1. October 2005K.Woźniak TIME 20051 ‘ Vertex Reconstruction Algorithms in the PHOBOS Experiment at RHIC Krzysztof Woźniak for the PHOBOS Collaboration Institute of Nuclear Physics Polish Academy of Sciences Kraków

2. October 2005K.Woźniak TIME 20052 Burak Alver, Birger Back, Mark Baker, Maarten Ballintijn, Donald Barton, Russell Betts, Richard Bindel, Wit Busza (Spokesperson), Zhengwei Chai, Vasundhara Chetluru, Edmundo García, Tomasz Gburek, Kristjan Gulbrandsen, Clive Halliwell, Joshua Hamblen, Ian Harnarine, Conor Henderson, David Hofman, Richard Hollis, Roman Hołyński, Burt Holzman, Aneta Iordanova, Jay Kane,Piotr Kulinich, Chia Ming Kuo, Wei Li, Willis Lin, Constantin Loizides, Steven Manly, Alice Mignerey, Gerrit van Nieuwenhuizen, Rachid Nouicer, Andrzej Olszewski, Robert Pak, Corey Reed, Eric Richardson, Christof Roland, Gunther Roland, Joe Sagerer, Iouri Sedykh, Chadd Smith, Maciej Stankiewicz, Peter Steinberg, George Stephans, Andrei Sukhanov, Artur Szostak, Marguerite Belt Tonjes, Adam Trzupek, Sergei Vaurynovich, Robin Verdier, Gábor Veres, Peter Walters, Edward Wenger, Donald Willhelm, Frank Wolfs, Barbara Wosiek, Krzysztof Woźniak, Shaun Wyngaardt, Bolek Wysłouch ARGONNE NATIONAL LABORATORYBROOKHAVEN NATIONAL LABORATORY INSTITUTE OF NUCLEAR PHYSICS PAN, KRAKOWMASSACHUSETTS INSTITUTE OF TECHNOLOGY NATIONAL CENTRAL UNIVERSITY, TAIWANUNIVERSITY OF ILLINOIS AT CHICAGO UNIVERSITY OF MARYLANDUNIVERSITY OF ROCHESTER ‘ Collaboration

3. October 2005K.Woźniak TIME 20053 ‘Heavy Ion Collisions at RHIC large number of produced particles (>>1000) large rapidity coverage collisions of two beams – vertices spread along beam line (  1 m) central Au+Au collision at  s NN = 200 GeV

4. October 2005K.Woźniak TIME 20054 ‘Basic Concepts of PHOBOS Detector Design register produced charged particles in very large rapidity range measure precisely ~1% of particles in two arm magnetic spectrometer determine the vertex position using specialized vertex detector

5. October 2005K.Woźniak TIME 20055 ‘PHOBOS Detector Subsystems vertex detectorspectrometer octagon

6. October 2005K.Woźniak TIME 20056 ‘Subsystems Used in Vertex Reconstruction spectrometer  (x, y, z) vertex detector  (-, y, z) multiplicity detector (octagon)  (-, -, z) trigger detectors  (-, -, z)

7. October 2005K.Woźniak TIME 20057 ‘Trigger Counters Trigger system (scintilator or Cerenkov counters) is used for on-line selection of the vertex position range accuracy and efficiency of vertex determination to small to be useful for off-line reconstruction Reconstruction error  (Z v )  5 cm

8. October 2005K.Woźniak TIME 20058 ‘Spectrometer 8 first layers of spectrometer used for vertex reconstruction silicon sensors with pads 1x1 mm 2 and 0.427x6 mm 2 negligibly small magnetic field – straight line tracks reconstructed track direction in 3 D is well determined Reconstruction error  (Z v )  0.2-0.3 cm

9. October 2005K.Woźniak TIME 20059 ‘ Spectrometer – 3 D Method Straight line part of reconstructed tracks used to calculate common vertex of all tracks in 3 D find approximate vertex position minimizing sum of distances reject tracks too far from approximate vertex repeat fit using only „good” tracks Z - X

10. October 2005K.Woźniak TIME 200510 ‘ Spectrometer – 2 D + 1 D Method Uses points of closest approach for all pairs of tracks: make X-Z and Y histograms for points compatible with beam orbit find maxima of both histograms – approximate position of the vertex calculate mean values of X, Y, Z using only points close to approximate vertex Z - X

11. October 2005K.Woźniak TIME 200511 ‘Vertex Detector four layers of silicon sensors, in two pairs below and under beam pipe strips perpendicular to the beam direction, 473  m wide, 1.2 cm (inner layers) and 2.4 cm (outer layers) long, to ensure the same  angle coverage X-Y view Reconstruction error  (Z v ) < 0.2 cm

12. October 2005K.Woźniak TIME 200512 ‘Vertex Detector hypothetical tracks are extrapolated to fixed Y and histogram of Z values are created vertex position in Z = maximum of the histogram procedure is repeated for several Y values Y position is determined by selecting the Z histogram with best maximum results of vertex fit are used for quality cuts

13. October 2005K.Woźniak TIME 200513 ‘Octagonal Multiplicity Detector single layer of silicon sensors covering 110 cm along the beam pipe pads 0.27 cm long in Z, 0.87 cm long in X-Y plane (covering 32 bins in  angle) primary particles traverse only one sensor any use for vertex reconstruction??

14. October 2005K.Woźniak TIME 200514 ‘Octagonal Multiplicity Detector Z v = -13 cmZ v = 15 cmZ v = 0 cm hit density largest close to the vertex position the error > 5 cm

15. October 2005K.Woźniak TIME 200515 ‘Octagonal Multiplicity Detector Geometrical calculations: particles traverse one, two or more pads, depending on the emission angle – and thus distance of the hit from the vertex in case of multiple pad hits two ranges of vertex position are possible overlap of many hits points to the vertex For the octagonal multiplicity detector:  (Z hit -Z v )  15 cm

16. October 2005K.Woźniak TIME 200516 ‘Octagonal Multiplicity Detector energy loss  E registered in silicon depends on the length of the particle trajectory – and this on emission angle for PHOBOS octagonal multiplicity detector the uncertainty of the Z hit -Z v distance is smaller than from geometrical calculations  E = ~ 1.2 MIP  E = ~3 MIP  E = ~6 MIP  E = ~15 MIP  E = ~30 MIP

17. October 2005K.Woźniak TIME 200517 ‘Octagonal Multiplicity Detector Calibration of Z hit -Z v distance and the width of the distribution  (Z hit -Z v ) < 15 cm Reconstruction error  (Z v )  1 cm

18. October 2005K.Woźniak TIME 200518 ‘Octagon I Method for each hit two ranges of compatible vertex positions can be defined at hypothetical vertex positions the number of compatible hits is counted at the real vertex position the maximum of the histogram is expected the position of the maximum is fitted to improve it’s precision Example of three primary particles emitted at different angles which deposit different amount of energy in silicon sensors

19. October 2005K.Woźniak TIME 200519 ‘Octagon II Method for each hit two vertex positon probability distributions are defined at hypothetical vertex positions the sum of probability values is calculated at the real vertex position the maximum of the histogram is expected the maximum is accepted when it is high enough and sufficiently higher than the continuum Example of three primary particles emitted at different angles which deposit different amount of energy in silicon sensors

20. October 2005K.Woźniak TIME 200520 ‘Octagon III Method for each hit two vertex positon probability distributions are defined at hypothetical vertex positions the values of probability are multiplied at the real vertex position a distinct maximum of the histogram is expected Example of three primary particles emitted at different angles which deposit different amount of energy in silicon sensors

21. October 2005K.Woźniak TIME 200521 Results of vertex reconstruction for Au+Au collisions at  s NN = 200 GeV ‘ Results

22. October 2005K.Woźniak TIME 200522 red histogram for events with incorrectly reconstructed vertex for vertex detector such events can be rejected after comparison with Octagon results ‘Acceptance in Z – Au+Au 200 GeV OctagonVertexSpectrometer  Z < 3 cm  Z < 0.2 cm  Z < 0.2

23. October 2005K.Woźniak TIME 200523 ‘Vertex Reconstruction Accuracy |Z v | < 10 cm the most central Au+Au collisions at 200 GeV (15%) – according to the number of charged primary particles in octagonal multiplicity detector acceptance Method  (X v )  (Y v )  (Z v ) efficiency Spec 3D0.0150.0220.020100% Spec 2D+1D0.0250.0220.030100% Vertex det.-0.0150.006100% Octagon I---0% Octagon II--0.800100% Octagon III--0.500100% * all errors in cm

24. October 2005K.Woźniak TIME 200524 ‘Vertex Reconstruction Accuracy |Z v | < 10 cm the most peripheral Au+Au collisions at 200 GeV (30%) – according to the number of charged primary particles in octagonal multiplicity detector acceptance (errors for the central events are also given for comparison) Method  (X v )  (Y v )  (Z v ) efficiency Spec 3D0.350 (0.015) 0.100 (0.022) 0.300 (0.020) 4% Spec 2D+1D0.150 (0.025) 0.150 (0.022) 0.250 (0.030) 7% Vertex det.-0.030 (0.015) 0.023 (0.006) 28% Octagon I--1.000 (-) 50% Octagon II--1.300 (0.800) 40% Octagon III--1.100 (0.500) 85% * all errors in cm

25. October 2005K.Woźniak TIME 200525 ‘MC and Real Data Comparison  (Z v ) from vertex detector is the smallest – we can use it in place of real vertex position In ~50 % of Au+Au events with | Z v |< 10 all methods find vertices method  (Z method - Z vertex ) [cm] MCreal data Spec 3 D 0.0290.028 Spec 2 D +1 D 0.0440.045 Octagon II0.590.55 Octagon III0.440.36 The error of Z vertex  (Z vertex - Z MC ) = 0.007 cm is negilgible in these calculations  (Z vertex -Z method ) is similar in real data and MC

26. October 2005K.Woźniak TIME 200526 ‘Reconstruction Efficiency |Z v | < 10 cm primaries = number of all charged primary particles with hits  Z < 0.5 cm  Z < 3 cm  Z < 0.5 cm Spectrometer 3 D Spectrometer 2 D+ 1D VertexOctagon

27. October 2005K.Woźniak TIME 200527 ‘Reconstruction Efficiency |Z v | < 10 cm Spectrometer methods start to reconstruct vertex from 2 tracks Vertex method needs at least 3 tracks and is about 80% efficient from 5 tracks  Z < 0.2 cm primaries = number of charged primary particles in spectrometer or vertex acceptance (respectively) Spectrometer 3 D Spectrometer 2 D+ 1D Vertex

28. October 2005K.Woźniak TIME 200528 ‘Reconstruction Efficiency |Z v | < 10 cm Octagon III method efficiently reconstructs vertices in events with > 10 primary tracks Other methods need > 40 primary tracks  Z < 3 cm Octagon III Octagon II Octagon I primaries = number of charged primary particles in octagon acceptance, about 35% of events in the range shown

29. October 2005K.Woźniak TIME 200529 Results of vertex reconstruction for Au+Au collisions at  s NN = 19.6 GeV for Cu+Cu collisions at  s NN = 200 GeV for d+Au collisions at  s NN = 200 GeV for p+p collisions at  s NN = 200 GeV ‘ Results – Different Energy or Beams

30. October 2005K.Woźniak TIME 200530 red histogram for events with incorrectly reconstructed vertex for vertex detector such events can be rejected after comparison with Octagon results ‘Acceptance in Z - Au+Au 19.6 GeV OctagonVertexSpectrometer  Z < 3 cm  Z < 0.2 cm  Z < 0.2

31. October 2005K.Woźniak TIME 200531 red histogram for events with incorrectly reconstructed vertex for vertex detector such events can be rejected after comparison with Octagon results ‘Acceptance in Z - Cu+Cu 200 GeV OctagonVertexSpectrometer  Z < 3 cm  Z < 0.2 cm  Z < 0.2

32. October 2005K.Woźniak TIME 200532 red histogram for events with incorrectly reconstructed vertex for vertex detector such events can be rejected after comparison with Octagon results ‘Acceptance in Z - d+Au 200 GeV OctagonVertexSpectrometer  Z < 3 cm  Z < 0.2 cm  Z < 0.2

33. October 2005K.Woźniak TIME 200533 red histogram for events with incorrectly reconstructed vertex for vertex detector such events can be rejected after comparison with Octagon results ‘Acceptance in Z - p+p 200 GeV OctagonVertexSpectrometer  Z < 3 cm  Z < 0.2 cm  Z < 0.2

34. October 2005K.Woźniak TIME 200534 ‘ Summary Vertex reconstruction algorithms performance: spectrometer: (from 2 tracks in the acceptance) Z v range -50  +15 cm  (X v ) = 0.015  0.150 cm,  (Y v ) 0.022  0.150 cm,  (Z v ) = 0.020  0.250 cm vertex detector: (from 3 tracks in the acceptance) Z v range -20  +20 cm X v undefined,  (Y v ) 0.015  0.030 cm,  (Z v ) = 0.006  0.023 cm octagon: (from 6 tracks in the acceptance) Z v range -60  +60 cm X v undefined, Y v undefined,  (Z v ) = 0.5  1.1 cm

35. October 2005K.Woźniak TIME 200535 ‘ Conclusions reconstruction of the vertex in collisions of heavy nuclei is easy – due to the large number of primary particles small acceptance detectors can be used in the reconstruction without significant loss of precision the main problem is proper selection of „good” tracks, especially in the events with low multiplicities in the collider experiments single layer silicon detector can be used to obtain position of the vertex with the error smaller than 1 cm agreement of methods using different parts of the detector is necessary for rejection of poorly reconstructed vertices

36. October 2005K.Woźniak TIME 200536 ‘Tracking in Spectrometer x 10 cm 1 2 ByBy z Beam 1) find straight tracks in the field- free region 2) curved tracks found in B field by clustering in (1/p,  ) space 3) Pieces matched 4) Momentum fit using the full track, and detailed field map 5) Quality cuts, DCA cuts

37. October 2005K.Woźniak TIME 200537 ‘Particle Identification in Spectrometer Particle identification based on dE/dx measurements in Si sensors (resolution  7%) Positive charges Negative charges p K+K+ ++ p K—K— ——

38. October 2005K.Woźniak TIME 200538 ‘Identified Particles from Spectrometer Momentum resolution 1 – 2 % z -x 10 cm y 70 cm Acceptance of the spectrometer 0.35 – 1.3 0.10 – 0.6 0.25 – 0.8 0.10 – 0.5 0.20 – 0.7 0.15 – 0.9 y p T (GeV/c)  KK p,p Reversible 2T magnetic field Two symmetric spectrometer arms B=2T

39. October 2005K.Woźniak TIME 200539 ‘Tracking in Spectrometer – High p T AcceptanceMomentum resolution

40. October 2005K.Woźniak TIME 200540 ‘Particles with Very Low p T Mass measurements (‘energy-range’ method)  Cuts on dE/dx per plane mass hypothesis X[cm ] A B C D E F Z[cm] Beam pipe 0 10 20 0 10 20 Z [cm] Search for particles stopping in the 5 th spectrometer plane A B C D E dE/dx  E k = 8 MeV P E k =21 MeV K E k =19 MeV  Cuts on E loss (E k =kinetic energy) momentum hypothesis E i kin =dE i +dE i+1 +dE i+2 … M i p = dE/dx i * E i kin  m (  1/  2 ) (  m  2 )  Corrections acceptance, efficiency absorption, background silicon plane MC

41. October 2005K.Woźniak TIME 200541 ‘Particles with Very Low p T Test of the method: Reconstruction of low momentum MC particles Au+Au  s NN =200 GeV 15% central MC p+p K++K–K++K– ++ ++ DATA