Charged Particle Reconstruction in HIC Detectors

Transcription

1 Charged Particle Reconstruction in HIC Detectors Ralf-Arno Tripolt, Qiyan Li [ H-QM Lecture Week on Introduction to Heavy Ion Physics Kloster Marienburg/Mosel, 7-11 May May 2012 TU Darmstadt Ralf-Arno Tripolt 1

2 Introduction particles to be reconstructed: I 8000 charged particles per unit rapidity in central Pb-Pb collisions I particles travel a distance L = βγ c τ before decaying. Particles with τ? s live long enough to travel (partially) through the detector: e±, µ±, π ±, K ±, K 0, p, n, γ, ν [ 9 May 2012 TU Darmstadt Ralf-Arno Tripolt 2

3 Outline I track reconstruction overview I track finding strategies: Kalman filtering I primary vertex reconstruction I track reconstruction in the TPC I track reconstruction in the ITS I secondary vertex and cascade reconstruction 9 May 2012 TU Darmstadt Ralf-Arno Tripolt 3

4 Overview - track reconstruction (I) in the beginning was light in the TPC: start from the best tracker device which is the TPC and from the outer radius where track density is minimal track candidates, seeds, are found by assigning small number of clusters new clusters at smaller TPC radii are associated with the track using Kalman filtering the ITS takes over: ITS tracker tries to prolong the TPC tracks to the primary vertex ITS clusters are assigned to the tracks left-over ITS clusters are reconstructed and tracking is restarted from vertex back to outer wall of TPC 9 May 2012 TU Darmstadt Ralf-Arno Tripolt 4

5 Overview - track reconstruction (II) other detectors are included: once the outer radius of the TPC is reached, the precision of the estimated track parameters is sufficient to extrapolate the tracks to TRD, TOF, HMPID and PHOS finally: all the tracks are refitted using Kalman filtering backwards to the primary vertex (or secondary vertices) [ 9 May 2012 TU Darmstadt Ralf-Arno Tripolt 5

6 Overview - High-Level Trigger (HLT) the network does the work: HLT combines and processes the full information from all major detectors of ALICE in a large computer cluster selects relevant part of incoming data and reduces data volume complete event can be reconstructed [ 9 May 2012 TU Darmstadt Ralf-Arno Tripolt 6

7 2 track finding strategies global methods: all track measurements are treated simultaneously decision to include or exclude measurement is taken when all the information about the track is known local methods (Kalman filtering): track parameters are always estimated locally, don t need knowledge of global track model decision to accept or reject measurement is made using local information [ 9 May 2012 TU Darmstadt Ralf-Arno Tripolt 7

8 Kalman Filtering (I) quite general and powerful method for statistical estimations and predictions assumptions: underlying system is a linear dynamical system which is determined at time t k by state vector x k which varies with time according to deterministic (known) function f k : x k = f k (x k 1 ) + ε k noise terms (ε k ) and measurements have a Gaussian distribution: ( ε k = 0) principle is a two step process: prediction step: Kalman filter produces estimates of the current state variables, along with their uncertainties update or filtering step: new measurement is made and estimates are updated, with more weight on estimates with higher certainty 9 May 2012 TU Darmstadt Ralf-Arno Tripolt 8

9 Kalman Filtering (II) [ 9 May 2012 TU Darmstadt Ralf-Arno Tripolt 9

10 Kalman Filtering (III) - example application [ 9 May 2012 TU Darmstadt Ralf-Arno Tripolt 10

11 Primary-vertex reconstruction - ITS (I) primary vertex: is found using the clusters reconstructed in the Silicon Pixel Detector precision is 5 µm in beam and 25 µm in transverse direction (one order of magnitude worse for pp collisions) 9 May 2012 TU Darmstadt Ralf-Arno Tripolt 11

12 Primary-vertex reconstruction - ITS (II) algorithm: distribution of z coordinates measured by SPD gives approximated value z 0 v ± z of vertex coordinate confidence region given by z = a + bz 0 v + c(z0 v )2 final vertex position found by using points z 1 and z 2 which give z 0 within confidence region z combinatorical background further reduced by cut on ϕ = ϕ 2 ϕ May 2012 TU Darmstadt Ralf-Arno Tripolt 12

13 Primary-vertex reconstruction - ITS Distribution of z v for a central Pb-Pb collision fitted to a sum of a constant and a Gaussian function f (z v ) = B + Y exp [ (z v z found ) 2 /2σ 2 z ] 9 May 2012 TU Darmstadt Ralf-Arno Tripolt 13

14 Primary-vertex reconstruction - ITS transverse plane similar approach as for z-axis: linear track approximation reasonable since SPD radii are small (4 and 7 cm) points selected that give intersection with z axis wihtin 4σ z around z v and ϕ 0.1 vertex coordinates X, Y found by looking at distribution of (x 1, y 1 )-(x 2, y 2 ) lines 9 May 2012 TU Darmstadt Ralf-Arno Tripolt 14

15 Track reconstruction in the TPC (I) cluster finding: before reconstructing the tracks, two dimensional clusters in pad row-time are found position of cluster is reconstructed as its centre of gravity 9 May 2012 TU Darmstadt Ralf-Arno Tripolt 15

16 Track reconstruction in the TPC (II) cluster unfolding: since occupancies reach 40% in the inner sectors of the TPC and 20% in the outer sectors, clusters from different tracks may overlap clusters are unfolded using fast spline method, assuming that tracks have same r.m.s, i.e. same angle 9 May 2012 TU Darmstadt Ralf-Arno Tripolt 16

17 Track reconstruction in the TPC (III) seed finding: 2 strategies: with or without primary vertex constraint search for pairs of points ( 20) in TPC which can project to primary vertex if clusters in between are found, helix is used as initial track approximation Kalman filter starts from outer to inner pad row if half the points are associated to the track candidate, seed is saved 9 May 2012 TU Darmstadt Ralf-Arno Tripolt 17

18 Track reconstruction in the TPC (IV) seed finding: 2 strategies: with or without primary vertex constraint search for pairs of points ( 20) in TPC which can project to primary vertex if clusters in between are found, helix is used as initial track approximation Kalman filter starts from outer to inner pad row if half the points are associated to the track candidate, seed is saved number of clusters associated with a track, per pad row 9 May 2012 TU Darmstadt Ralf-Arno Tripolt 18

19 Track reconstruction in the ITS (I) ITS reconstruction software tries to find prolongation for all the tracks in the TPC using Kalman filtering clusters in the ITS: one-dimensional clusters on the P and N sides of the SSD are localized two sides are combined creating two-dimensional space points for the SPD, a cluster is a group of neighbouring activated pixels 9 May 2012 TU Darmstadt Ralf-Arno Tripolt 19

20 Track reconstruction in the ITS (II) tracks in the ITS: track finding starts with TPC-ITS matching difficult due to large distance and high track density in ITS first, all reasonable hits are assigned to the track: hypothesis tree most probable track is chosen, using least χ 2 etc. 9 May 2012 TU Darmstadt Ralf-Arno Tripolt 20

21 Track reconstruction in the ITS - Distribution of the number of wrong clusters per track (left) and per layer (right) 9 May 2012 TU Darmstadt Ralf-Arno Tripolt 21

22 Track reconstruction in the ITS - 2 ways of assigning hits to a track asymmetric algorithm: hits cannot be shared by different tracks hits are assigned to track with smallest track position uncertainty symmetric algorithm: hits can be shared between two tracks hits are assigned to track with smallest track position uncertainty with biggest probability 9 May 2012 TU Darmstadt Ralf-Arno Tripolt 22

23 stand-alone ITS track finding - high-p t (left) and low-p t (right) 9 May 2012 TU Darmstadt Ralf-Arno Tripolt 23

24 Secondary vertex reconstruction V 0 and cascade finding procedure: start with selection of secondary tracks tracks which have too small impact parameter with respect to primary vertex are eliminated pairs rejected if distance of closest approach (DCA) is too large momentum of the V 0 candidate has to point back to primary vertex 9 May 2012 TU Darmstadt Ralf-Arno Tripolt 24

25 Cascade reconstruction Ξ π Λ 0 π π p Ω K Λ 0 K π p cascade finding procedure: looking for V 0 candidates with large impact parameter b V 0 to reduce background (they come from cascade decay and don t have to point to primary vertex) V 0 candidates are combined with possible secondary tracks (bachelor candidates) cascade candidate has to point back to primary vertex 9 May 2012 TU Darmstadt Ralf-Arno Tripolt 25

26 Summary Kalman filtering primary vertex reconstruction track reconstruction in the TPC track reconstruction in the ITS secondary vertex and cascade reconstruction 9 May 2012 TU Darmstadt Ralf-Arno Tripolt 26