Vertex Reconstruction Algorithms in the PHOBOS Experiment at

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

‘ Collaboration 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 LABORATORY INSTITUTE OF NUCLEAR PHYSICS PAN, KRAKOW NATIONAL CENTRAL UNIVERSITY, TAIWAN UNIVERSITY OF MARYLAND October 2005 BROOKHAVEN NATIONAL LABORATORY MASSACHUSETTS INSTITUTE OF TECHNOLOGY UNIVERSITY OF ILLINOIS AT CHICAGO UNIVERSITY OF ROCHESTER K. Woźniak TIME 2005 2

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

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 October 2005 K. Woźniak TIME 2005 4

‘ PHOBOS Detector Subsystems vertex detector spectromete r octagon October 2005 K. Woźniak TIME 2005 5

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

‘ 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 (Zv) 5 cm October 2005 K. Woźniak TIME 2005 7

‘ Spectrometer • 8 first layers of spectrometer used for vertex reconstruction • silicon sensors with pads 1 x 1 mm 2 and 0. 427 x 6 mm 2 • negligibly small magnetic field – straight line tracks reconstructed Reconstruction error (Zv) 0. 2 - • track direction in 3 D is well determined 0. 3 cm October 2005 K. Woźniak TIME 2005 8

‘ Spectrometer – 3 D Method Z-X 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 October tracks 2005 „good” K. Woźniak TIME 2005 9

‘ Spectrometer – 2 D + 1 D Method Uses points of closest approach for all pairs of tracks: Z-X • 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 October 2005 K. Woźniak TIME 2005 10

‘ 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 (Zv) < 0. 2 cm October 2005 K. Woźniak TIME 2005 11

‘ 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 October 2005 • results of vertex fit are used for quality cuts 12 K. Woźniak TIME 2005

‘ 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? ? October 2005 K. Woźniak TIME 2005 13

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

‘ 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: (Zhit-Zv) 15 cm October 2005 K. Woźniak TIME 2005 15

‘ 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 Zhit-Zv distance is smaller than from geometrical calculations E = ~ 1. 2 MIP E = ~3 MIP E = ~6 MIP October 2005 E = ~15 MIP E = ~30 MIP K. Woźniak TIME 2005 16

‘ Octagonal Multiplicity Detector Calibration of Zhit-Zv distance and the width of the distribution (Zhit-Zv) < 15 cm Reconstruction error (Zv) 1 cm October 2005 K. Woźniak TIME 2005 17

‘ Octagon I Method Example of three primary particles emitted at different angles which deposit different amount of energy in silicon sensors • 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 October 2005 K. Woźniak TIME 2005 18

‘ Octagon II Method Example of three primary particles emitted at different angles which deposit different amount of energy in silicon sensors • 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 October 2005 • the maximum is accepted when it is high enough and sufficiently higher than the continuum K. Woźniak TIME 2005 19

‘ Octagon III Method Example of three primary particles emitted at different angles which deposit different amount of energy in silicon sensors • 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 October 2005 K. Woźniak TIME 2005 20

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

‘ Acceptance in Z – Au+Au 200 Ge. V Spectrometer Z < 0. 2 cm Vertex Z < 0. 2 Octagon Z < 3 cm • red histogram for events with incorrectly reconstructed vertex • for vertex detector such events can be rejected after comparison with Octagon results October 2005 K. Woźniak TIME 2005 22

Vertex Reconstruction Accuracy |Zv| < 10 ‘ cm the most central Au+Au collisions at 200 Ge. V (15%) – according to the number of charged primary particles in octagonal multiplicity detector acceptance Method (Xv) (Yv) (Zv) efficiency Spec 3 D 0. 015 0. 022 0. 020 100% Spec 2 D+1 D 0. 025 0. 022 0. 030 100% Vertex det. - 0. 015 0. 006 100% Octagon I - - - 0% Octagon II - - 0. 800 100% Octagon III - - 0. 500 100% * all errors in cm October 2005 K. Woźniak TIME 2005 23

Vertex Reconstruction Accuracy |Zv| < 10 ‘ cm the most peripheral Au+Au collisions at 200 Ge. V (30%) – according to the number of charged primary particles in octagonal multiplicity (errors detector acceptance for the central events are also given for comparison) Method (Xv) (Yv) (Zv) efficiency Spec 3 D 0. 350 (0. 015) 0. 100 (0. 022) 0. 300 (0. 020) 4% Spec 2 D+1 D 0. 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 October 2005 K. Woźniak TIME 2005 24

‘ MC and Real Data Comparison (Zv) from vertex detector is the smallest – we can use it in place of real vertex position In ~50 % of Au+Au events with |Zv|< 10 all methods find vertices method Spec 3 D Spec 2 D+1 D Octagon III (Zmethod- Zvertex) [cm] MC 0. 029 0. 044 0. 59 0. 44 The error of Zvertex (Zvertex-Zmethod) is similar in real data and MC October 2005 real data 0. 028 0. 045 0. 55 0. 36 (Zvertex- ZMC) = 0. 007 cm is negilgible in these calculations K. Woźniak TIME 2005 25

‘ Reconstruction Efficiency |Zv| < 10 cm Spectrometer 3 D Spectrometer 2 D+ 1 D Z < 0. 5 cm Vertex Octagon Z < 3 cm Z < 0. 5 cm primaries = number of all charged primary particles with hits October 2005 K. Woźniak TIME 2005 26

‘ Reconstruction Efficiency |Zv| < 10 cm Spectrometer 3 D 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 Spectrometer 2 D+ 1 D Vertex primaries = number of charged primary particles in spectrometer or vertex acceptance (respectively) October 2005 K. Woźniak TIME 2005 27

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

‘ Results – Different Energy or Beams Results of vertex reconstruction • for Au+Au collisions at s. NN = 19. 6 Ge. V • for Cu+Cu collisions at s. NN = 200 Ge. V • for d+Au collisions at s. NN = 200 Ge. V October 2005 K. Woźniak TIME 2005 29

‘ Acceptance in Z - Au+Au 19. 6 Ge. V Spectrometer Z < 0. 2 cm Vertex Z < 0. 2 Octagon Z < 3 cm • red histogram for events with incorrectly reconstructed vertex • for vertex detector such events can be rejected after comparison with Octagon results October 2005 K. Woźniak TIME 2005 30

‘ Acceptance in Z - Cu+Cu 200 Ge. V Spectrometer Vertex Octagon Z < 3 cm Z < 0. 2 cm Z < 0. 2 • red histogram for events with incorrectly reconstructed vertex • for vertex detector such events can be rejected after comparison with Octagon results October 2005 K. Woźniak TIME 2005 31

‘ Acceptance in Z - d+Au 200 Ge. V Spectrometer Vertex Octagon Z < 0. 2 cm Z < 3 cm • red histogram for events with incorrectly reconstructed vertex • for vertex detector such events can be rejected after comparison with Octagon results October 2005 K. Woźniak TIME 2005 32

‘ Acceptance in Z - p+p 200 Ge. V Spectrometer Z < 0. 2 cm Vertex Z < 0. 2 Octagon Z < 3 cm • red histogram for events with incorrectly reconstructed vertex • for vertex detector such events can be rejected after comparison with Octagon results October 2005 K. Woźniak TIME 2005 33

‘ Summary Vertex reconstruction algorithms performance: spectrometer: (from 2 tracks in the acceptance) Zv range -50 +15 cm (Xv) = 0. 015 0. 150 cm, (Yv) 0. 022 0. 150 cm, (Zv) = 0. 020 0. 250 cm vertex detector: (from 3 tracks in the acceptance) Zv range -20 +20 cm Xv undefined, (Yv) 0. 015 0. 030 cm, (Zv) = 0. 006 0. 023 cm octagon: (from 6 tracks in the acceptance) Zv range -60 +60 cm Xv undefined, October 2005 Yv undefined, (Zv) = 0. 5 1. 1 cm K. Woźniak TIME 2005 34

‘ 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 October 2005 K. Woźniak TIME 2005 35

‘ Tracking in Spectrometer Beam z By 1) find straight tracks in the fieldfree region 2 1 x 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 10 cm October 2005 K. Woźniak TIME 2005 36

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

‘ Identified Particles from Spectrometer Acceptance of the spectrometer y B=2 T cm 0 7 10 cm 0. 35 – 1. 3 K 0. 25 – 0. 8 p, p 0. 20 – 0. 7 p. T (Ge. V/c) 0. 10 – 0. 6 0. 10 – 0. 5 0. 15 – 0. 9 Momentum resolution 1 – 2 % z y October 2005 -x Reversible 2 T magnetic field Two symmetric spectrometer arms K. Woźniak TIME 2005 38

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

‘ Particles with Very Low p. T X[cm] Search for particles stopping in the 5 th spectrometer plane 20 E F 10 B A D C Ø Cuts on d. E/dx per plane mass hypothesis 0 Beam pipe 0 10 20 Z [cm] MC P Ek=21 Me. V d. E/dx Mass measurements (‘energy-range’ method) K Ek=19 Me. V Z[cm] Ø Cuts on Eloss (Ek=kinetic energy) momentum hypothesis Ø Corrections acceptance, efficiency absorption, background Ek= 8 Me. V • Eikin=d. Ei+1+d. Ei+2… • Mip = d. E/dxi * Eikin m ( 1/ 2) ( m 2) A B October 2005 C D E K. Woźniak TIME 2005 silicon plane 40

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