1. Photon reconstruction and matching Prokudin Mikhail

2. Outline ► Requirements ► Cluster finder  algorithm and performance ► Cluster fitting  requirements ► Matching algorithm

3. Photon reco. Requirements ► Robust reconstruction of single photons ► Two close photons case:  robust reconstruction of parameters in case of two separate maximums  separation one/two photons in case of one local maximum ► Fast!

4. Cluster finder Cluster formation ► Remove maximums near charged tracks  real tracking ► Precluster:  formed near local maximum ► cut on maximum energy  find maximum 2x2 matrix near maximum  add a neighbor to local maximum cell with minimal energy deposition ► to add information  check precluster energy ► >0.5GeV ► Cluster: group of preclusters with common cells ------------------------------------------------- ► Clusters with 2 maximums >10%  Fit procedure is necessarily!  >3 ( 3 (<1% γ ) maximums can be omitted Requirements ► Clusters should be large  information for unfolding ► Clusters should be small  hadrons background

5. Fitting basics ► 2 clusters ► Simple methods  Fit not required ► 1 cluster  2 maximums ► Fit  shower shape ► 1 cluster  1 maximum  2 photons ► Should be rejected ► Fit  shower shape Same photons, but different distance between them.

6. Fitting basics ► 2 clusters ► Simple methods  Fit not required ► 1 cluster  2 maximums ► Fit  shower shape ► 1 cluster  1 maximum  2 photons ► Should be rejected ► Fit  shower shape Same photons, but different distance between them.

7. Fitting basics. Shower shape + or ? Precise knowledge of shower shape is essential. If χ 2 is used, than what is σ 2 (error)?

8. Fitting basics. Shower library ► Store mean energy deposition vs. (x, y) for each  Energy  Theta  Phi ► Energy deposition in cluster cells are not independent  RMS value storing useless ► Should use analytical formula for σ 2  with correlations h4 h5 h4 h5

9. σ 2 formula ► σ 2 =c 2 (E meas  (1-E meas /E cluster )+c 0 +c 1  E 2 cluster )  c 2 is normalization ► 95% of photons have χ 2 <2  c 1 and c 0 ► exact values are found requiring:  χ 2 should not depend on photon’s energy  independence from φ ► due to shower library  c is different for each calorimeter region/cell size  c i is different for each calorimeter region/cell size

10. Energy reconstruction quality Calibration is good Calibration is good

11. Photon separation. Cluster with 2 maximums ► χ 2 criteria allows identify ~40% of two photons clusters  efficiency highly depend on distance between photons/calorimeter region Inner calorimeter region

12. Energy reconstruction quality. Cluster with 2 maximums ► Reconstructed energy distribution for both photons is Ok ► But for each of them…

13. Energy reconstruction quality. Cluster with 2 maximums Reconstruction algorithm tends to increase asymmetry in energy of photons (also by PHENIX experience)

14. AuAu 25 GeV UrQMD events ► 730 photons in event ► 299 photons in calorimeter acceptance  131 with energy > 0.7 GeV ► 35% reconstruction efficiency ► 91% for isolated photons  rises with increasing isolation

15. AuAu 25 GeV UrQMD events ► 35% reconstruction efficiency ► Boundaries between calorimeter regions  occupancy Reconstruction efficiency vs. θ and energy

16. Matching ► Matching between MC and reconstructed particles  not only MC photons ► Why?  check origin of cluster  misidentification ► neutron ► …  physics processes ► π 0 and η decays ► prompt photons ► … Requirements ► Matching for many maximums clusters ► Correct matching with converted γ and brem e Available information ► Energy deposition in each cell of cluster by each MC particle  CbmEcalStructure ► Shower shape for each reconstructed particle  CbmEcalShowerLib CbmEcalMatching. At SVN

17. Matching. Multimaximum cluster ► Idea: use shape of reconstructed photons ► For each MC/reconstructed particle compute:  only cells with energy deposition of current particle are in play  match with MC particle with P i >0.6 ► Clusters with 2 maximums: 99.97% efficiency

18. Matching (Numerous converted γ) ► Idea: for γ( e ± ) look at mother e ± ( γ), grandmother, …  for each γ and e ± MCTrack: P=P this +ΣP daughter ► Several realizations available  Choose γ /e ± with maximum P  Choose parent e ± if daughter γ have P>const*P γ  …  Exact algorithm/constants are defined in configuration file ► still under development γ e+e+ e-e- γ Reco

19. Conclusions and next steps ► Reconstruction algorithms are completed and tested  35% reconstruction efficiency ► occupancy! ► Calorimeter geometry optimization  cost  physical observables sensitivity ► reconstruction efficiency ► Digitization and response nonuniformity impact  moving towards final and realistic geometry

21. Fitting the cluster ► first approximation  see simple reconstruction for details ► χ 2 minimization ► Fitter  TFitterMinuit ► shower shape E pred  shower library (CbmEcalShowerLib) ► σ 2 formula

22. Cluster finder performance before and after bug correction. Cluster size under control. bug correction. Cluster size under control.

23. χ 2 distributions χ 2 does not depend on impact angle! E=1 GeV. Middle ECAL regionE=16 GeV. Middle ECAL region Other calorimeter region

24. χ 2 distributions Shape is different, but 95% of γ have χ 2 <2 Shape is different, but 95% of γ have χ 2 <2 E=1 GeV. Middle ECAL regionE=16 GeV. Middle ECAL region

25. σ 2 formula. Free parameters ► Idea:  find c 0 and c 1 which minimize difference in χ 2 cut for different energies ► calculate χ 2 cut for each energy ► find among them χ 2 min ► choose c 0 and c 1 which minimize Σ( χ 2 cut / χ 2 min -1) 2  for each calorimeter region ► Two variables  one constraint  one free parameter Minimum Inner calorimeter region

26. σ 2 formula. Different regions Middle calorimeter regionOuter calorimeter region Optimal C 0 and C 1 is different for each region!

27. σ 2 formula. Tuning the parameters Dependency can be fitted with pol1 For each C 0 find C 1 which minimizes Σ( χ 2 cut / χ 2 min -1) 2 Middle calorimeter region

28. σ 2 formula. Tuning the parameters ► Idea: chose a different (not 95%) efficiency and look at C 1 vs C 0 dependency  They does not intersect!!! ► Shape of χ 2 is different for each energy! ► Idea (TODO): two photon separation power vs. C 0 and C 1 Middle calorimeter region

29. χ 2 reconstruction quality. Cluster with 2 maximums Middle calorimeter region. 1 clusterMiddle calorimeter region. 2 clusters χ 2 is a little bit different

30. Separation vs. C 0 ► Separation power depends weakly on C 0  3 σ cut  can be enhanced by tighten cuts ► 45% for 2 σ cut

31. Fitter requirements ► Robust reconstruction of single photons ► Two close photons case:  robust reconstruction of parameters in case two separate maximums  separation one/two photons in case of one maximum ► χ 2 criteria ► all analyzed approaches have failed to reconstruct photons energy/position correctly ► χ 2 shape should not depend on photon’s energy  same value for efficiency cut ► separation power of one/two photons in case of one maximum as a criteria  example: with 95% efficiency for clusters formed by single photon