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Angular resolution study Angular resolution study of isolated gamma with of isolated gamma with GLD detector simulationGLD detector simulation
2007/Feb/2007/Feb/
ACFA ILC WorkshopACFA ILC Workshop
M1 ICEPP, TokyoM1 ICEPP, Tokyo
Hitoshi HANOHitoshi HANO collaborated with Acfa-Sim-J group
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Contents
Introduction Angular Resolution Study
position resolution of ECAL cluster direction of reconstructed gamma
Calorimeter Component DependenceCell size dependenceMaterial dependence
Summary
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Motivation and PFA analysis
G~~ 0
1
Measurement of the direction of non-pointing photon is important for GMSB (gauge mediated supersymmetry breaking) scenarios.
To identify a non-pointing photon, we need to know angular resolution of the detector (EM Calorimeter).
We have studied angular resolution using full-simulator (Jupiter)
35 10~10 [m]
decay length :
ECAL
IP G~
01
~
G~
01
~
In this study, we have used single-gamma shot from IP to evaluate angular resolution.
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Jupiter for GLD detectorGLD detector has large-radius and fine-segmented Calorimeter.
It’s important to optimize cost
vs. physics performance.
R [m] Z [m]
ECAL2.1-2.3
0.4-2.3
0-2.8
2.8-3.0
Structure
W/Scinti./gap3/2/1(mm) x 33 layers cell size 1x1(cm2)
ECAL geometry in Jupiter :
barrel
endcap
Calorimeter cell sizeand absorber material
can be changed.
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IP (generated point)
1. Clustering
2. Find an energy-weighted central point of each layer
3. Fit each point with least-square method
4. Evaluate an angle between gamma-line and reconstructed gamma
Method of reconstructed gamma
γ
reconstructed gamma
Calorimeter
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Angular Resolution Study
position resolution of cluster
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Method (position resolution study of aaaaaaa each hit cluster)
1. Shoot single-gamma from IP with random direction
2. Clustering (more details in next page)
3. Search energy-weighted central point of cluster
4. Evaluate θ, φ of a central point
5. Compare with MC truth
θ ( φ ) resolution [rad] = θ ( φ ) meas – θ( φ ) MC
central point
γIP
(generated point)
ECAL
clustering
(θ,φ)
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Clustering method
1. Find the highest energy deposit cell
2. Make the cone with a focus on it
3. Define cells which are inside of the cone as one cluster (around all layers)
4. Find energy-weighted central point
clustering angle = 10°γ@10GeV
IP (generated point)
highest energy deposit cellcentral
point
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Position resolution of cluster (cell : 1 cm)
|cos(θ)| |cos(θ)|
σ [
mra
d]
σ [
mra
d]
barrel endcapendcap barrel
1 GeV2 GeV5 GeV
10 GeV
θ resolution is better for larger cos(θ)
φ resolution is worse for larger cos(θ)
IP (generated point)
ECAL geometrical effect
Position resolution : ~0.3 [cm]
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Energy Dependent Result of position resolution
15.091.0
E
22.081.0
E
θ barrel :
θ endcap :
09.008.1
E
23.078.1
E
φ barrel :
φ endcap
:
[mrad]
[mrad]
[mrad]
[mrad]
1/√E 1/√E
σ [
mra
d]
σ [
mra
d]
10GeV
1GeV
2GeV
5GeV
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Angular Resolution Study
direction of reconstructed gamma
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IP (shot point)
1. Clustering
2. Find an energy-weighted central point of each layer
3. Fit each point with least-square method
4. Evaluate an angle between gamma-line and reconstructed gamma
Method (Angular resolution study of reconstructed gamma)
γ
reconstructed gamma
Calorimeter
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anglepeakr peakr
Histogram and angular resolution
fitting function )12
exp(**02
2
p
xxp r histogram F(r)
σ = 48.3 ± 0.3 [mrad]
)(*)( rfrrF
)2
exp(*)(2
2
r
Arf
IP central point of cluster
r
d
r d
γ
reconstructed gamma
angle [rad] = r/d
gamma@10GeV
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Energy dependence (1,2,5,10,50GeV)
Eangle
125 [mrad]
Average over full acceptance
1GeV2GeV
5GeV10GeV
50GeV
1/√E
σ [
mra
d]
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Shoot from IP
Shoot from another point gamma@10GeV
IP
ECAL
Shoot from x=y=20, z=0
σ= 48.3±0.3[mrad]
IP
ECAL
σ= 48.6±0.3[mrad]
If gamma has been shot from another position, we could not observed significant
difference.
reconstructed gamma
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Calorimeter Component Dependence
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Structure (cell size dependence)
Absorbercell size
[cm]X0
Energy Resolution
W[3mm] 0.5~10 28 14.8%
gamma : E = 10GeV
How about cell size dependence?
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Cell size dependence
1 [cm] : 48.3 ± 0.3 [mrad] 0.5 [cm] : 46.4 ± 0.3 [mrad]
gamma @10GeV
<5%
We could not observed significant improvement from 1cm to 0.5cm
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Structure (energy dependence)
Absorbercell size
[cm]X0
Energy Resolution
W[3mm] 0.5~2 28 14.8%
gamma : E = 1~10GeV
How about energy dependence between 1cm and 0.5cm?
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Energy dependence (1,2,5,10GeV)
1GeV
2GeV
5GeV
10GeV
No significant difference has been observed between 1cm and 0.5cm around all of energy.
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Absorbercell size
[cm]X0
Energy Resolution
W [3mm] 0.5~2 28 14.8%
Pb [4.8mm] 0.5~2 28 15.0%
Pb [3mm] 0.5~2 22
Structure (Absorber dependence)gamma : E = 10GeV
How about absorber dependence?
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Absorber dependence (Tungsten, Lead)
@1x1 [cm]
Lead[4.8mm]
Tungsten[3mm]
Tungsten [3mm] : 48.3 ± 0.3 [mrad] Lead [4.8mm] : 45.5 ± 0.3 [mrad]
Lead[3mm]
Same total radiation length
Angular resolution with Lead is better than Tungsten
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Cause
depth depth
gamma MC
gamma MC
reconstructed gamma
reconstructed gamma
Angular resolution is better than Tungsten, since Lead has deeper distribution.
Average of gamma @10GeV
Angular Resolution Energy Resolution
Tungsten [3mm] 48.3 ± 0.3 [mrad] 14.8%
Lead [4.8mm] 45.5 ± 0.3 [mrad] 15.0%
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Angular resolution of default-GLD Calorimeter (W:1cm)The angular resolution is estimated to be 125mrad/
√(E/GeV) Dependence on cell size granularity and materi
al dependence (W, Pb) has been studiedNo significant difference has been observed betwee
n 1cm and 0.5cmLead is better than Tungsten for isolated gammaEnergy resolution is sameHow about energy resolution for jet ? Next talk
Summary
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θ, φ resolution study of cluster
1. Shoot single-gamma from IP with random direction
2. Clustering - use hit data from ECAL(,HCAL)
3. Search central point of cluster
4. Find θ, φ of a central point
5. Compare with MC truth
θ ( φ ) resolution [rad] = θ ( φ ) MC – θ( φ ) meas
IP
central point
γ
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Clustering1. Find the highest energy deposit cell
2. Make a cone with centering around it
3. Define cells which are inside of a cone as one cluster
4. Find a central point by energy weighted mean
clustering angle = 10°γ@10GeV
IP
Judging by inner productIP
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1cell ( 1cm x 1cm ) θ, φ
z=0 ( |cos(θ)|=0 ) max θ1cell
210c
m
IP
1cm1c
m
θ ( φ ) 1cell = 1/210 ≒ 4.7 [mrad]
z=280 ( |cos(θ)|=0.8 ) min θ1cell
IP
θ1cell ≒ 1.71 [mrad]
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θ resolution (cell size : 1x1 cm)
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φ resolution (cell size : 1x1 cm)
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Result (θ, φ resolution) gamma@10GeV
• θ ,φ resolution
θbarrel : 0.430±0.004 [mrad] θendcap : 0.282±0.006 [mrad] φbarrel : 0.423±0.004 [mrad] φendcap : 0.699±0.014 [mrad]
θ1cell 1.71≒ ~ 4.70 [mrad]
Angular resolution is good as well as cell size (1x1cm)
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1. Clustering
2. Find a central point of each layer by energy weighted mean
3. Fit each point with least-square method
4. Find an angle between IP and reconstructed line
Angular resolution study ofreconstructed line
IP
γ
reconstructed line
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Fitting methodFind a central point of each layer by energy weighted mean
x
y
weighted by energy deposit
Fitting 2-dimentions (x-y)
y’
z
y’
Fitting new 2-dimentions (y’-z)
Distance[cm]
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2-dimension normal distribution
)2
exp(*),(2
22
yx
Ayxf
)2
exp(*)(2
2
r
Arf
)(*)( rfrrF
peakr
r histogram F(r)
peakr
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Distance (d) and angle
angle [rad] = d/r
)12
exp(**02
2
p
xxp fitting function
IP
central point of cluster
r
d r d
γ
reconstructed line
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Linearity(1,2,5,10,50 GeV)
2x2 cm
1x1 cm
Linearity is kept below 10GeV.E
angle
125 [mrad]
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Angular resolution Absorber (Tungsten, Lead)
@1x1 [cm]
Lead[4.8mm]
Tungsten[3mm]
Tungsten : 48.26 ± 0.29 [mrad] Lead : 45.51 ± 0.28 [mrad]
Lead[3mm]
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Average (10000 events)
Hit cell number
Highest energy layer
Energy sum
Tungsten 252 5.7 0.412
Lead 284 5.6 0.429gamma @10GeV
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Hitting distribution and Average
Hit cell numberLayer number of
central pointEnergy
Resolution
Tungsten 252 5.7 14.8%
Lead 284 5.6 15.0%gamma @10GeV
Fitting of Lead makes successfully than Tungsten, because Lead has deep distribution.
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Fitting
0.068*x-14 0.031*x+6.8
Lrad [g/cm2] Lrad [cm] RM [cm]
Tungsten 6.96 0.699 0.71(?)
Lead 6.57 0.908 1.29(?)
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Cause
Hit cell numberLayer number of
central pointEnergy
Resolution
Tungsten [3mm] 252 5.7 14.8%
Lead [4.8mm] 284 5.6 15.0%
Average of gamma @10GeV
depth (layer) depth (layer)
gamma MC
gamma MC
reconstructed gamma
reconstructed gamma
Since Lead has deeper distribution, angular resolution is better than Tungsten.