Analysis on Shower Fractal Dimension & GRPC Digitizer Manqi - - PowerPoint PPT Presentation

29/03/2011 CALICE Meeting @ CERN 1

Manqi RUAN

Laboratoire Leprince-Ringuet (LLR) Ecole polytechnique 91128, Palaiseau

Analysis on Shower Fractal Dimension & GRPC Digitizer

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Shower fractal dimension

Nature: Shower particle, to interact or not

shower ~ self similar (Mandelbrot Set) Measure shower Fractal Dimension (FD) at high granularity calorimeter

• Varying scale by grouping neighbouring cells
• Count Number of hits at different scale

( define RN(x) = N1mm/Nxmm )

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Shower: Self Similar

D = < lnR(N1/Na)/ln(a) >

• Be observed within
• Low scale: minimal interaction energy & sensor layer thickness ( 1.2mm )
• High scale: fully containment ~ 1 hits per layer
• Characteristic constant

based on energy/PID:

• Global parameter based on

local density

• Cell Sizes: 2 – 10, 20, 30,

50, 60, 90, 120, 150mm.

• Samples: Particles shot

directly to GRPC DHCAL with only B Field

rms as error bar

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• Higher compactness @ large E: density increases with Energy ( volume increases

slower/logarithm than Energy )

• Order of compactness: Fractal Dimension ( FD )
• Left: FD( positron ) > FD( EM @ K0 ) > FD( K0 ) > FD ( MIP @ K0 )
• Right: FD( K0 ) > FD( Pion ), K0 shower is more compact: no initial mip tail

Compactness of shower

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Fractal in Nature

Straight line: Dim = 1 Muon ( 2 GeV ) Dim ~ 1

Hadrons: Dim( pi ) < Dim( K0 ) ~ 1.5 Positron ( 40GeV ) Dim ~ 1.75

Rectangle: Dim = 2

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Promising tool for PID

FD – 1 = 0.68, N1 = 500

e+ u h e+

998 2

u

1 994 5

h 15

14 971

e+ pi

u

KL γ E+ 945 2 53 Pi+ 5.0 882 12 102

u

1 12 921 67

Reference: PFOID @ Full Detector Characteristic Parameter for PID: to be used together with other information in full detector environment Handput Cut on Calo info @ 1mm Cell

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PID with FD @ larger cell

FD: Clear separation @ larger cell size

FD_10mm: Counts at 20, 30, 50, 60, 90, 120, 150mm cells FD_30mm: Counts at 60, 90, 120, 150mm cells

1mm e+ u h e+

998 2

u

1 994 5

h

15 14 971

10mm e+ u h e+

1000

u

995 5

h

17 14 969

30mm e+ u h e+

1000

u

996 4

h

18 11 971 FD = 1.68, N10 = 150 N30 - FD*200 = 40, FD = 1.5, N10 = 100 Remark: cuts might be energy dependent ~ easier to be used for charged particles

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FD @ different size

From FD( 1mm ) to FD( 10/30mm ): Better µ – h separation: µ acts more like a line ( FD = 1 ); ( Anyhow we can

create large cells from small ones... )

Positron Peak Smeared Pi: continuous from MIP to EM

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Muon with large Fractal Dimension: Together with Nhit information: Possibility to identify Muon radiation & String noise (typical for gaseous detector)...

Extreme Cases: Muon

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Extreme Cases: Pion

Pion: Pion decay ~ MIP Pure EM interaction ( pi + N = P + pi0 ); could be partially identified by tagging interaction point

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σ/M: Large cell better at low energy & Smaller cell at high energy. Linearity: Better at 2 – 5 mm, stronger saturation effects at larger cell... Naively: 5mm seems a nice choice...

Energy Estimation with Naive Counting

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FD @ Energy Estimation

• For example: Compensation based on the correlation of NH_30mm & FD1mm:

E = a * NH_30 + b * FD ~ 30%/sqrt(E)! But...

• Correlation coefficient depending on Energy: b ~ 0.0266*E. To measure cluster

energy of charged particle (with trk info): better matching

• A set of energy independent ( LO ) estimator: E = a' * NH_x/(1 – FD*b')

28%/sqrt(E) @ FD1mm 35%/sqrt(E) @ FD10mm If energy is known...

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E.E with FD Correction

Had put Energy Estimator with FD: NH10/(1-0.65*FD10) Energy resolution improved at high energy: ~ saturation effect correction Linearity improved: closed to 5mm Cell

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Summary

• Shower Fractal Dimension can be measured at high granular Calorimeter.

Provide a rich era to investigate.

• Application at single particle:
• PID: Very promising
• Energy Estimation:

–

Self-eating snake: 30%/sqrt(E) achieved for charged particle, better cluster – track linking

–

Linearity & Resolution @ high energy improved for neutral clusters

• To do:
• Fine tune the definition of Fractal Dimension
• Optimization of FD based energy estimation
• Test/optimize with clustering algorithms & Integration
• ... to investigate other possibilities: flavour-tagging @ VTX?

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GRPC Digitizer

• Introduction
• Avalanche development at GRPC
• Idea: cut off at 1mm
• Parameters to be fixed with experimental Input
• MIP charge inducing: Polya function, 2 parameters
• Treatment of Multiplicity: 2 parameters
• Analysis
• Dependencies
• Multiplicity
• Energy resolution with changing thresholds
• Summary

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Avalanche @ RPC

• Characteristic Parameter: from test beam data
• Multiplicity: global ~ 1.4 – 1.5 @ Thresholds ~ 0.1 mip (160 fC)
• Charge Image Size (depending on resistive plates thickness) : ~ 1mm

( as convoluted with spatial resolution )

• K. BELKADHI

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A little Mathematics: General Polya function:

Mean = (a+1)/b, MPV = a/b ;

• R. Han: measured from cosmic ray data: a = 16.3, b = 10.8

Mean = 1.6 pC, MPV = 1.51 pC More details: R. Han's presentation at tomorrow

Experiment input: Induced Charge of Single MIP

Polya-distribution: Cosmic Charge 7400V Polya Fitting

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Idea on multiplicity

Keep simulation level information to 1mm cells: count corresponding number

• f hits in/nearby 1 square cm²
• Advantages:

–

Natural cut off: 1mm ~ gas gap thickness ~ size of charge image

• Self Saturation & easy to integrate other saturation effects

–

Reliable estimation of multiplicity

–

Samples: available for other analysis ( optimized cell size, fractal dimensional analysis...)

• Cost:

–

Machine time: the same

–

Data size: increased ~ 5% ( ParticleCont recorded & Nhits increased by 2 – 3 times, Test on 20GeV Klong sample with only PRC HCAL & B Field: )

–

Negligible at full detector event: Utilize as Simulation base line?

Alternative ideas: keep particle hit position, see Ran's prensation

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Multiplicity treatment

• No threshold: Boundary (2 hits) or Corner (4 hits) * corresponding weights
• Spatial distribution of Charge: 2 parameters to be fine tuned ~ Weight Side &

Weight Corner with corresponding smearing

4 2 2 2 2 2 2 2 2 4 f e e c d b a

Remark: If image size ~ 1mm ( affect nearby 3 * 3 region ) & eff = 100%: M = ((N+2)/N)² = 1.44 @ N = 10...

5 10 5 10 40 10 5 10 5

A conservative guess:

=

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Simu & Digi hits

Left: simulation level ( 1 mm cell: size zoned by 5 for display. Colour: EM, MIP or Neutron hit ) Right: Digitization level ( 10mm cell. Colour according to Charge)

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Count 1mm hits inside ( neighbour to ) 10mm cell... Digitized hit colour to charge: ~ 1.5 - 1.6pC/mip

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For each digitized hits, count 1mm Cells: 1) direct sailing through (center): ≤100 2) induce charge from side (corner): ≤ 40 (4)

Multiplicity treatment

Electron Strings

Define: Multiplicity hit = Hit without Sail through/center hits Global Multiplicity = N(total)/N(non-Multiplicity)

Sample: 1k 40GeV Pion 1k events, shot normally to DHCAL with B Field

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Induced Charge

Multiplicity hits: Peak at 0.05 mip, 0.2 mip; Non – Multiplicity hits: Peak at 1 mip (~ 1.5 pC), 2 mips; Peak Positions: depend on the boundary weights. Statistic should be stable (only depend

• n sample PID/energy), and easy to be cleaned by threshold

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Q: Induced Charge

From Left to right: Q Vs total hits, non-multiplicity hits and multiplicity hits Linearly depend on Nhits, especially number of non-multiplicity hits Easy to add other saturation effects ( for example, local density of 1mm hits ) on induced charge: waiting for experimental evidence.

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Q Vs E

From left to right: Induced Charge Vs Deposited energy for all the hits, non- multiplicity hits and multiplicity hits. Correlation between Q & E exist, but with large smearing. Stronger Correlation at non-multiplicity hits.

Remark: Huge fluctuation in energy deposition: smeared over 5 - 6 orders of magnitude

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Multiplicity hits

Strong correlations & Worse resolution with Multiplicity hits

Resolution @ Naive counting (40GeV Pion): 11.7% @ non-Multiply hits, 12.1% @ total hits;

Multiplicity hits: no information ~ fluctuation

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Global Multiplicity Vs E & PID

Global Multiplicity : anti-proportional to density/Shower Fractal Dimension

M = 1.36 M = 1.34 M = 1.32 M = 1.25 M = 1.42

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Energy resolution & Threshold

First Thresholds: Naive Counting: Resolution slightly depend on thresholds; Optimized thresholds: depend on energy

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Thresholds optimization on single particle events

Reference: 40GeV Pion Thresholds: First: 0.8 pC ~ 0.5mip; Second & Third: to maximal information: to equalize statistics of three kinds of hits: Second: 2.11 pC ~ 1.32 mips; Third: 4.56pC ~ 2.84 mips;

Additional Parameter(s): Smearing of Thresholds according to electronics ( ~fC level )

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Thresholds optimization

Optimized Coefficient (energy depend) : ~30% improvements at 80GeV; N1 + 1.2 * N2 + 4.5 * N3 @ 80GeV, N1 + 3.0 * N2 + 3.5 * N3 @ 40GeV

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Summary

• GRPC Digitizer is ready:
• Multiplicity: add fluctuations, easy to be removed/compensated from cuts
• Global Multiplicity decrease with density
• Input parameters to be Xchecked/tuned from test beam
• Spatial charge distribution ( 2 para, + 2 corresponding fluctuation if necessary )
• Parameters for polya function ( 2 para )
• Thresholds fluctuation from electronics ( 1 - 3 para )
• Remark: negligible noise rate @ SDHCAL: 3hits/evt
• Preliminary analysis on energy resolution
• Semi-Digital Vs Digital: possible to improve resolution up to 30% at high energy,

but need to be fine tuned & applied with other information...

• Proposal on simulation base line: keep 1mm information

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Druid 2.0: What's new

• 3D display + Projections
• Geometry:
• Less dependency: gear supporting dropped
• More detector models supported: ILD00, ILD00_Dhcal,

clic01_ild, sidloi3, clic_sid_cdr_b, CALICE TBs...

• Options:
• Cut on calo hits energy
• Hit time display
• Faster: cleaning & acceleration

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500GeV ttbar @ ILD00

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Cut on Calo Hit Energy

• Tunable Cut on Hit energy: in Mips
• Hide low energy hits as default. If

shown, coloured with grey.

• Example:

Simulated CALICE TB event with Scintillator HCAL: 50GeV Pion event with/without default energy cut at 0.2 Mip

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Display Hit time: DHCAL

Neutron @ Gaseous Calorimeter:

Direct hits: very few Indirect hits: Electromagnetic hits illuminated by Neutrons – iron interaction, T > 100 ns ( Ongoing study: affection on energy resolution )

7.2% hits comes after 150 ns: 0.3% hits comes at 500 – 650 ns

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Time & 0.2 mip Cut Type & 0.2 mip Cut Type & No Cut Time & No Cut

Hit time @ AHCAL:

Neutron @ Scintillator Calorimeter:

Huge statistic, most with energy < 0.2 mip, occurs during the whole duration ( ~ 10k ns), and illuminate late EM hits

43% hits/6% energy comes after 150 ns

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Faster

~ 3 sec for ttH event @ 1 TeV with Projection

• Beta test version: http://llr.in2p3.fr/~ruan/ILDDisplay/Druid_1.9.7.tar.gz

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Special Thanks to ...

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Back up slides

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To Improve: clean string noise

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EM/MIP @ hadronic shower

• Hadronic Shower = MIPs + EM core ( leaves? )
• MIPs: loose ~ smaller Fractal Dimension

EM: compact ~ large Fractal Dimension

• EM/MIP Ratio/Correlation changes at different scale
• Possibility & method of identify EM/MIP at reconstruction?

40 GeV Pion Shower at DHCAL ( 10 mm Cell Size)

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Hadronic shower: EM/MIP @ different Scale

CC = 2.2 CC = 1.7 CC = 1.3 CC = 1.1 Energy Estimator: NH_EM + CC*NH_Had: CC = 1 ~ total hits CC = 0.9 CC = 0.8

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Hadronic shower: EM/MIP @ different Scale

CC = 0.4

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Thresholds & Resolution

σ/M for 40GeV Pion: 11.7% @ non-Multiply hits, 12.1% @ total hits; + Thresholds: 11.8% @ 0.4pC, 11.5% @ 0.8pC, 11.2% @ 1.0pC 10.8% @ 1.2pC, 11.2% @ 1.4pC, 12.2% @ 1.6pC Multiplicity: weak effects @ energy estimation. Could be compensated from Threshold optimization ( what's the affection on shower reconstruction? )

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• Remark on Minimal bias event dominated

noise:

• 500GeV: 132 evt/train, with 30.7 hits in total;
• Thus noise: 2% * 132/2000 * 30.7 ~ 0.04hits/evt
• Other sources maybe also important
• For AHCAL: leading effect should be scintillator

timing response.