1. 10th China HEPS Particle Physics Meeting
Measurement of Single Top Quark s-channel Cross Section at the ATLAS Experiment
10th China HEPS Particle Physics Meeting
Jie Yu
Nanjing University

2. 10th China HEP Particle Physics meeting / Nanjing
Outlines
Introduction
S-channel cut analysis and results
Multivariate analysis and results
Summary
11/11/2018
10th China HEP Particle Physics meeting / Nanjing

3. 10th China HEP Particle Physics meeting / Nanjing
Introduction
The reasons of doing single-top analysis:
a key particle in the quest for the origin of particle mass.
EW interaction of the top quark is sensitive to many types of new physics.
the only known way to directly measure CKM matrix element Vtb
an important background to many searches for new physics ……
11/11/2018
10th China HEP Particle Physics meeting / Nanjing

4. three different single top mechanisms in Standard Model:
Figue1. (a) t-channel (b) W+t channel (c) s-channel
q2 ≤ 0, q2 = M2W, q2 ≥ (mt + mb)2.
Where q is the four momentum of W boson
time
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10th China HEP Particle Physics meeting / Nanjing

5. 10th China HEP Particle Physics meeting / Nanjing
The main backgrounds
ttbar events
ttbar l+jets mode
ttbar2l+jets mode (with one lepton lost)
W/Z + jets
di-boson ( like: WWlvjj )
QCD background ( like: ppbbbar)
For the lack of MC data, we are only using ttbar background till now!
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10th China HEP Particle Physics meeting / Nanjing

6. 10th China HEP Particle Physics meeting / Nanjing
Process cross section and decay mode (1)
process: t-channel s-channel Wt channel ttbar
σ(pb): ± ± ±
Decay mode and probability:
tWb ~100%
Wl v ~2/9 ( l = electron or muon)
Wτv ~1/9 (τ decays into muon 17.8%, electron 17.2%)
Wjj ~6/9
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10th China HEP Particle Physics meeting / Nanjing

7. 10th China HEP Particle Physics meeting / Nanjing
Process cross section and decay mode (2)
t-channel: ppWgtb¯qWbb¯ql v b b¯q
Wt channel: pptW  WWb j j l v b
S-channel: ppW*tb¯Wbb¯ l v b b¯
Final state of the three single top channels :
2 or 3 jets, 1 or 2 b jet, 1 lepton, with missing energy
Preslection cuts
Final state of the signal s-channel :
2 b jets, 1 lepton, with missing energy
s-channel selection cuts
Final state of ttbar events:
ttbar: ppttbar  W+ b W- b ¯  l v b j j b ¯
 l+ v l- v¯bb¯
τ+ τ - v v ¯ b b¯
τv b j j b ¯
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10th China HEP Particle Physics meeting / Nanjing

8. 10th China HEP Particle Physics meeting / Nanjing
Preselection cuts:
Selection for three single top channels
Step0: Triggers , Passed e25i or e60 or mu20i
Step1: One high Pt lepton at least, with electron pt larger than
25GeV/c muon 20GeV/c
Step2: Veto of any 2nd lepton with pt larger than 10GeV/c ΔR>0.4
Step3: at least 2 high pt jets, pt larger than 30GeV/c
Step4: Veto on the 5th jet with pT(jet)>15GeV/c
Step5: At least 1 btagged high pt jet above 30GeV/c η less than 2.5
Step6: Missing Energy no less than 20GeV
11/11/2018
10th China HEP Particle Physics meeting / Nanjing

9. 10th China HEP Particle Physics meeting / Nanjing
Strategy(1): s-channel selection cuts
Step1: two b-tagged jets with pT>30GeV/c
Step2: Veto on any 3rd Jet with pT>15GeV/c
Step3: Total Ht (pT combined jets only): 80<Ht<220 GeV/c
Step4: Seperation between 2 btagged jets:
0.5 <ΔR(b1,b2) < 4.0 ;
Step5: Sum of missing Et and pT of leptons:
60 <mEt+pT(e,u) < 130 GeV/c;
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10th China HEP Particle Physics meeting / Nanjing

10. 10th China HEP Particle Physics meeting / Nanjing
Total Ht
mEt+pT(e,u)
We may find out the separation of the variables is not that distinct
Discriminant variables distributions corresponding to an integrated luminosity of 1 fb-1
11/11/2018
10th China HEP Particle Physics meeting / Nanjing

11. The s-ch cut analysis results
Processes muon channel electron channel nEvt to L= 1 fb-1
s-channel ±0.12% ±0.10%
s-ch (τ)l ±0.16% ±0.15%
t-channel ±0.04% ±0.03%
t-chan (τ)l ±0.04% ±0.00%
W+t channel ±0.03% ±0.03%
W+t chan (τ)l ±0.00% ±0.00%
ttl+jets ±0.01% ±0.01%
tt(τ)l+j ±0.01% ±0.01%
tte + e ±0.05%
ttμ+μ ±0.06%
ttμ+ e ±0.04%
ttμ+τ ±0.05%
tt e +τ ±0.05%
ttτ+τ ±0.04%
S/B = 46/741 = 6.2%, S/ √ S+B = 1.64
Not good enough
Search for improvement
11/11/2018
10th China HEP Particle Physics meeting / Nanjing

12. 10th China HEP Particle Physics meeting / Nanjing
Strategy (2): MultiVariate Analysis
MVA uses multi-variables as input and get an output which in the most of the cases obtain better separation
Step1: two b-tagged jets with pT>30GeV/c
Step2: Veto on any 3rd Jet with pT>15GeV/c
Using MVA
Events selected by steps above the line will be used as MVA input
11/11/2018
10th China HEP Particle Physics meeting / Nanjing

13. MultiVariate data Analysis
Methods in MVA
Rectangular cut optimisation
Likelihood estimator (PDE approach)
Multidimensional likelihood estimator (PDE Range Search approach)
Fisher discriminant
HMatrix approach (2 estimator)
Multilayer Perceptron Artificial Neural Network (three different implementations)
Boosted Decision Trees
RuleFit …
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10th China HEP Particle Physics meeting / Nanjing

14. No Single Best    / Methods Criteria Performance Training Speed
Cuts
Likelihood
PDERS/ kNN
HMatri
Fisher
MLP
BDT
RuleFit
SVM
Performance
no / linear correlations  
nonlinear correlations 
Speed
Training
Response
/
Robustness
Overtraining
Weak input variables
Curse of dimensionality
Clarity
No Single Best
11/11/2018
10th China HEP Particle Physics meeting / Nanjing

15. Projected Likelihood Estimator (PDE Approach)
Combine probability density distributions to likelihood estimator
Reference PDF’s
Output is a likelihood ratio
is an output of Likelihood for every single event,
1 (signal like) , 0 ( background like)
Assumes uncorrelated input variables
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10th China HEP Particle Physics meeting / Nanjing

16. MVA methods output variables ( take Likelihood as an example )
five main background processes
ttbarlepton+jet,
ttbardilepton,
ttbarτ+lepton,
W+jets,
t−channel
define likelihood functions specific to suppress each background:
yttbar/lepton+jets,
yttbar/dilepton,
yttbar/τ+lepton,
yW+jets,
yt−channel
Every event has such five MVA output value , and then we shall apply proper cuts on them
11/11/2018
10th China HEP Particle Physics meeting / Nanjing

17. 10th China HEP Particle Physics meeting / Nanjing
Note: each yLh(i ) use some of the variables as input
Variables yttbar/lepton+jets, yttbar/dilepton, yttbar/τ+lepton,yW+jets, yt−channel
11/11/2018
10th China HEP Particle Physics meeting / Nanjing

18. Cut value for each method:
MVA method to suppress the Bkg: tt->l+jets,tt->l+l,tt->l+tau,W+jets,t-ch
--- Factory :
--- Factory : Method: Cut value:Cut value:Cut value:Cut value:Cut value:
--- Factory :
--- Factory : Likelihood:
--- Factory : LikelihoodD:
--- Factory : LikelihoodPCA:
--- Factory : HMatrix:
--- Factory : Fisher:
--- Factory : MLP:
--- Factory : CFMlpANN:
--- Factory : TMlpANN:
--- Factory : BDT:
--- Factory : BDTD:
--- Factory : RuleFit:
--- Factory : which correspond to the working point: eff(signal) = 1 - eff(background)
11/11/2018
10th China HEP Particle Physics meeting / Nanjing

19. Cut on no stack histgrams of TMlpANN method
Cut here
Signal events tend to be more likely in the right side of the figure
11/11/2018
10th China HEP Particle Physics meeting / Nanjing

20. 10th China HEP Particle Physics meeting / Nanjing
s-ch Vs ttl+jets
Cut on stacked histgrams of BDT method
s-ch Vs ttdi-lep
11/11/2018
10th China HEP Particle Physics meeting / Nanjing

21. 10th China HEP Particle Physics meeting / Nanjing
MVA output cut results (1)
channel\classifiers
Likelihood
LikelihoodD
LikelihoodPCA
HMatrix
Fisher
sch-cut
s-channel
44.7
40.1
39.4
41.2
35.8 46
t-channel
52.4
36.5
28.6
30.2
41.3 84
W+t channel
9.4
5.0
7.2
10.5 11
tt-->l+jets
174.7
114.7
112.3
93.6
137.3
223
tt-->di-lep
92.0
67.1
67.9
55.4
62.4
150
tt-->l+tau
198.1
141.2
135.7
119.3
129.5
273
all BKG
526.6
364.5
351.7
307.9
381.0
741
S/B
8.5%
11.0%
11.2%
13.4%
9.4%
6.2%
S/sqrt(S+B)
1.87
1.99
2.21
1.75
1.64
see:MVA do bring some improvement
Number of events are normalized to L=1fb-1
11/11/2018
10th China HEP Particle Physics meeting / Nanjing

22. 10th China HEP Particle Physics meeting / Nanjing
MVA output cut results (2)
channel\classifiers
BDT
BDTD
MLP
CFMlpANN
TMlpANN
RuleFit
sch-cut
s-channel
50.3
46.0
36.0
3.7
40.0
35.0 46
t-channel
39.7
15.9
19.0
9.5
17.0
31.7 84
W+t channel
6.1
6.6
4.4
3.3
8.2 11
tt-->l+jets
88.9
64.7
70.2
15.6
45.2
104.5
223
tt-->di-lep
48.4
29.6
35.1
5.5
23.4
150
tt-->l+tau
75.7
74.1
60.1
97.5
273
all BKG
287.6
192.5
205.0
58.4
149.0
290.3
741
S/B
17.5%
23.9%
17.6%
6.3%
26.8%
12.1%
6.2%
S/sqrt(S+B)
2.74
2.98
2.32
0.47
2.91
1.94
1.64
Number of events are normalized to L=1fb-1
11/11/2018
10th China HEP Particle Physics meeting / Nanjing

23. TMVA cut efficiency for signal and background
channel\classifiers
Likelihood
LikelihoodD
LikelihoodPCA
HMatrix
Fisher
sch-cut
signal efficiency
1.74%
1.56%
1.53%
1.60%
1.39%
1.79%
t-chan efficiency
0.10%
0.07%
0.05%
0.06%
0.08%
0.16%
W-tchan efficiency
0.03%
tt-->l+jets efficiency
0.04%
tt-->di-lep efficiency
0.23%
0.17%
0.14%
0.15%
0.37%
tt-->l+tau efficiency
0.39%
0.28%
0.27%
0.24%
0.26%
0.54%
channel\classifiers
BDT
BDTD
MLP
CFMlpANN
TMlpANN
RuleFit
signal efficiency
1.95%
1.79%
1.40%
0.14%
1.55%
1.36%
t-chan efficiency
0.08%
0.03%
0.04%
0.02%
0.06%
W-tchan efficiency
0.05%
tt-->l+jets efficiency
0.01%
tt-->di-lep efficiency
0.12%
0.07%
0.09%
tt-->l+tau efficiency
0.21%
0.15%
0.19%
11/11/2018
10th China HEP Particle Physics meeting / Nanjing

24. Combine two or more MVA methods
--- Factory : Inter-MVA overlap matrix (signal):
--- Factory :
--- Factory : Likelihood LikelihoodD LikePCA HMatrix Fisher MLP CFMlpANN TMlpANN BDT BDTD RuleFit
--- Factory : Likelihood:
--- Factory : LikelihoodD:
--- Factory : LikelihoodPCA:
--- Factory : HMatrix:
--- Factory : Fisher:
--- Factory : MLP:
--- Factory : CFMlpANN:
--- Factory : TMlpANN:
--- Factory : BDT:
--- Factory : BDTD:
--- Factory : RuleFit:
If two classifiers have similar performance, but significant non-overlapping classifications  check if they can be combined
The combining job is kind of trivial: do cuts on different classifier output!
11/11/2018
10th China HEP Particle Physics meeting / Nanjing

25. 10th China HEP Particle Physics meeting / Nanjing
Summary
It is no doubt that top quark analysis can lead us to some new physics
MVA methods can positively improve the cut efficiency in our analysis
Now that real data is in the air, we couldn’t be too prepared
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10th China HEP Particle Physics meeting / Nanjing

26. 10th China HEP Particle Physics meeting / Nanjing
Thank you ! !
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10th China HEP Particle Physics meeting / Nanjing

27. 10th China HEP Particle Physics meeting / Nanjing
Backup slides
11/11/2018
10th China HEP Particle Physics meeting / Nanjing

28. Fisher Linear Discriminant Analysis (LDA)
Well known, simple and elegant classifier
LDA determines axis in the input variable hyperspace such that a projection of events onto this axis pushes signal and background as far away from each other as possible
Classifier computation couldn’t be simpler:
“Fisher coefficients”
F0 centers the sample mean yFi of all NS + NB events at zero
Fisher coefficients given by: , where W is sum CS + CB
Fisher requires distinct sample means between signal and background
Optimal classifier for linearly correlated Gaussian-distributed variables
11/11/2018
10th China HEP Particle Physics meeting / Nanjing

29. Nonlinear Analysis: Artificial Neural Networks
Achieve nonlinear classifier response by “activating” output nodes using nonlinear weights
Call nodes “neurons” and arrange them in series: 1 i
. . . N
1 input layer
k hidden layers
1 ouput layer j M1 Mk
2 output classes (signal and background)
Nvar discriminating input variables
(“Activation” function)
with:
Feed-forward Multilayer Perceptron
Weierstrass theorem: can approximate any continuous functions to arbitrary precision with a single hidden layer and an infinite number of neurons
Three different MultiLayer Per-ceptrons available in TMVA
Adjust weights (=training) using “back-propagation”:
For each training event compare received and desired MLP outputs  {0,1}: ε = d – r
Correct weights, depending on ε and a “learning rate” η
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10th China HEP Particle Physics meeting / Nanjing

30. 10th China HEP Particle Physics meeting / Nanjing
Boosted Decision Trees (BDT)
A decision tree is a series of cuts that split sample set into ever smaller sets, leafs are assigned either S or B status
Like this phase space is split into regions classified as signal or background
Each split uses the variable that at this node gives the best separation
Some variables may be used at several node, others may not be used at all
11/11/2018
10th China HEP Particle Physics meeting / Nanjing