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

Contents

Introduction Angular Resolution Study

position resolution of ECAL cluster direction of reconstructed gamma

Calorimeter Component DependenceCell size dependenceMaterial dependence

Summary

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.

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.

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

Angular Resolution Study

position resolution of cluster

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)

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

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]

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

Angular Resolution Study

direction of reconstructed gamma

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

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

Energy dependence (1,2,5,10,50GeV)

Eangle

125 [mrad]

Average over full acceptance

1GeV2GeV

5GeV10GeV

50GeV

1/√E

σ [

mra

d]

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

Calorimeter Component Dependence

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?

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

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?

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.

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?

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

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%

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

Backup

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

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

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]

θ resolution (cell size : 1x1 cm)

φ resolution (cell size : 1x1 cm)

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)

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

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]

2-dimension normal distribution

)2

exp(*),(2

22

yx

Ayxf

)2

exp(*)(2

2

r

Arf

)(*)( rfrrF

peakr

r histogram F(r)

peakr

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

Linearity(1,2,5,10,50 GeV)

2x2 cm

1x1 cm

Linearity is kept below 10GeV.E

angle

125 [mrad]

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]

Average (10000 events)

Hit cell number

Highest energy layer

Energy sum

Tungsten 252 5.7 0.412

Lead 284 5.6 0.429gamma @10GeV

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.

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(?)

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.