1. Angular resolution study of isolated gamma with GLD detector simulation 2007/Feb/ ACFA ILC Workshop M1 ICEPP, Tokyo Hitoshi HANO collaborated with Acfa-Sim-J group

2. Contents Introduction Angular Resolution Study  position resolution of ECAL cluster  direction of reconstructed gamma Calorimeter Component Dependence  Cell size dependence  Material dependence Summary

3. Motivation and PFA analysis 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) [m] decay length : ECAL IP In this study, we have used single-gamma shot from IP to evaluate angular resolution.

4. Jupiter for GLD detector GLD detector has large-radius and fine-segmented Calorimeter. It’s important to optimize cost vs. physics performance. R [m]Z [m] ECAL 2.1-2.3 0.4-2.3 0-2.8 2.8-3.0 Structure W/Scinti./gap 3/2/1(mm) x 33 layers cell size 1x1(cm 2 ) ECAL geometry in Jupiter ： barrel endcap Calorimeter cell size and absorber material can be changed.

5. 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

6. Angular Resolution Study position resolution of cluster

7. 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 γ IP (generated point) ECAL clustering (θ,φ)

8. 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 cell central point

9. Position resolution of cluster (cell : 1 cm) |cos(θ)| σ [mrad] barrel endcap barrel 1 GeV 2 GeV 5 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]

10. Energy Dependent Result of position resolution θ barrel ： θ endcap ： φ barrel ： φ endcap ： [mrad] 1/√E σ [mrad] 10GeV 1GeV 2GeV 5GeV

11. Angular Resolution Study direction of reconstructed gamma

12. 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

13. Histogram and angular resolution fitting function r histogram F(r) σ = 48.3 ± 0.3 [mrad] IP central point of cluster r d rd γ reconstructed gamma angle [rad] = r/d gamma@10GeV

14. Energy dependence (1,2,5,10,50GeV) [mrad] Average over full acceptance 1GeV 2GeV 5GeV 10GeV 50GeV 1/√E σ [mrad]

15. 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

16. Calorimeter Component Dependence

17. Structure (cell size dependence) Absorber cell size [cm] X0X0 Energy Resolution W[3mm]0.5~102814.8% gamma : E = 10GeV How about cell size dependence?

18. 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

19. Structure (energy dependence) Absorber cell size [cm] X0X0 Energy Resolution W[3mm]0.5~22814.8% gamma : E = 1~10GeV How about energy dependence between 1cm and 0.5cm?

20. 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.

21. Absorber cell size [cm] X0X0 Energy Resolution W [3mm]0.5~22814.8% Pb [4.8mm]0.5~22815.0% Pb [3mm]0.5~222 Structure (Absorber dependence) gamma : E = 10GeV How about absorber dependence?

22. 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

23. Cause depth gamma MC reconstructed gamma Angular resolution is better than Tungsten, since Lead has deeper distribution. Average of gamma @10GeV Angular ResolutionEnergy Resolution Tungsten [3mm]48.3 ± 0.3 [mrad]14.8% Lead [4.8mm]45.5 ± 0.3 [mrad]15.0%

24. Angular resolution of default-GLD Calorimeter (W:1cm)  The angular resolution is estimated to be 125mrad/√(E/GeV) Dependence on cell size granularity and material dependence (W, Pb) has been studied  No significant difference has been observed between 1cm and 0.5cm  Lead is better than Tungsten for isolated gamma  Energy resolution is same  How about energy resolution for jet ? Next talk Summary

25. Backup

26. 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

27. Clustering 1. 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 product IP

28. 1cell ( 1cm x 1cm ) θ, φ z=0 ( |cos(θ)|=0 ) max θ 1cell 210cm IP 1cm θ （ φ ） 1cell = 1/210 ≒ 4.7 [mrad] z=280 ( |cos(θ)|=0.8 ) min θ 1cell IP θ 1cell ≒ 1.71 [mrad]

29. θ resolution (cell size : 1x1 cm)

30. φ resolution (cell size : 1x1 cm)

31. Result (θ, φ resolution) gamma@10GeV θ,φ resolution θ barrel ： 0.430±0.004 [mrad] θ endcap ： 0.282±0.006 [mrad] φ barrel ： 0.423±0.004 [mrad] φ endcap ： 0.699±0.014 [mrad] θ 1cell ≒ 1.71 ～ 4.70 [mrad] Angular resolution is good as well as cell size (1x1cm)

32. 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 of reconstructed line IP γ reconstructed line

33. Fitting method Find a central point of each layer by energy weighted mean x y weighted by energy deposit Fitting 2-dimentions (x-y) y’ z Fitting new 2-dimentions (y’-z) Distance[cm]

34. 2-dimension normal distribution r histogram F(r)

35. Distance (d) and angle angle [rad] = d/r fitting function IP central point of cluster r d rd γ reconstructed line

36. Linearity(1,2,5,10,50 GeV) 2x2 cm 1x1 cm Linearity is kept below 10GeV. [mrad]

37. 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]

38. Average (10000 events) Hit cell number Highest energy layer Energy sum Tungsten2525.70.412 Lead2845.60.429 gamma @10GeV

39. Hitting distribution and Average Hit cell number Layer number of central point Energy Resolution Tungsten2525.714.8% Lead2845.615.0% gamma @10GeV Fitting of Lead makes successfully than Tungsten, because Lead has deep distribution.

40. Fitting 0.068*x-140.031*x+6.8 L rad [g/cm 2 ] L rad [cm] R M [cm] Tungsten6.960.6990.71(?) Lead6.570.9081.29(?)

41. Cause Hit cell number Layer number of central point Energy Resolution Tungsten [3mm]2525.714.8% Lead [4.8mm]2845.615.0% Average of gamma @10GeV depth (layer) gamma MC reconstructed gamma Since Lead has deeper distribution, angular resolution is better than Tungsten.