = 235 GeV and mtop ∈[150,200]GeV, mW ∈[60,100]GeV with a 5GeV step).
Data SamplesLuminosity= 35.9f b−1 SingleElectronRun2016B Rereco v3 SingleElectronRun2016C Rereco v1 SingleElectronRun2016D Rereco v1 SingleElectronRun2016E Rereco v1 SingleElectronRun2016F Rereco v1 SingleElectronRun2016G Rereco v1 SingleElectronRun2016H Prompt v2 SingleElectronRun2016H Prompt v3 SingleMuonRun2016B Rereco v3 SingleMuonRun2016C Rereco v1 SingleMuonRun2016D Rereco v1 SingleMuonRun2016E Rereco v1 SingleMuonRun2016F Rereco v1 SingleMuonRun2016G Rereco v1 SingleMuonRun2016H Prompt v2 SingleMuonRun2016H Prompt v3
Table 6.1: Data samples used in the analysis.
The ratio of the absolute number of data events over the number of MC events scaled to the Data luminosity is called k-factor, and is calculated as follows:
k=#Data events
#M C events (6.1)
Here the k-factor is the ratio of the first over the third column of Table 6.2, and as a result is equal to k =1.2 As a cross-check of the resulting k-factor, it is interesting to compare against the HIG-16-038 analysis. In Table 6.3, we can observe that the resulting k-factor agrees with the one of our analysis, having only a∼3% difference.
Absolute number of Data events after
pre-selection
MC - Total Signal+ Background
MC total events scaled up by 15%
308 223 257
Table 6.2: Data and MC event yields. The first column correspond to the absolute number of events that pass the event selection (L= 35.9f b−1), the second column corresponds to the number of MC events that pass the event selection scaled to the data luminosity and the third column correspods to the second column scaled up by 15%, the nessesity of which was discussed in section 5.2.1.
Absolute number of Data events after
pre-selection
MC - Total Signal+ Background
k-factor of HIG-16-038 analysis
144 117 1.23
Table 6.3: Data and MC events yields of the HIG-16-038 analysis. The first column corre- spond to the absolute number of events that pass the event selection (L= 12.9f b−1), the second column corresponds to the number of MC events that pass the event selection scaled to the data luminosity and the third column, which is the ratio of the first two, corresponds to the k-factor of the HIG-16-038 analysis.
Figure 6.1: Datamb¯b distribution corresponding toL= 35.9f b−1.
Data and simulation distributions are shown superimposed. In Figure 6.3(b), we expect the ratio to be flat and∼1. The fluctuations are a result of low statistics of the Data sample, which after the event selection had an event yield of ∼300 events.
Figure 6.2: mb¯b distribution of the Data with black points, superimposed with the corre- sponding MC distribution (red line) scaled to the Data luminosity, L= 35.9f b−1.
(a) (b)
Figure 6.3: In the left figure, we can observe the mb¯b distribution of the Data with black points, superimposed with the corresponding MC distribution (red line) scaled to the Data luminosity, L= 35.9f b−1, where the x-axis has been zoomed in. In the right figure, we can observe the ratio of the Data over the MC events.
6.2 Kinematic variables distributions
(a)DR between the two b-jets that are assigned from the method to the Higgs mass reconstruction.
(b) DR between the b-jet and corresponding lepton (of the same t decay branch) that are assigned by the method to ei- ther branch of the ¯tsystem re- construction.
(c)DRbetween the lepton and corresponding neutrino (of the same W decay branch) that are assigned by the method to ei- ther branch of the ¯tsystem re- construction.
Figure 6.4: DR=p
Dφ2+Dη2 between the different objects that the analytical solution method yields when choosing the maximum weight solution per event. The black points correspond to the data, while the red distribution corresponds to the MC.
(a) Dφ between the two b-jets that are assigned from the method to the Higgs mass reconstruction.
(b) Dφ between the b-jet and corresponding lepton (of the same t decay branch) that are assigned by the method to ei- ther branch of the ¯tsystem re- construction.
(c)Dφ between the lepton and corresponding neutrino (of the same W decay branch) that are assigned by the method to ei- ther branch of the ¯tsystem re- construction.
Figure 6.5: Dφ between the different objects that the analytical solution method yields when choosing the maximum weight solution per event. The black points correspond to the data, while the red distribution corresponds to the MC.
(a) (b)
Figure 6.6: Themt¯tdistribution (left) and themttH¯ distribution (right) for the data (black points) and MC (red), superimposed and normalized the number of events.
(a) M ET distribution of the data (black points) and MC (red).
(b) pT asymmetry distribution of the data (black points) and MC (red).
Figure 6.7: M ET = q
M ETx2+M ETy2(left) andpT assymetry=ppT1−pT2
T1+pT2
(right) distribu- tions.
(a) Distribution of momentum fraction x1 for the data (black points) and MC (red).
(b) Distribution of momentum fraction x2 for the data (black points) and MC (red).
(c) Distribution of the quantity log10(x1x2) for the data (black points) and MC (red).
Figure 6.8
7 Outlook
In the current thesis, a study of the ttH, H¯ →b¯b process was performed, using a model independent method which was able to reconstruct the Higgs boson mass by scanning the 2D mass plane and calculating the most probable - to originate from a pp collision- point in the 2D mass plane, with the help of the pp PDF functions. The study of associated production of a Higgs boson and a t¯t pair is essential, due to the fact that it is a direct probe of the measurement of the top-Higgs Yukawa coupling. Furthermore, the Higgs boson decay into a b¯b pair is attractive as a final state because it features the largest branching fraction of 0.58±0.02 for a 125 GeV Higgs boson, which has not yet been observed.
By solving analytically the system of equations that describe thet¯tdileptonic decay, we are able to reconstruct Higgs bosons mass int¯tH, H→b¯bevents. The methods performance is model independent and does not depend on the choice of a particular PDF set. The meth- ods performance is tested using generator lever events. We observe that the performance improves, when constraining the values ofmtop andmW, within their proposed resolution.
Approximately ∼45% of the events are correctly reconstructed, with respect to the Higgs mass. Furthermore, we also test the performance of the method using CMS reconstructed events. After a quick sanity check against HIG-16-038, we derive an optimised pre-selection for our model and conclude that the main background contribution comes from t¯t+jets events. The estimated significance is s = 1.5.
Future studies that will be performed in order to increase the significance is the use of a multi-variate technique, which will have as inputs a majority of the kinematic variables included in this thesis, and will take advantage of the shape differences between the signal and background distributions. As a result, it will create a discriminator, which will allow us to separate signal over background events even better. Also, a data driven estimation of the background shape as well as scale factor will be performed, using the Tagging Rate Function (TRF).
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