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e / - Separation in AHCAL using shower shapes Justas Zalieckas AHCAL - PowerPoint PPT Presentation

Mar 20, 2023 •342 likes •507 views

e / - Separation in AHCAL using shower shapes Justas Zalieckas AHCAL Analogue Hadronic Calorimeter Outline Analogue Hadronic Calorimeter (AHCAL) separation problem e / e / Shower shape variables for separation

  1. e / - Separation in AHCAL using shower shapes Justas Zalieckas AHCAL – Analogue Hadronic Calorimeter

  2. Outline ● Analogue Hadronic Calorimeter (AHCAL) ● separation problem e / e / ● Shower shape variables for separation ● Boosted Decision Trees (BDT) and Multivariate Data Analysis (MDA) ● Results ● Conclusions 2

  3. Analogue Hadronic Calorimeter (AHCAL) AHCAL Sampling calorimeter ● 30 layers of sandwich ● structure One layer – 10 mm W + ● 5 mm scintillator tiles High scintillator ● granularity Wavelength shifting ● fibers are read out with Silicon Photomultipliers Used to determine the coordinates of the incident point of the particles on the (SiPM) calorimeter surface: x trk and y trk . Cherenkov counters in ● front of AHCAL Granularity: 3x3 cm 2 , 6x6 cm 2 , 12x12 cm 2 . 3

  4. e / separation problem e / separation based on Cherenkov counters - efficiency for electron identification becomes low for low pressure - purity for electron identification drops with increasing pion content of the beam e / --> difficult to separate in low energy range (E<10 GeV) Proposed solution - use shower shape information from calorimeter to distinguish between electromagnetic and hadronic showers - combine information using multivariate data analysis technique My tasks: 1. Write Marlin processor to create ROOT files with trees containing separation variables. 2. Use TMVA 4 (Toolkit for Multivariate Data Analysis with ROOT) package with e / created ROOT files for separation. 4

  5. e / separation problem Scatter plot of two shower ● shape variables: - energy weighted radial distance d = ∑ E i   x i − x trk  2  y i − y trk  2 ∑ E i E i - = energy of cell i E 5 - = energy sum in the first 5 AHCAL layers - = total energy sum E tot x i , y i - = cells center coordinates Overlapping regions ● 5 GeV samples ● For better electrons ● separation – use more 5 shower shape variables

  6. e / Shower shape variables for separation - energy weighted radial distance d 1 = ∑ E i   x i − x trk  2  y i − y trk  2 ∑ E i E tot E 5 / E tot - = fraction of contained in the first 5 layers - third momentum of E 5 / E tot d 1 [ mm ] radial distance 3   x i − x trk  2  y i − y trk  2 d 3 = ∑ E i ∑ E i 3 - energy density ∑ E i / V i N - = cell volume V i 3 ] log  d 3 [ mm ] Energy density [ MIPs / cm N 6 - = cells number

  7. Shower shape variables for separation e / - second momentum of radial distance 3   x i − x trk  2  y i − y trk  2 d 2 = ∑ E i ∑ E i 2 - radial distance R 90 E tot containing 90% - number of hits N 90 E tot containing 90% d 2 [ mm ] R 90 [ mm ] N - total hits number N 90 / N - is fraction of cells containing 90% E tot of - cells average energy ∑ E i N 7 Cellsaverage energy [ MIPs ] N 90 / N

  8. e / Shower shape variables for separation - maximum energy L max loss layer number - shower start layer L start number L max − L start - is number of layers to reach shower maximum L max − L start Shower start layer number L start Max.energylosslayernumber L max 8

  9. Decision tree for events classification Leaf node ● Root node ● Events sample ● Classification/separation ● variables for split decisions Repeated yes/no split decisions ● Phase space is divided in many ● regions Events end in final leaf node ● ∑ W S Purity ● S p = ∑ W S  ∑ W B S B W S , W B – signal and background weights. 9 If p>0.5 – signal, if p<0.5 - background.

  10. Boosted Decision Trees Boosting the decision tree Training sample Reweight events ● f  err  W i W i  W i e New trees are derived from the ● same training sample Trees form a forest ● Average weights ● (misclassification) Combine into a single classifier ● Test classifier with test sample ● Boosting stabilizes fluctuations ● in the training sample and considerably enhances classifier Single classifier Testing sample performance w.r.t. a single tree. 10

  11. Correlation of input variables for signal Correlation matrix for electrons 11

  12. Correlation of input variables for background Correlation matrix for pions 12

  13. Results Variable ranking: ● Rank Variable Importance 1 N 90 /N 1.288e-01 2 d 1 1.269e-01 3 E 5 /E tot 1.165e-01 4 d 2 1.145e-01 5 1.100e-01 Energy density 6 R 90 1.018e-01 7 d 3 1.015e-01 8 L start 7.623e-02 9 6.687e-02 Cells average energy 10 L max 4.406e-02 1.272e-02 11 L max -L start Electron: 22586 (training), 22587 (testing). Pion: 18045 (training), 18046 (testing). 13

  14. Results Electron eff. with Electron eff. with Input variables in Separation ● Electron efficiency contamination contamination BDT <S 2 > fraction eff pion =0.01 fraction eff pion =0.1 eff el. = N el.selected d 1 , E 5 /E tot 0.977 1 0.956 N el.total ● Pion efficiency N 90 /N, d 1 , E 5 /E tot , d 2 , 0.988 1 0.97 Energy density, eff pion = N pion. selected R 90 , d 3 N pion.total N 90 /N, d 1 , E 5 /E tot , d 2 , ● Separation Energy density, R 90 , d 3 , L start , Cells 0.991 1 0.973 ∫  y el. − y pion  2 2 〉= 1 〈 S dy average energy, 2 y el.  y pion L max , L max -L start Input variables in is PDFs of classifier . y el. , y pion y optimized Cut method 2 〉 〈 S is 1 with no overlap and is 0 d 1 , E 5 /E tot 0.975 0.992 - with full overlap. Cut on and d 1 ≤ 40 E 5 / E tot ≥ 0.875 gives . eff el. = 0.48, eff pion = 0.00047 Using BDT with 11 input variables for: - --> eff pion = 0.00027 eff el. = 0.48 - --> eff el. = 0.61 eff pion = 0.00047 14 --> Large improvement with multivariate selection.

  15. Conclusions ● Increase in input variables number increases electron separation efficiency ● BDT classifier allows better electron/pion separation than simple cut method ● Further analysis with real data sample 15

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