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• Separation in AHCAL using shower shapes

Justas Zalieckas

AHCAL – Analogue Hadronic Calorimeter

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Outline

• Analogue Hadronic Calorimeter (AHCAL)
• separation problem
• Shower shape variables for separation
• Boosted Decision Trees (BDT) and Multivariate Data

Analysis (MDA)

• Results
• Conclusions

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Analogue Hadronic Calorimeter (AHCAL)

Used to determine the coordinates of the incident point of the particles on the calorimeter surface: xtrk and ytrk. Granularity: 3x3 cm2, 6x6 cm2, 12x12 cm2.

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 (SiPM)

• Cherenkov counters in

front of AHCAL

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separation problem

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

• -> 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

created ROOT files for separation.

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• Scatter plot of two shower

shape variables:

• energy weighted radial distance
• = energy of cell i
• = energy sum in the first 5

AHCAL layers

• = total energy sum
• = cells center coordinates
• Overlapping regions
• 5 GeV samples
• For better electrons

separation – use more shower shape variables

separation problem

d=∑ Eixi−xtrk

2 yi− ytrk 2

∑ Ei

E5 Etot

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Ei xi, yi

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Shower shape variables for separation

• energy weighted radial

distance

• = fraction of

contained in the first 5 layers

• third momentum of

radial distance

• energy density
• = cell volume
• = cells number

E5/Etot d1[mm] logd 3[mm]

d1=∑ Eixi−xtrk2 yi−ytrk2

∑ Ei

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Energy density[MIPs/cm

3]

∑ Ei/V i

N

d3=∑ Ei

3xi−xtrk2 yi−ytrk2

∑ Ei

3

E5/Etot Etot

V i N

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Shower shape variables for separation

• second momentum
• f radial distance
• radial distance

containing 90%

• number of hits

containing 90%

• total hits number
• is fraction of

cells containing 90%

• f
• cells average energy

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Etot Etot

R90[mm]

R90

N 90/N

N 90 N

∑ Ei

N

Cellsaverage energy[MIPs] d 2[mm]

d2=∑ Ei

3xi−xtrk2 yi− ytrk2

∑ Ei

2

N 90/N

Etot

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Shower shape variables for separation

• maximum energy

loss layer number

• shower start layer

number

• is number of

layers to reach shower maximum

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Max.energylosslayernumber Lmax Shower start layer number Lstart Lmax−Lstart

Lmax Lstart Lmax−Lstart

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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
• Purity

WS, WB – signal and background weights. If p>0.5 – signal, if p<0.5 - background. p=

∑

S

W S

∑

S

W S∑

B

W B

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Boosted Decision Trees

Boosting the decision tree

• Reweight events
• 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 performance w.r.t. a single tree.

W iW ie

f err

W i Training sample Single classifier Testing sample

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Correlation of input variables for signal

Correlation matrix for electrons

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Correlation of input variables for background

Correlation matrix for pions

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Results

• Variable ranking:

Rank Variable Importance 1 N90/N 1.288e-01 2 d1 1.269e-01 3 E5/Etot 1.165e-01 4 d2 1.145e-01 5

Energy density

1.100e-01 6 R90 1.018e-01 7 d3 1.015e-01 8 Lstart 7.623e-02 9

Cells average energy

6.687e-02 10 Lmax 4.406e-02

11 Lmax-Lstart

1.272e-02

Electron: 22586 (training), 22587 (testing). Pion: 18045 (training), 18046 (testing).

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Results

Input variables in BDT Electron eff. with contamination fraction effpion=0.01 Electron eff. with contamination fraction effpion=0.1 Separation <S2> d1, E5/Etot

0.977 1 0.956

N90/N, d1, E5/Etot, d2, Energy density, R90, d3

0.988 1 0.97

N90/N, d1, E5/Etot, d2, Energy density, R90, d3, Lstart, Cells average energy, Lmax, Lmax-Lstart

0.991 1 0.973

Input variables in

• ptimized Cut

method d1, E5/Etot

0.975 0.992

• eff pion= N pion. selected

N pion.total 〈S

2〉=1

2

∫ yel.−y pion2

yel.y pion dy

• Electron efficiency
• Pion efficiency
• Separation

is PDFs of classifier .

is 1 with no overlap and is 0 with full overlap. eff el.=N el.selected Nel.total yel., y pion y 〈S

2〉

Cut on and gives . Using BDT with 11 input variables for:

• -->
• -->
• -> Large improvement with

multivariate selection.

E5/Etot≥0.875 d1≤40 eff el.=0.48,eff pion=0.00047 eff el.=0.48 eff pion=0.00047 eff pion=0.00027 eff el.=0.61

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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