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

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 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, ...

Event Shapes in t ¯ t and QCD Events @ LHC Introduction ROOT TMVA The Event Shapes Event Shapes used: Jet Broadening Thrust, Thrust Minor C-Parameter Y Flip Values (3D only) Transverse Sphericity (2D) Fox Wolfram Moments SumPt (2D only) Jet Masses 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

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)

Event Shapes in t ¯ t and QCD Events @ LHC Results Without Cuts Results: Without Cuts ROC Curve MVA_Likelihood_rejBvsS MVA_Likelihood_rejBvsS Entries Entries 100 100 Mean Mean 0.4808 0.4808 backgr rejection (1-eff) 1 RMS RMS 0.2793 0.2793 0.8 0.6 Likelihood LikelihoodD 0.4 LikelihoodPCA 0.2 Fisher 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 signal eff Figure: ROC Curve of Transverse Event Shapes

Event Shapes in t ¯ t and QCD Events @ LHC Results Without Cuts Results: Without Cuts ROC Curve MVA_Likelihood_rejBvsS MVA_Likelihood_rejBvsS Entries Entries 100 100 Mean Mean 0.4855 0.4855 backgr rejection (1-eff) 1 RMS RMS 0.2816 0.2816 0.8 0.6 Likelihood LikelihoodD 0.4 LikelihoodPCA 0.2 Fisher 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 signal eff Figure: ROC of 3D Event Shapes

Event Shapes in t ¯ t and QCD Events @ LHC Results Without Cuts Results: No Cuts 2D 3D Method Area η S @ η B =10% Area η S @ η B =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!

Event Shapes in t ¯ t and QCD Events @ LHC Results Medium Cuts Results: Medium Cuts (2x40, 4x20) ROC Curve MVA_Likelihood_rejBvsS MVA_Likelihood_rejBvsS ROC Curve MVA_Likelihood_rejBvsS MVA_Likelihood_rejBvsS Entries Entries 100 100 Entries Entries 100 100 Mean Mean 0.3955 0.3955 Mean Mean 0.4103 0.4103 backgr rejection (1-eff) backgr rejection (1-eff) 1 1 RMS RMS 0.2526 0.2526 RMS RMS 0.2576 0.2576 0.8 0.8 0.6 0.6 Likelihood Likelihood LikelihoodD LikelihoodD 0.4 0.4 LikelihoodPCA LikelihoodPCA 0.2 0.2 Fisher Fisher 0 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 signal eff signal eff Figure: ROC of Transverse Figure: ROC of 3D Event Shapes Event Shapes

Event Shapes in t ¯ t and QCD Events @ LHC Results Medium Cuts Results: Medium Cuts (2x40, 4x20) 2D 3D Method Area η S @ η B =10% Area η S @ η B =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

Event Shapes in t ¯ t and QCD Events @ LHC Results Hard Cuts Results: Hard Cuts (4x40, 2x20) ROC Curve MVA_Likelihood_rejBvsS MVA_Likelihood_rejBvsS ROC Curve MVA_Likelihood_rejBvsS MVA_Likelihood_rejBvsS Entries Entries 100 100 Entries Entries 100 100 Mean Mean 0.3659 0.3659 Mean Mean 0.3905 0.3905 backgr rejection (1-eff) backgr rejection (1-eff) 1 1 RMS RMS 0.2463 0.2463 RMS RMS 0.2497 0.2497 0.8 0.8 0.6 0.6 Likelihood Likelihood LikelihoodD LikelihoodD 0.4 0.4 LikelihoodPCA LikelihoodPCA 0.2 0.2 Fisher Fisher 0 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 signal eff signal eff Figure: ROC of Transverse Figure: ROC of 3D Event Shapes Event Shapes

Event Shapes in t ¯ t and QCD Events @ LHC Results Hard Cuts Results: Hard Cuts (4x40, 2x20) 2D 3D Method Area η S @ η B =10% Area η S @ η B =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

Event Shapes in t ¯ t and QCD Events @ LHC Outlook Variable Ranking for Fisher 2D No Cut Medium Cut Hard Cut 1. y 34 y 56 y 56 2. y 45 y 45 y 45 3. Transv. Sphericity y 56 y 34 4. SumPt25 SumPt25 H 30 5. Transv. Sphericity y 23 H 20 3D No Cut Medium Cut Hard Cut 1. y 34 y 56 H 20 2. y 45 y 45 y 56 3. Heavy Jet Mass y 56 y 34 4. SumPt25 Heavy Jet Mass C-Parameter 5. C-Parameter y 23 y 45 Y Flip Values important in almost every configuration But: Always calculated in 3D → strong bias in transverse MVA?

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

Event Shapes in t ¯ t and QCD Events @ LHC Conclusion Correlation Matrix Correlation Matrix (signal) log(SumPt25) -19 -16 84 79 73 68 13 -30 100 -7 7 12 -11 -11 -2 log(RecoTransverseSphericityEta25) 27 25 -44 -10 3 -5 -37 -21 -37 17 19 15 100 -30 log(RecoCParameterEta25) -41 -36 3 -23 -75 -29 -49 -30 100 15 -7 4 -2 log(RecoWideBroadeningEta25) 76 81 -22 -18 -13 -8 -20 91 100 -30 19 -2 4 -7 -11 log(RecoHeavyJetMassEta25) 82 84 -23 -19 -14 -8 2 17 -19 -3 100 91 -49 17 -11 log(RecoFoxWolframH40Eta25) -11 -8 32 12 -7 8 23 18 100 -3 -7 -29 -37 12 log(RecoFoxWolframH30Eta25) -15 -14 23 -5 28 -1 100 18 -19 -20 11 1 -21 7 log(RecoFoxWolframH20Eta25) 6 4 24 9 1 -2 9 100 -1 23 17 4 -75 -37 13 log(RecoFoxWolframH10Eta25) 28 19 1 -2 -5 -8 100 9 28 8 2 -2 -23 -5 -7 log(RecoFlipY56Eta25) -10 -8 43 58 75 100 -8 -5 -8 -8 3 68 -2 -7 4 log(RecoFlipY45Eta25) -16 -14 52 74 100 75 -5 1 1 -14 -13 3 73 log(RecoFlipY34Eta25) -22 -19 70 100 74 58 -2 9 11 12 -19 -18 -10 79 log(RecoFlipY23Eta25) -29 -25 100 70 52 43 23 32 -23 -22 -44 84 1 24 -7 log(RecoThrustMinorEta25) 96 100 -25 -19 -14 -8 19 4 -14 -8 84 81 -36 25 -16 log(RecoTauEta25) 100 96 -29 -22 -16 -10 28 6 -15 -11 82 76 -41 27 -19 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)