october 2005k.woźniak time 20051 ‘ vertex reconstruction algorithms in the phobos experiment at...

October 2005 K.Woźniak TIME 2005 1

‘

Vertex Reconstruction Algorithms

in the PHOBOS Experiment

at RHIC

Krzysztof Woźniak

for the PHOBOS Collaboration

Institute of Nuclear Physics

Polish Academy of Sciences

Kraków


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 BROOKHAVEN NATIONAL LABORATORYINSTITUTE OF NUCLEAR PHYSICS PAN, KRAKOW MASSACHUSETTS INSTITUTE OF TECHNOLOGY

NATIONAL CENTRAL UNIVERSITY, TAIWAN UNIVERSITY OF ILLINOIS AT CHICAGOUNIVERSITY OF MARYLAND UNIVERSITY OF ROCHESTER

‘ Collaboration


‘ 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 sNN = 200 GeV


‘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


‘ PHOBOS Detector Subsystems

vertex detector spectrome

ter

octagon


‘Subsystems Used in Vertex Reconstruction

• spectrometer

(x, y, z)

• vertex detector

(-, y, z)

• multiplicity detector (octagon)

(-, -, z)

• trigger detectors

(-, -, z)


‘ 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


‘ Spectrometer

• 8 first layers of spectrometer used for vertex reconstruction

• silicon sensors with pads 1x1 mm2 and 0.427x6 mm2

• negligibly small magnetic field – straight line tracks reconstructed

• track direction in 3D is well determined

Reconstruction

error (Zv) 0.2-0.3 cm


‘ Spectrometer – 3D Method

Straight line part of reconstructed tracks used to calculate common vertex of all tracks in 3D

• find approximate vertex position minimizing sum of distances

• reject tracks too far from approximate vertex

• repeat fit using only „good” tracks

Z - X


‘ Spectrometer – 2D + 1D MethodUses 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


‘ 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


‘ 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


‘ 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??



Zv = -13 cm

Zv = 15 cm

Zv = 0 cm

• hit density largest close to the vertex position

• the error > 5 cm


‘ 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


‘ 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 calculationsE = ~ 1.2

MIP

E = ~3 MIPE = ~6

MIP E = ~15 MIP E = ~30

MIP



Calibration of Zhit-Zv distance and the width of the distribution

(Zhit-Zv) < 15 cm

Reconstruction

error (Zv) 1 cm


‘ 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


‘ 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



‘ 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



Results of vertex reconstruction

for Au+Au collisions

at sNN = 200 GeV

‘ Results


• 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 GeVOctagonVertexSpectromet

er

Z < 3 cmZ < 0.2 cm

Z < 0.2


‘Vertex Reconstruction Accuracy |Zv| < 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 (Xv) (Yv) (Zv) efficiency

Spec 3D 0.015 0.022 0.020 100%

Spec 2D+1D 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


‘Vertex Reconstruction Accuracy |Zv| < 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 (Xv) (Yv) (Zv) efficiency

Spec 3D 0.350 (0.015) 0.100 (0.022) 0.300 (0.020) 4%

Spec 2D+1D 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


‘ 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(Zmethod- Zvertex) [cm]

MC real data

Spec 3D 0.029 0.028

Spec 2D+1D 0.044 0.045

Octagon II 0.59 0.55

Octagon III 0.44 0.36The error of Zvertex (Zvertex- ZMC) = 0.007 cm is negilgible in these calculations

(Zvertex-Zmethod)

is similar in real data and MC


‘Reconstruction Efficiency |Zv| < 10 cm

primaries = number of all charged primary particles with hits

Z < 0.5 cm

Z < 0.5 cm

Z < 3 cm

Z < 0.5 cm

Spectrometer 3D

Spectrometer 2D+ 1D

Vertex Octagon



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 3D

Spectrometer 2D+ 1D

Vertex



Octagon III method efficiently reconstructs vertices in events with > 10 primary tracks

Other methods need > 40 primary tracks

Z < 3 cmOctagon III

Octagon II

Octagon I

primaries = number of charged primary particles in octagon acceptance,

about 35% of events in the range shown


Results of vertex reconstruction

• for Au+Au collisions at sNN = 19.6 GeV

• for Cu+Cu collisions at sNN = 200 GeV

• for d+Au collisions at sNN = 200 GeV

• for p+p collisions at sNN = 200 GeV

‘ Results – Different Energy or Beams




‘ Acceptance in Z - Au+Au 19.6 GeVOctagonVertexSpectromet

er

Z < 3 cm

Z < 0.2 cm

Z < 0.2




‘ Acceptance in Z - Cu+Cu 200 GeVOctagonVertexSpectromet

er

Z < 3 cm

Z < 0.2 cm

Z < 0.2




‘ Acceptance in Z - d+Au 200 GeVOctagonVertexSpectromet

er

Z < 3 cmZ < 0.2 cm

Z < 0.2




‘ Acceptance in Z - p+p 200 GeVOctagonVertexSpectromet

er

Z < 3 cmZ < 0.2 cm

Z < 0.2


‘ 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, Yv undefined, (Zv) = 0.5 1.1 cm


‘ 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


‘ Tracking in Spectrometer

x10 cm

1

2

By

z

Bea

m

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


‘Particle Identification in Spectrometer

Particle identification based on dE/dx measurements in Si sensors

(resolution 7%)Positive charges

Negative charges

pK+

+

p

K—

—


‘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 – 0.60.25 – 0.8 0.10 – 0.50.20 – 0.7 0.15 – 0.9

y pT (GeV/c)

K

p,p

Reversible 2T magnetic fieldTwo symmetric spectrometer arms

B=2T


‘ Tracking in Spectrometer – High pT

Acceptance Momentum resolution


‘ Particles with Very Low pT

Mass measurements

(‘energy-range’ method)

Cuts on dE/dx per plane mass hypothesis

X[c

m] AB

CDE F

Z[cm]

Beam pipe

0 10 20

0

10

20

Z [cm]

Search for particles stopping in

the 5th spectrometer plane

A B C D E

dE

/dx

Ek= 8 MeV

P Ek=21 MeV

K Ek=19 MeV

Cuts on Eloss (Ek=kinetic energy)

momentum hypothesis

• Eikin=dEi+dEi+1+dEi+2…

• Mip = dE/dxi * Ei

kin m (1/2) ( m2)

Corrections acceptance, efficiency absorption, background

silicon plane

MC


‘ Particles with Very Low pT

Test of the method:

Reconstruction of lowmomentum MC particles

Au+Au sNN=200 GeV 15% central

MC

p+p

K++K–

++ DATA

october 2005k.woźniak time 20051 ‘ vertex reconstruction algorithms in the phobos experiment at...

Documents

woniak time

z vertex detector

common vertex

approximate vertex position

vertex position range

specialized vertex detectork

reconstructed tracks

pairs of tracks