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

October 2005K.Woźniak TIME 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

October 2005K.Woźniak TIME ‘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

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

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

October 2005K.Woźniak TIME ‘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

October 2005K.Woźniak TIME ‘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 )  cm

October 2005K.Woźniak TIME ‘ 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

October 2005K.Woźniak TIME ‘ 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

October 2005K.Woźniak TIME ‘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

October 2005K.Woźniak TIME ‘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

October 2005K.Woźniak TIME ‘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 2005K.Woźniak TIME ‘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

October 2005K.Woźniak TIME ‘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

October 2005K.Woźniak TIME ‘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

October 2005K.Woźniak TIME ‘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

October 2005K.Woźniak TIME ‘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

October 2005K.Woźniak TIME ‘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

October 2005K.Woźniak TIME ‘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

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

October 2005K.Woźniak TIME 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

October 2005K.Woźniak TIME ‘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 3D % Spec 2D+1D % Vertex det % Octagon I---0% Octagon II % Octagon III % * all errors in cm

October 2005K.Woźniak TIME ‘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) (0.022) (0.020) 4% Spec 2D+1D0.150 (0.025) (0.022) (0.030) 7% Vertex det (0.015) (0.006) 28% Octagon I (-) 50% Octagon II (0.800) 40% Octagon III (0.500) 85% * all errors in cm

October 2005K.Woźniak TIME ‘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 Spec 2 D +1 D Octagon II Octagon III The error of Z vertex  (Z vertex - Z MC ) = cm is negilgible in these calculations  (Z vertex -Z method ) is similar in real data and MC

October 2005K.Woźniak TIME ‘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

October 2005K.Woźniak TIME ‘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

October 2005K.Woźniak TIME ‘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

October 2005K.Woźniak TIME 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

October 2005K.Woźniak TIME 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

October 2005K.Woźniak TIME 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

October 2005K.Woźniak TIME 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

October 2005K.Woźniak TIME 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

October 2005K.Woźniak TIME ‘ Summary Vertex reconstruction algorithms performance: spectrometer: (from 2 tracks in the acceptance) Z v range -50  +15 cm  (X v ) =  cm,  (Y v )  cm,  (Z v ) =  cm vertex detector: (from 3 tracks in the acceptance) Z v range -20  +20 cm X v undefined,  (Y v )  cm,  (Z v ) =  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

October 2005K.Woźniak TIME ‘ 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 2005K.Woźniak TIME ‘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

October 2005K.Woźniak TIME ‘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— ——

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

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

October 2005K.Woźniak TIME ‘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 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

October 2005K.Woźniak TIME ‘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