1. Centrality Categorization and its Application to Physics Effects in High-Energy d+A Collisions Javier Orjuela-Koop University of Colorado Boulder For the PHENIX Collaboration 30 th Winter Workshop on Nuclear Dynamics Galveston, Texas April 6-12, 2014 gaveston_entertainment by optictopic CC/BY

2. Motivation Numerous physics effects can be studied in d+Au collisions. 2 30 th WWND J. Orjuela-Koop

3. Motivation Numerous physics effects can be studied in d+Au collisions. Modifications of parton distribution functions in nuclei Gluon saturation Color neutralization Collective flow in small systems (!) 2 30 th WWND J. Orjuela-Koop

4. Motivation Numerous physics effects can be studied in d+Au collisions. Modifications of parton distribution functions in nuclei Gluon saturation Color neutralization Collective flow in small systems (!) We need to characterize the event geometry! 2 30 th WWND J. Orjuela-Koop

5. Motivation Numerous physics effects can be studied in d+Au collisions. Modifications of parton distribution functions in nuclei Gluon saturation Color neutralization Collective flow in small systems (!) We need to characterize the event geometry! b Au d How to select centrality classes? How to validate the selection? Are there any bias effects? How do they affect ‘the physics’ at the GeV and TeV scales ? 2 30 th WWND J. Orjuela-Koop

6. Experiment 30 th WWND J. Orjuela-Koop PHENIX determines centrality by cutting on backward (Au-going) rapidity multiplicity. SIDE VIEW 3 TOP VIEW Au d d

7. Experiment 30 th WWND J. Orjuela-Koop PHENIX determines centrality by cutting on backward (Au-going) rapidity multiplicity. BBC Range: BBCs Vertex pos. Centrality Event timing SIDE VIEW 3 TOP VIEW Au d d

8. Experiment 30 th WWND J. Orjuela-Koop PHENIX determines centrality by cutting on backward (Au-going) rapidity multiplicity. BBC Range: ZDC Range: BBCs Vertex pos. Centrality Event timing ZDC Spectator neutrons SIDE VIEW 3 TOP VIEW Au d d

9. Centrality Categorization 30 th WWND J. Orjuela-Koop Physical Observable Charge in BBC (Au-going) Event Geometry N coll, N part, etc. Monte Carlo Glauber 4

10. Centrality Categorization 30 th WWND J. Orjuela-Koop Physical Observable Charge in BBC (Au-going) Event Geometry N coll, N part, etc. Monte Carlo Glauber Hulthén Wavefunction (deuteron) 4 http://arxiv.org/abs/1310.4793

11. Centrality Categorization 30 th WWND J. Orjuela-Koop Physical Observable Charge in BBC (Au-going) Event Geometry N coll, N part, etc. Monte Carlo Glauber Hulthén Wavefunction (deuteron) Woods-Saxon Distribution (Au) 4 http://arxiv.org/abs/1310.4793

12. Centrality Categorization 30 th WWND J. Orjuela-Koop Physical Observable Charge in BBC (Au-going) Event Geometry N coll, N part, etc. Monte Carlo Glauber Hulthén Wavefunction (deuteron) Woods-Saxon Distribution (Au) We use Monte Carlo methods to simulate d+Au collisions by sampling the position of nucleons from a Hulthén wavefunction (d) and a Woods- Saxon distribution (Au). 4 http://arxiv.org/abs/1310.4793

13. BBC Charge (Au-going) N coll Centrality Categorization 30 th WWND J. Orjuela-Koop Ok, so we know N coll and N part. How to map them to experimental observables? MinBias trigger requirement: At least one hit in both (Au-going and d-going) BBCs. 5 http://arxiv.org/abs/1310.4793 0-5% 5-10% 10-20% 20-30% 30-40%

14. BBC Charge (Au-going) N coll Centrality Categorization 30 th WWND J. Orjuela-Koop Ok, so we know N coll and N part. How to map them to experimental observables? MinBias trigger requirement: At least one hit in both (Au-going and d-going) BBCs. Fluctuations from Negative Binomial Distribution 5 http://arxiv.org/abs/1310.4793 0-5% 5-10% 10-20% 20-30% 30-40%

15. BBC Charge (Au-going) N coll Centrality Categorization 30 th WWND J. Orjuela-Koop Ok, so we know N coll and N part. How to map them to experimental observables? MinBias trigger requirement: At least one hit in both (Au-going and d-going) BBCs. Fluctuations from Negative Binomial Distribution determined from fitting experimental data. 5 http://arxiv.org/abs/1310.4793 0-5% 5-10% 10-20% 20-30% 30-40%

16. BBC Charge (Au-going) N coll Centrality Categorization 30 th WWND J. Orjuela-Koop Ok, so we know N coll and N part. How to map them to experimental observables? MinBias trigger requirement: At least one hit in both (Au-going and d-going) BBCs. Fluctuations from Negative Binomial Distribution Fold in the Glauber N coll distribution Gl(n) determined from fitting experimental data. 5 http://arxiv.org/abs/1310.4793 0-5% 5-10% 10-20% 20-30% 30-40%

17. BBC Charge (Au-going) N coll Centrality Categorization 30 th WWND J. Orjuela-Koop Ok, so we know N coll and N part. How to map them to experimental observables? MinBias trigger requirement: At least one hit in both (Au-going and d-going) BBCs. Fluctuations from Negative Binomial Distribution Fold in the Glauber N coll distribution Gl(n) determined from fitting experimental data. Trigger inefficiency for low charge! 5 http://arxiv.org/abs/1310.4793 0-5% 5-10% 10-20% 20-30% 30-40%

18. 6 Centrality Categorization 30 th WWND J. Orjuela-Koop Centrality0-20%20-40%40-60%60%-88% 15.1 ± 1.010.2 ± 0.76.6 ± 0.43.2 ± 0.2 15.2 ± 0.611.1 ± 0.67.8 ± 0.44.3 ± 0.2 13.3 ± 0.89.3 ± 0.66.2 ± 0.43.0 ± 0.2 1.95 ± 0.011.84 ± 0.011.65 ± 0.021.36 ± 0.02 http://arxiv.org/abs/1310.4793 Using Monte Carlo Glauber to map BBC multiplicity to geometry, we get numbers like…

19. 6 Centrality Categorization 30 th WWND J. Orjuela-Koop Centrality0-20%20-40%40-60%60%-88% 15.1 ± 1.010.2 ± 0.76.6 ± 0.43.2 ± 0.2 15.2 ± 0.611.1 ± 0.67.8 ± 0.44.3 ± 0.2 13.3 ± 0.89.3 ± 0.66.2 ± 0.43.0 ± 0.2 1.95 ± 0.011.84 ± 0.011.65 ± 0.021.36 ± 0.02 http://arxiv.org/abs/1310.4793 Using Monte Carlo Glauber to map BBC multiplicity to geometry, we get numbers like… What about the ZDCs? What information can they provide?

20. Checking Centrality Selection 30 th WWND J. Orjuela-Koop What if only one nucleon in the deuteron collides with the Au? Measure spectator neutron energy with d-going ZDC. Au d 7 D=4 fm D=14 fm

21. Checking Centrality Selection 30 th WWND J. Orjuela-Koop What if only one nucleon in the deuteron collides with the Au? Measure spectator neutron energy with d-going ZDC. Single Neutron Peak Double Interaction Contribution Exp. Backg. Monte Carlo Glauber Data Good agreement between data and Monte Carlo Glauber values! Au d 7 http://arxiv.org/abs/1310.4793 D=4 fm D=14 fm

22. Systematic Uncertainties 30 th WWND J. Orjuela-Koop Nucleon-nucleon inelastic cross section Woods-Saxon Au nucleus parameters Include hard-core repulsive potential Change z-vertex range BBC charge proportional to N part (not shown in plot) 8 http://arxiv.org/abs/1310.4793

23. Bias Factor Corrections 30 th WWND J. Orjuela-Koop BBC Multiplicity Event Geometry How is this mapping affected for events with charged particles at midrapidity? Invariant Yields Consider p+p @ 200 GeV BBC MB trigger fires 52% of the time BBC MB trigger fires 75% of the time for events with charged particle at midrapidity 9

24. Bias Factor Corrections 30 th WWND J. Orjuela-Koop BBC Multiplicity Event Geometry How is this mapping affected for events with charged particles at midrapidity? Invariant Yields Consider p+p @ 200 GeV BBC MB trigger fires 52% of the time BBC MB trigger fires 75% of the time for events with charged particle at midrapidity Small chance of particle production at midrapidity 9

25. Bias Factor Corrections 30 th WWND J. Orjuela-Koop BBC Multiplicity Event Geometry How is this mapping affected for events with charged particles at midrapidity? Invariant Yields Consider p+p @ 200 GeV BBC MB trigger fires 52% of the time BBC MB trigger fires 75% of the time for events with charged particle at midrapidity Small chance of particle production at midrapidity MB Trigger biased towards non-diffractive events with greater particle production at midrapidity! 9

26. Bias Factor Corrections 30 th WWND J. Orjuela-Koop What are the implications for d+Au? 10 http://arxiv.org/abs/1310.4793 N collisions 1 Biased N-1 Unbiased

27. Bias Factor Corrections 30 th WWND J. Orjuela-Koop What are the implications for d+Au? BBC charge deposition is scaled up! 10 http://arxiv.org/abs/1310.4793 N collisions 1 Biased N-1 Unbiased

28. Bias Factor Corrections 30 th WWND J. Orjuela-Koop What are the implications for d+Au? BBC charge deposition is scaled up! 0%-20%20-40%40-60%60%-88% Bias Factor Correction 0.94 ± 0.011.00 ± 0.011.03 ± 0.021.03 ± 0.006 10 http://arxiv.org/abs/1310.4793 N collisions 1 Biased N-1 Unbiased

29. Bias Factor Corrections 30 th WWND J. Orjuela-Koop Conservation of energy Change in the rapidity distribution The bias effect seems to be p T dependent. 11 http://arxiv.org/abs/1310.4793

30. 30 HIJING Study 30 th WWND J. Orjuela-Koop We use the HIJING MC Generator to simulate p+p and d+Au events @ 200 GeV HIJING results are model-dependent, but they capture the desired bias! 12

31. 31 HIJING Study 30 th WWND J. Orjuela-Koop We use the HIJING MC Generator to simulate p+p and d+Au events @ 200 GeV Data Simulation HIJING results are model-dependent, but they capture the desired bias! 12 http://arxiv.org/abs/1310.4793

32. HIJING Study at RHIC Energy 30 th WWND J. Orjuela-Koop d+Au @ 200 GeV 13

33. HIJING Study at RHIC Energy 30 th WWND J. Orjuela-Koop Glauber ModelHIJING CentralityBias Correction Factor Mean Bias Factor 1< p T <5 GeV/c 0-20%0.94 ± 0.010.951 ± 0.001 20-40%1.00 ± 0.010.996 ± 0.001 40-60%1.03 ± 0.021.010 ± 0.001 60-88%1.03 ± 0.061.030 ± 0.001 d+Au @ 200 GeV 13

34. HIJING Study at RHIC Energy 30 th WWND J. Orjuela-Koop We observe a slight p T dependence of the bias factors. Less than 5% variation. Glauber ModelHIJING CentralityBias Correction Factor Mean Bias Factor 1< p T <5 GeV/c 0-20%0.94 ± 0.010.951 ± 0.001 20-40%1.00 ± 0.010.996 ± 0.001 40-60%1.03 ± 0.021.010 ± 0.001 60-88%1.03 ± 0.061.030 ± 0.001 d+Au @ 200 GeV 13 http://arxiv.org/abs/1310.4793 Good agreement with Glauber calculation!

35. HIJING Study at LHC Energy 30 th WWND J. Orjuela-Koop p+Pb @ 5.02 TeV Large auto-correlation in p+p. Large and strongly p T -dependent bias correction factors. 14 http://arxiv.org/abs/1310.4793 HIJING

36. HIJING Study at LHC Energy 30 th WWND J. Orjuela-Koop p+Pb @ 5.02 TeV Large auto-correlation in p+p. Large and strongly p T -dependent bias correction factors. Recall Q pPb ~ 1/Bias Factor 14 http://arxiv.org/abs/1310.4793 HIJING

37. Charged Particle and E T Production 30 th WWND J. Orjuela-Koop Linear scaling with N part. Central d+Au matches peripheral Au+Au. 15 dE T /d  dN ch /d  N part

38. 16 Bjorken Energy Density 30 th WWND J. Orjuela-Koop N part

39. 16 Bjorken Energy Density 30 th WWND J. Orjuela-Koop The overlap area is centrality-dependent 0-100%0-5%20-30%40-50%70-88% 4.36 ± 0.248.0 ± 0.86.8 ± 0.44.8 ± 0.41.64 ± 0.02 6.96 ± 0.2010.8 ± 0.89.2 ± 0.47.2 ± 0.44.28 ± 0.24 N part

40. Collective Flow in d+Au 30 th WWND J. Orjuela-Koop There is recent compelling evidence for collective flow in p+Pb and d+Au. This is an example of a physics observable where comparison with theory requires an understanding of the geometry. 17

41. Collective Flow in 3 He+Au 30 th WWND J. Orjuela-Koop 3 He+Au collisions have been proposed as a test system whose intrinsic triangularity can be used to discriminate initial state effects and those from viscous damping. 18

42. Collective Flow in 3 He+Au 30 th WWND J. Orjuela-Koop 3 He+Au collisions have been proposed as a test system whose intrinsic triangularity can be used to discriminate initial state effects and those from viscous damping. 18 http://arxiv.org/abs/1312.4565

43. Summary 30 th WWND J. Orjuela-Koop We described the PHENIX methodology for selecting centrality classes. The centrality determination method is subject to inherent bias effects that can be accounted for. Bias correction factors are small for d+Au @ 200 GeV, but large and pT-dependent for p+Pb @ 5.02 TeV. There is evidence for collective flow in small systems. This is one of many physics analyses that depend on a careful characterization of the event geometry. 19

44. Thank you! 30 th WWND J. Orjuela-Koop 20

45. Backup Slides 30 th WWND J. Orjuela-Koop 21

46. Double-Interaction Study 30 th WWND J. Orjuela-Koop Double inelastic interactions result in greater BBC charge deposition. We need to account for this extra charge when categorizing centrality. 22