Primary Vertex Reconstruction Andrea Dainese Padova University and

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Primary Vertex Reconstruction Andrea Dainese Padova – University and INFN Based on work by:

Primary Vertex Reconstruction Andrea Dainese Padova – University and INFN Based on work by: A. D. , M. Masera, B. Nilsen, N. Bustreo, L. Vannucci, A. Badala’, R. Barbera, F. Riggi, G. Lo Re, A. Palemeri, G. Pappalardo, I. Belikov, E. Bruna, F. Prino ALICE PWG 1 - May 31, 2005 Andrea Dainese 1

Contents Intro: motivation LHC beams and interaction point Vertex reconstruction from pixel layers (pp

Contents Intro: motivation LHC beams and interaction point Vertex reconstruction from pixel layers (pp and Pb-Pb) Vertex reconstruction with tracks in pp ALICE PWG 1 - May 31, 2005 Andrea Dainese 2

Motivation Position of interaction vertex used in seeding and track finding in TPC and

Motivation Position of interaction vertex used in seeding and track finding in TPC and ITS Analyses on displaced decay vertices/tracks: measurement of tracks impact parameter track d 0(rf) in the direction to the track reconstruction of flight-line in space Crucial in open charm (d 0~100 m) and open beauty (d 0~500 m) detection Relevant (but less critical) for strange hadrons ALICE PWG 1 - May 31, 2005 Andrea Dainese 3

Interaction vertex at the LHC Bunch “length” will be the same for all kinds

Interaction vertex at the LHC Bunch “length” will be the same for all kinds of ions (the same for pp and Pb-Pb): sb = 7. 5 cm Position in z of the vertex: sz = sb / 2 = 5. 3 cm (cut 1 ) z coord. has to be measured E-by-E in Pb-Pb and in pp Position of the beam in (x, y) stable for a given LHC fill (few hours) centre of ‘beam spot’ as average over many events vertex resolution = size of ‘beam spot’ Size of the beam: s = 15 mm in Pb-Pb s = 15 mm in pp (L = 1031 cm-2 s-1) s = 150 mm in pp (L = 1029 cm-2 s-1) (x, y) position has to measured in pp ALICE PWG 1 - May 31, 2005 Andrea Dainese 4

Vertex from pixels z coordinate can be measured using the correlation between clusters in

Vertex from pixels z coordinate can be measured using the correlation between clusters in the 2 pixel layers Also x and y coordinates if multiplicity is larger (AA) Int. Notes by Ohio/LNL, Catania group for Pb-Pb Method (for z): pair of clusters in SPD 1 and SPD 2 straight line in (z, r) (tracklet) at r = 0, estimate of zvtx if N tracklets are used, resolution 1/ N (+ background / misallignments) N d. Nch/dy ALICE PWG 1 - May 31, 2005 Andrea Dainese 5

Pb-Pb results Catania results for ion-ion 5. 5 m @ 6000 x, y resolutions

Pb-Pb results Catania results for ion-ion 5. 5 m @ 6000 x, y resolutions ~ 25 m for d. Nch/dy~6000 ALICE PWG 1 - May 31, 2005 Andrea Dainese 6

pp results Same method as in Pb-Pb (adapted to pp by M. Masera) (z)

pp results Same method as in Pb-Pb (adapted to pp by M. Masera) (z) = 155 m ALICE PWG 1 - May 31, 2005 Andrea Dainese 7

3 D reconstruction with tracks Track reconstruction in TPC+ITS track seeding uses the position

3 D reconstruction with tracks Track reconstruction in TPC+ITS track seeding uses the position of the primary vertex: Ø (x, y) from beam position (resolution ~ 150 m) Ø z from pixels information (resolution ~ 150 m) Vertex reconstruction in 2 steps: VERTEX FINDING: using DCA for (linearized) track pairs VERTEX FITTING: Ø give optimal estimate of the position of the vertex Ø give vertex covariance matrix Ø give a c 2 ALICE PWG 1 - May 31, 2005 Andrea Dainese 8

Expected resolutions Average # rec. tracks = 7 (average on events with # >

Expected resolutions Average # rec. tracks = 7 (average on events with # > 1) Average p. T of rec. tracks = 0. 6 Ge. V/c Resolutions of track position parameters @ 0. 6 Ge. V/c: (d 0(rf)) 100 m (d 0(z)) 240 m ALICE PWG 1 - May 31, 2005 [ d 0(rf) is to the track! ] Andrea Dainese 9

Vertex Finding Algorithm Aim: get a first estimate of the vertex position in (x,

Vertex Finding Algorithm Aim: get a first estimate of the vertex position in (x, y) to be used as a starting point for vertex fitter independent of beam size improved w. r. t. beam size (hopefully) Method: 1. propagate tracks to vertex nominal position 2. calculate DCA (in space) for each possible pair of tracks (using straight line approximation) 3. get estimate of xvtx and yvtx from mean of results from all pairs ALICE PWG 1 - May 31, 2005 Andrea Dainese 10

Vertex Fitting Algorithm Use method described in CMS Note 1997/051 Tracks are propagated to

Vertex Fitting Algorithm Use method described in CMS Note 1997/051 Tracks are propagated to the point given by the vertex finder A c 2 is written as the sum of the single track c 2 s w. r. t. a generic vertex position rvtx: where Wi is track “covariance matrix in global ref. frame” The solution that minimizes this c 2 is analytic: covariance matrix vertex ALICE PWG 1 - May 31, 2005 Andrea Dainese 11

Tuning of the algorithm Criterion used to reject mismeasured and secondary tracks from the

Tuning of the algorithm Criterion used to reject mismeasured and secondary tracks from the fit: cut on the maximum contribution to the c 2 ci 2 < c 2 max if c 2 max is too low too many tracks are rejected and we loose resolution if c 2 max is too high bad or secondary tracks enter the fit and we loose resolution This cut is tuned, as a function of event multiplicity, in order to optimize the resolution ALICE PWG 1 - May 31, 2005 Andrea Dainese 12

Results: resolutions (x) = 55 m ALICE PWG 1 - May 31, 2005 (y)

Results: resolutions (x) = 55 m ALICE PWG 1 - May 31, 2005 (y) = 55 m Andrea Dainese (z) = 90 m 13

Results: pulls The covariance matrix of the vertex describes correctly the resolutions ALICE PWG

Results: pulls The covariance matrix of the vertex describes correctly the resolutions ALICE PWG 1 - May 31, 2005 Andrea Dainese 14

Results: reduced c 2 ALICE PWG 1 - May 31, 2005 Andrea Dainese 15

Results: reduced c 2 ALICE PWG 1 - May 31, 2005 Andrea Dainese 15

Resolution VS # tracks ALICE PWG 1 - May 31, 2005 Andrea Dainese 16

Resolution VS # tracks ALICE PWG 1 - May 31, 2005 Andrea Dainese 16

Results VS multiplicity ALICE PWG 1 - May 31, 2005 Andrea Dainese 17

Results VS multiplicity ALICE PWG 1 - May 31, 2005 Andrea Dainese 17

First attempt to use vertexer for D+ Kpp secondary vtx (E. Bruna, F. Prino)

First attempt to use vertexer for D+ Kpp secondary vtx (E. Bruna, F. Prino) Select “by hand” 3 tracks and just ask for the vertex (outliers rejection switched off) 3 tracks from one “true” secondary vertex 3 tracks from 3 different vertices 3 tracks from 2 different vertices ALICE PWG 1 - May 31, 2005 Andrea Dainese 18

D+ Kpp D 0 Kp ALICE PWG 1 - May 31, 2005 Andrea Dainese

D+ Kpp D 0 Kp ALICE PWG 1 - May 31, 2005 Andrea Dainese 19

Vertexing in Ali. Root Ali. ESDVertex data members: position (3 #s), covariance matrix 3

Vertexing in Ali. Root Ali. ESDVertex data members: position (3 #s), covariance matrix 3 x 3 (6 #s), c 2 (1 #), # tracks used (1 #) Ali. ITSVertexer mother class: some common methods and deal with I/O; idea inherited classes: Ø Ali. ITSVertexer. Ions: (x, y, z) from pixels in Ion-Ion (Catania) Ø Ali. ITSVertexer. Z: similar to previous but only z Ø Ali. ITSVertexer. PPZ: z from pixels in pp Ø Ali. ITSVertexer. Tracks: (x, y, z) from tracks in pp Ø Ali. ITSVertexer. Fast: (x, y, z) with smearing of true position using resolutions ALICE PWG 1 - May 31, 2005 Andrea Dainese 20

EXTRAS ALICE PWG 1 - May 31, 2005 Andrea Dainese 21

EXTRAS ALICE PWG 1 - May 31, 2005 Andrea Dainese 21

zvtx from pixels z coordinate can be measured using the correlation between clusters in

zvtx from pixels z coordinate can be measured using the correlation between clusters in the 2 pixel layers Int. Notes by Ohio/LNL, Catania group for Pb-Pb Method: pair of clusters in SPD 1 and SPD 2 straight line in (z, r) (tracklet) at r = 0, estimate of zvtx if N tracklets are used, resolution 1/ N (+ background / misallignments) N d. Nch/dy The expected resolution can be estimated as: ALICE PWG 1 - May 31, 2005 Andrea Dainese 22

“Back-of-the-envelope” calculation Exercise: estimate zvtx resolution from SPD geometry/resolution SPD 2 2 clusters 1

“Back-of-the-envelope” calculation Exercise: estimate zvtx resolution from SPD geometry/resolution SPD 2 2 clusters 1 tracklet SPD 1 PIPE BEAM (r 1 , z 1) (r 2 , z 2) (0 , z 0) r = 7 cm x/X 0 = 1% r = 4 cm r = 3 cm x/X 0 = 1% x/X 0 = 0. 3% z Estimate of zvtx: z 0 = 7/3 z 1 - 4/3 z 2 [error on r and correlation of errors Estimated error: (z 0)= 7/3 (z 1) 4/3 (z 2) in the two layers neglected] Error on z position of clusters in the pixels: (z)= RES(z) SCATTERING(z) Pixels position resolution in z is RES(z) = 120 m Contribution of multiple scattering has to be estimated. . . ALICE PWG 1 - May 31, 2005 Andrea Dainese 23

… one envelope is not enough The first principles: the RMS of the distribution

… one envelope is not enough The first principles: the RMS of the distribution of the deflection angles (proj. on a plane) for a particle of momentum p crossing a layer of thickness x is: Simplest case: particle flying perpendicular to the layers ( =p/2, p=p. T) In central Pb-Pb (HIJING): <b c p. T> 400 Me. V If the particle flyes for a distance L, the hit on the next layer will have: z. RMS L RMS For the PIPE+SPD 1+SPD 2 system we have: SPD 1 SCATTERING(z) = (r 1 -r. PIPE) RMSPIPE SPD 2 SCATTERING(z) = (r 2 -r. PIPE) RMSPIPE (r 2 -r 1) RMSSPD 1 ALICE PWG 1 - May 31, 2005 Andrea Dainese 24

If the particle has a generic polar angle : the crossed thickness increses x

If the particle has a generic polar angle : the crossed thickness increses x x/sin the flight distance to the next layer increases r r/sin the spread on z has to be projected on the layer surface z. RMS/sin SCATTERING(z)/(sin )3/2 Average value of 1/(sin )3/2 for particles that hit both SPD layers is 1. 8 We have: SPD 1: (z) = 120 m 30 m = 125 m SPD 2: (z) = 120 m 200 m = 240 m Error on z with 1 tracklet: s(z) = 430 mm ALICE PWG 1 - May 31, 2005 Andrea Dainese 25

In Pb-Pb (6000) # of good tracklets (two clusters from the same track) ~

In Pb-Pb (6000) # of good tracklets (two clusters from the same track) ~ 8000 Catania results for ion-ion 5. 5 m @ 6000 In pp the multiplicity is lower by a factor ~1000 s(zvtx) worse by a factor ~30 ALICE PWG 1 - May 31, 2005 Andrea Dainese 26