Event Shapes in t t and QCD Events @ LHC Using transverse, 3D Event - - PowerPoint PPT Presentation

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Event Shapes in t t and QCD Events @ LHC Using transverse, 3D Event - - PowerPoint PPT Presentation

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Event Shapes in t t and QCD Events @ LHC Event Shapes in t t and QCD Events @ LHC Using transverse, 3D Event Shapes in Multivariate Analysis Martin H artig Werner Heisenberg Institut Universit at W urzburg November 9, 2009 Event

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Event Shapes in t¯ t and QCD Events @ LHC

Event Shapes in t¯ t and QCD Events @ LHC

Using transverse, 3D Event Shapes in Multivariate Analysis Martin H¨ artig

Werner Heisenberg Institut Universit¨ at W¨ urzburg

November 9, 2009

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Event Shapes in t¯ t and QCD Events @ LHC Introduction ROOT TMVA

Multivariate Analysis with ROOT TMVA

Multivariate Analysis (MVA) Using multiple input variables (for example) to discriminate signal from background Usually performed on kinematic observables (p⊥ of jets, ...) Here: Different kinds of Event Shapes ROOT TMVA Toolkit for Multivariate Data Analysis with ROOT ROOT’s MVA facility Automates variable decorrelation, includes several methods of MVA: Fisher, Likelihood, BDT, ANN, ...

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Event Shapes in t¯ t and QCD Events @ LHC Introduction ROOT TMVA

The Event Shapes

Event Shapes used: Thrust, Thrust Minor Y Flip Values (3D only) Fox Wolfram Moments Jet Masses Jet Broadening C-Parameter Transverse Sphericity (2D) SumPt (2D only) All Event Shapes calculated in a central region, |η| < 2.5 3D vs. Transverse Most Event Shapes are available in a transverse/3D definition. Does the z component add to the discrimination power? → Try out by doing a MVA with transverse/3D Event Shapes

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SLIDE 4

Event Shapes in t¯ t and QCD Events @ LHC Introduction ROOT TMVA

In this study

Samples 84,855 events t¯ t full hadronic (signal) 266,499 events QCD J2-J5 (background) Training with 5k signal, 5k background (random selection) Methods Fisher Discriminant Likelihood (with/without variable decorrelation, PCA) Cuts Event preselection: No Cuts, Medium Cuts (Jet-p⊥: 2 · 40 GeV/c, 4 · 20 GeV/c), Hard Cuts (Jet-p⊥: 4 · 40 GeV/c, 2 · 20 GeV/c)

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SLIDE 5

Event Shapes in t¯ t and QCD Events @ LHC Results Without Cuts

Results: Without Cuts

MVA_Likelihood_rejBvsS

Entries 100 Mean 0.4808 RMS 0.2793

signal eff 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 backgr rejection (1-eff) 0.2 0.4 0.6 0.8 1

MVA_Likelihood_rejBvsS

Entries 100 Mean 0.4808 RMS 0.2793

Likelihood LikelihoodD LikelihoodPCA Fisher

ROC Curve

Figure: ROC Curve of Transverse Event Shapes

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SLIDE 6

Event Shapes in t¯ t and QCD Events @ LHC Results Without Cuts

Results: Without Cuts

MVA_Likelihood_rejBvsS

Entries 100 Mean 0.4855 RMS 0.2816

signal eff 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 backgr rejection (1-eff) 0.2 0.4 0.6 0.8 1

MVA_Likelihood_rejBvsS

Entries 100 Mean 0.4855 RMS 0.2816

Likelihood LikelihoodD LikelihoodPCA Fisher

ROC Curve

Figure: ROC of 3D Event Shapes

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SLIDE 7

Event Shapes in t¯ t and QCD Events @ LHC Results Without Cuts

Results: No Cuts

2D 3D Method Area ηS@ηB=10% Area ηS@ηB=10% Fisher 0.973 0.947 0.974 0.950 Likelihood 0.936 0.875 0.943 0.887 Likelihood - PCA 0.946 0.862 0.924 0.802 Likelihood - D 0.877 0.703 0.879 0.758 → almost no difference between 2D/3D Cave! This is not signal/background, but the signal and background efficiency! You still have to factor in the much higher background rate!

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Event Shapes in t¯ t and QCD Events @ LHC Results Medium Cuts

Results: Medium Cuts (2x40, 4x20)

MVA_Likelihood_rejBvsS

Entries 100 Mean 0.3955 RMS 0.2526 signal eff 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 backgr rejection (1-eff) 0.2 0.4 0.6 0.8 1

MVA_Likelihood_rejBvsS

Entries 100 Mean 0.3955 RMS 0.2526

Likelihood LikelihoodD LikelihoodPCA Fisher

ROC Curve

Figure: ROC of Transverse Event Shapes

MVA_Likelihood_rejBvsS

Entries 100 Mean 0.4103 RMS 0.2576 signal eff 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 backgr rejection (1-eff) 0.2 0.4 0.6 0.8 1

MVA_Likelihood_rejBvsS

Entries 100 Mean 0.4103 RMS 0.2576

Likelihood LikelihoodD LikelihoodPCA Fisher

ROC Curve

Figure: ROC of 3D Event Shapes

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Event Shapes in t¯ t and QCD Events @ LHC Results Medium Cuts

Results: Medium Cuts (2x40, 4x20)

2D 3D Method Area ηS@ηB=10% Area ηS@ηB=10% Fisher 0.738 0.357 0.781 0.427 Likelihood 0.689 0.261 0.743 0.353 Likelihood - PCA 0.639 0.222 0.706 0.292 Likelihood - D 0.594 0.187 0.696 0.303 → Further growing difference between Transverse/3D MVA

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SLIDE 10

Event Shapes in t¯ t and QCD Events @ LHC Results Hard Cuts

Results: Hard Cuts (4x40, 2x20)

MVA_Likelihood_rejBvsS

Entries 100 Mean 0.3659 RMS 0.2463 signal eff 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 backgr rejection (1-eff) 0.2 0.4 0.6 0.8 1

MVA_Likelihood_rejBvsS

Entries 100 Mean 0.3659 RMS 0.2463

Likelihood LikelihoodD LikelihoodPCA Fisher

ROC Curve

Figure: ROC of Transverse Event Shapes

MVA_Likelihood_rejBvsS

Entries 100 Mean 0.3905 RMS 0.2497 signal eff 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 backgr rejection (1-eff) 0.2 0.4 0.6 0.8 1

MVA_Likelihood_rejBvsS

Entries 100 Mean 0.3905 RMS 0.2497

Likelihood LikelihoodD LikelihoodPCA Fisher

ROC Curve

Figure: ROC of 3D Event Shapes

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SLIDE 11

Event Shapes in t¯ t and QCD Events @ LHC Results Hard Cuts

Results: Hard Cuts (4x40, 2x20)

2D 3D Method Area ηS@ηB=10% Area ηS@ηB=10% Fisher 0.678 0.266 0.741 0.356 Likelihood 0.592 0.165 0.689 0.288 Likelihood - PCA 0.615 0.179 0.678 0.254 Likelihood - D 0.602 0.182 0.668 0.248 → Considerable difference between Transverse/3D MVA

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Event Shapes in t¯ t and QCD Events @ LHC Outlook

Variable Ranking for Fisher

2D No Cut Medium Cut Hard Cut 1. y34 y56 y56 2. y45 y45 y45 3. y56 y34

  • Transv. Sphericity

4. SumPt25 SumPt25 H30 5. y23

  • Transv. Sphericity

H20 3D No Cut Medium Cut Hard Cut 1. y34 y56 H20 2. y45 y45 y56 3. y56 y34 Heavy Jet Mass 4. SumPt25 Heavy Jet Mass C-Parameter 5. y23 C-Parameter y45 Y Flip Values important in almost every configuration But: Always calculated in 3D → strong bias in transverse MVA?

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Event Shapes in t¯ t and QCD Events @ LHC Conclusion

Conclusion

TMVA works well with Event Shapes, leading to background rejection of ∼ 80% at signal efficiency of ∼ 50% Need more information concerning Trigger/Preselection Cuts 3D Event Shapes, though theoretically more challenging, perform better than the transverse versions Y Flip Values proved to be important Event Shape, but may bias the transverse performance (only implemented in 3D) Plan to implement this MVA in an easy to use module

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SLIDE 14

Event Shapes in t¯ t and QCD Events @ LHC Conclusion

Correlation Matrix

100 96 -29 -22 -16 -10 28 6

  • 15 -11 82

76

  • 41 27 -19

96 100 -25 -19 -14

  • 8

19 4

  • 14
  • 8

84 81 -36 25

  • 16
  • 29 -25 100 70

52 43 1 24 23 32 -23 -22

  • 7
  • 44 84
  • 22 -19 70 100 74

58

  • 2

9 11 12 -19 -18

  • 10

79

  • 16 -14 52

74 100 75

  • 5

1 1

  • 14 -13

3 73

  • 10
  • 8

43 58 75 100 -8

  • 2
  • 5
  • 7
  • 8
  • 8

4 3 68 28 19 1

  • 2
  • 5
  • 8 100

9 28 8 2

  • 2
  • 23
  • 5
  • 7

6 4 24 9 1

  • 2

9 100 -1 23 17 4

  • 75 -37

13

  • 15 -14 23

11 1

  • 5

28

  • 1 100 18 -19 -20
  • 21

7

  • 11 -8

32 12

  • 7

8 23 18 100 -3

  • 7
  • 29 -37

12 82 84 -23 -19 -14

  • 8

2 17 -19

  • 3

100 91 -49 17

  • 11

76 81 -22 -18 -13

  • 8
  • 2

4

  • 20
  • 7

91 100 -30 19

  • 11
  • 41 -36
  • 7

3 4

  • 23 -75
  • 29 -49 -30 100 15
  • 2

27 25 -44 -10 3

  • 5
  • 37 -21 -37

17 19 15 100 -30

  • 19 -16 84

79 73 68

  • 7

13 7 12

  • 11 -11 -2
  • 30 100

log(RecoTauEta25) log(RecoThrustMinorEta25) log(RecoFlipY23Eta25) log(RecoFlipY34Eta25) log(RecoFlipY45Eta25) log(RecoFlipY56Eta25) log(RecoFoxWolframH10Eta25) log(RecoFoxWolframH20Eta25) log(RecoFoxWolframH30Eta25) log(RecoFoxWolframH40Eta25) log(RecoHeavyJetMassEta25) log(RecoWideBroadeningEta25) log(RecoCParameterEta25) log(RecoTransverseSphericityEta25) log(SumPt25) log(RecoTauEta25) log(RecoThrustMinorEta25) log(RecoFlipY23Eta25) log(RecoFlipY34Eta25) log(RecoFlipY45Eta25) log(RecoFlipY56Eta25) log(RecoFoxWolframH10Eta25) log(RecoFoxWolframH20Eta25) log(RecoFoxWolframH30Eta25) log(RecoFoxWolframH40Eta25) log(RecoHeavyJetMassEta25) log(RecoWideBroadeningEta25) log(RecoCParameterEta25) log(RecoTransverseSphericityEta25) log(SumPt25)

Correlation Matrix (signal)