ALICE Physics Forum, CERN - 07.03.07 Andrea Dainese 1 Vertex reconstruction in ALICE Andrea Dainese in collaboration with E.Bruna, E.Crescio, S.Gorbunov,

ALICE Physics Forum, CERN - 07.03.07 Andrea Dainese 1

Vertex reconstructionVertex reconstructionin ALICEin ALICE

Andrea Dainesein collaboration with

E.Bruna, E.Crescio, S.Gorbunov, I.Kisel,

S.Masciocchi, M.Masera, F.Prinoalie

ve, M

.Tad

el


OutlineInteraction diamond at LHC (pp)

Primary vertex reconstructions

along z with SPD tracklets

in 3D with SPD tracklets

in 3D with tracks

Secondary vertex reconstruction (heavy-flavour)

present algorithm

developments in progress


Primary vertex in pp collisionsPrimary vertex resolution affects impact param. resolution:

E-by-E vertex position reconstructed in 3D using tracks (or SPD tracklets, see talk by F.Prino)

Then, interaction diamond profile from many events in fill

Nominal spread of the diamond at LHC:

vertextrackrd )(0

2

*

2,,

,yx

bunchyxdiamond

yx

pp 14TeV nominal (ALICE) pp 14 (0.9)TeV initial Pb-Pb

3.75 m 3.75 (3.75) m 3.75 m

0.55 (10) m(+displacement)

10 (10) m 0.5 m

12 (150) m 50 (198) m 11 m

~1034 (30) cm-2s-1 ~1030 (1028-29) cm-2s-1 ~1027 cm-2s-1

yx,

diamondyx,

L

*


Algorithms for vertex reco

AliITSVertexerZ: z from SPD trackletsPROS: almost 100% efficient in triggered events;

CONS: only z; with large beam offsets has problems (loss of precision and accuracy);

AliITSVertexer3D: xyz from SPD trackletsPROS: 3D; no problem with beam offset;

CONS: not 100% efficient; cannot account for curvature;

AliVertexerTracks: xyz from tracksPROS: most precise (curvature known); gives cov matrix and 2;

CONS: can be done only after tracking;

Optimal performance by exploiting the pros of the different algorithms during event reconstruction (next slide)


Barrel Tracking & Vertex Recons.1) Vertex (x,y,z) from SPD tracklets (AliITSVertexer3D)

only z with AliITSVertexerZ when AliITSVertexer3D fails

2) Barrel Tracking

3) Compute diamond transverse profile, as mean and RMS of vertices in high-multiplicity events of each “LHC fill” ➔ stored in OCDB

4) Repeat step 1)important, to have zvtx for all events (even with one tracklet)

5) Barrel Tracking6) Vertex with tracks (AliVertexerTracks), using info on

diamond profile, taken from OCDB (in progress; not in PDC06)

final (x,y) resolution better than diamond RMS for ALL events

1st p

ass

on

sub

sam

ple

2nd p

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full

stat

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s


AliITSVertexerZ – the method

Beam axis

Layer 1

Layer 2

Build “tracklets” from SPD Clustersassociate each Cluster on layer1 to all the Clusters on layer2 within a window Δφ <0.01 rad

Calculate Zi = Z of closest approach of tracklet and nominal beam axis.

Fill a histogram of Zi with 100 m (200 in pp) bin size

define a z window (2 mm wide) around the “peak”

Calculate vertex position and errorZv = weighted average of the Zi of the tracklets in the window

after symmetrization around the peak

Error = propagation of errors on Clusters

also in case of just 1 tracklet

F.Prino, Münster


AliITSVertexer3D – the method1) Build tracklets (= straight lines) from pairs of Clusters

First selection done w.r.t. nominal beam axis

Loose selection: Δφ < 0.5 rad, DCA to beam < 2.5 cm, |zINT|<5.3 cm

2) Combine tracklet pairs and select them according to:small DCA (< 1 mm) between the two tracklets

Tracklet intersection close to beam axis (rINT < 2.5 cm )

Tracklet intersection in the diamond region (zINT< 5.3 cm)

3) Get a first estimate of the vertex from selected trackletssame vertex finder algorithm used with tracks (AliVertexerTracks)

4) Re-build trackletsSelection done w.r.t. beam position from vertex estimate in previuos step

Tight selection: Δφ < 0.01 rad, DCA to beam < 0.5 cm, |zINT - zVERT|<0.5 cm

5) Combine tracklet pairs and select them according to:small DCA (<1 mm) between the two tracklets

Tracklet intersection close to the estimated vertex (r < 0.5 cm)

Tracklet intersection in the diamond region (z < 0.5 cm)

6) Calculate the vertex using the selected tracklets

F.Prino, Münster


Vertexing with SPD: Efficiencypp 14 TeV events (PYTHIA minimum bias)

MC vertex: (0,0,0) with s = (50 m, 50 m, 5.3 cm) [*=10m]

No trigger selection

Efficiency = events with vertex / all eventsVertexer3D requires at least 2 selected tracklets

Events with just one tracklet are ≈10%

Z 3D

kPyMb 84% 75%

Non diffr. 98% 90%

SPDpp14TeV B = 0.5 T

SPDpp14TeV B = 0

Z 3D

kPyMb 84% 77%

Non diffr. 98% 92%


Vertexing with SPD: Resolutions

Resolution improved for both vertexers in last weeks

New procedure for VertexerZ Cut optimization and improved track selection for Vertexer3D

SPDpp14TeV B = 0.5 T

SPDpp14TeV B = 0

Everything working with B=0better resolution in (x,y) because tracks are straight


Vertexing with SPD:Beam offset in (x,y)

VertexerZ resolution dramatically worsens in case of large (and unknown) beam offset

The performance is completely recovered if the X,Y position of the beam is known

Vertexer3D performance not affected also in case of large and unknown beam offset

better resolutionwith large offsetdue to geom. effect


Barrel Tracking & Vertex Recons.1) Vertex (x,y,z) from SPD tracklets (AliITSVertexer3D)

only z with AliITSVertexerZ when AliITSVertexer3D fails

2) Barrel Tracking

3) Compute diamond transverse profile, as mean and RMS of vertices in high-multiplicity events of each “LHC fill” ➔ stored in OCDB

4) Repeat step 1)important, to have zvtx for all events (even with one tracklet)

5) Barrel Tracking6) Vertex with tracks (AliVertexerTracks), using info on

diamond profile, taken from OCDB final (x,y) resolution better than diamond RMS for ALL events

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2nd p

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AliVertexerTracks

Three main “tasks” implemented:TRACKS SELECTION reject secondary tracks

VERTEX FINDINGgive first estimate of vertex positionmethod: approximate tracks as straight lines and calculate the

minimum-distance point among all the tracks at once

VERTEX FITTING:give optimal estimate of the position of the vertexgive vertex covariance matrix

give a (vertex quality)


VertexerTracks::Vertex Fitter“Fast Vertex Fitting”, CMS Note 1997/051

Tracks are propagated to the point given by the vtx finder

Each track gives an independent measurement of the vertex position: a 2 is written as the sum of the single track

2s w.r.t. a generic vertex position rvtx:

where ri is the (x,y,z) position of the ith track and Vi = Wi-1 is

the cov matrix of ri, extracted from the track’s cov matrix

The solution that minimizes this 2 is analytic:

)rr( W)rr()r()r( 22ivtxi

T

iivtx

ivtxivtx

ii

ii

ivtx rWWr1

1

WV

ii

vertexvertex

covariancematrix


Easy to add “beam constraint”

Same procedure as before + constraint:

iii

iivtx

rWrVWVr bb

1

b

1

b WVV

ii

vertex

vertexcovariance

matrix

zz

yyxy

xyxx

z

y

x

wgtd

wgtd

wgtd

00

0

0

V ;r bbwhere:


VertexerTracks – the method

Primary vertex reconstruction: iterative procedureInput: interaction diamond (vtx0)

Select tracks with kITSrefit and 5 or 6 ITS clusters

1st iteration:TRACK SELECTION: |d0

r(vtx0)| < 15 d0

VERTEX FINDINGVERTEX FITTING vtx1

2nd iteration:TRACK SELECTION: |d0

r(vtx1)| < 3 d0

VERTEX FINDINGVERTEX FITTING vtx2 (final estimate)


VertexerTracks: Efficiencypp 14 TeV events (PYTHIA minimum bias)


No trigger selection

Vertex found if distance to MC vertex in (x,y) is < 1 mm

Efficiency: events with vertex found / all events

(with beam constraint; not yet in PDC, but soon)


VertexerTracks:Resolutions & Pulls

res: from gaussian fit of residuals distribution

pulls: from gaussian fit of residual/error distribution

3 track-cut

(with beam constraint; not yet in PDC, but soon)

3 track-cut


VertexerTracks: 2/ndf


New development in VertexerTracks: possibility to remove tracks

Why remove tracks?

systematic underestimate of d0 for tracks used for vertex fit

primary vertex has to be reconstructed for each D/B candidate excluding its daughters: time-consuming!

Shortcut:

our fit is a “weighted mean over tracks”

➔ can calculate ri and Wi and subtract them from rvtx and V

without recalculating the vertex from scratch

implemented in AliVertexerTracks::RemoveTrackFromVertex()

ii

ii

ivtx rWWr1

1

WV

ii


VertexerTracks w/o beam constraint(importance of event display)

tracks in TPC&ITS(≥5 pts)

problem spottedwith event display scanning(Y.Foka, M.Tadel)

trac

ks u

sed

for

vert

ex

“bad” verticesvertex

not found


VertexerTracks w/o beam constraint(importance of event display)

vertexnot found

Ladies and Gentlemen, (in)famous event #24 !Ladies and Gentlemen, (in)famous event #24 !before after


VertexerTracks- pp 0.9 TeV B = 0 = (198m,198m,7.9cm) -

pp14TeVB = 0.5 T

pp0.9TeVB = 0

SPDbarrel


x

zpu

llpu

ll

x

z

reso

lutio

n [

m]

reso

lutio

n [

m]

Secondary vertex reconstruction AliVertexerTracks::VertexForSelectedTracks()

Finder+Fitter ➔ errors ➔ heavy flvr cuts on normalized varsTest on D0K vertex: same resolution as V0 vertexer

Test on D+K in progress (E.Bruna, F.Prino) Münster


Implementation of a new vertexing package (Gorbunov, Kisel, Masciocchi)

Vertexing package based on the Kalman filterS. Gorbunov and I. Kisel, CBM-SOFT-note-2006-001, CBM-SOFT-note-2006-002

Used by HERA-B, CBM

Advanced fitting functionality included:Use of full track kinematics

Invariant mass constraint

Topological constraint (pointing to the primary)

Adapted to ALICE track format (AliESDtrack)

Tests in progress, using D0K as a benchmark


New vertexing package- resolutions and pulls on D0 vertex -

x

z

x

z

Preliminary,

Work in progress

reso

lutio

n [

m]

reso

lutio

n [

m]

pull

pull


Summary

3 complementary (not alternative) vertex reconstruction methods: all used during event reconstruction

AliITSVertexerZ: z from SPD trackletsPROS: almost 100% efficient in triggered events; error provided;

AliITSVertexer3D: xyz from SPD trackletsPROS: 3D; no problem with beam offset;

AliVertexerTracks: xyz from tracksPROS: most precise (curvature known); gives cov matrix and 2;

allows fast removal of tracks from fit; being tested for heavy-flavour vertexing (D0, D+,...): good

peformance

Kalman-filter vertex fitter on the way


EXTRA SLIDES


VertexerZ: average of residuals

Unbiased!The small bias (≈5 m) which was present in the previous releases of the code was due to a systematic error in finding the maximum of the histograms for few low multiplicity events

Corrected since Rev. 1.17 of AliITSVertexerZ.cxx


Vertexer3D: average of residuals

No apparent bias


VertexerZ vs. vertex position (II)

In events generated with AliRoot rev. after June 12th 2006 a bias (slope vs. ztrue) is observed

see Jan Fiete talk at first physics meeting on Jan 19th 2007

Major modifications in ITS geometry

ITS geometry changed to TGeo

SPD chip thickness reduced to 150 m

The bias is introduced by the SPD chip thickness

Bug found and fixed by L. Gaudichet on February 5th 2007


VertexerZ and beam offset (I)

Beam offset up to 1 cm assumed unknown

Efficiency not affectedResolution dramatically worsens with increasing beam offset


VertexerZ and beam offset (II)

Beam offset up to 1 cm assuming to know the beam position

Good performance for offsets up to 1 cm if the beam position is known


Vertexer3D and beam offset

Beam offset up to 1 cm assumed unknown

Performance maintained


Pile-upExpected interaction rate = 2×105 Hz at a luminosity of 5×1030 cm-2s-2

1 interaction every 200 bunch crossings

In case of SPD strobe duration of 100 ns 4 bunch crossings (0.02 interactions)

All events in the strobe are overlapped even if not belonging to the same bunch-cross

Caveat: high- multiplicity triggers will select piled-up events

First check on AliITSVertexerZ in the case of pile-up“Manual merging” of recpoints with an “ad hoc” macro

Results:Vertices with distances >600 μm: the vertex of the event with higher multiplicity is found

Vertices with distances <600 μm: an intermediate value of z is found

Under study: check if the vertexer can be used to “detect” the pile-up, searching for two peaks (possible in the case of well separated peaks)

Study to be performed also on the Vertexer3D


VertexerTracks: Efficiency for triggered events

pp 14 TeV events (PYTHIA minimum bias)


Select triggered events: [ (V0A or V0C) and SPDFO ]

Vertex found if distance to MC vertex in (x,y) is < 1 mm

Efficiency: events with vertex found / triggered events

(with beam constraint)

triggeredminimum bias


Performance w/o beam constraint(as in PDC events)

with constraint without constraint


Residuals vs zMC

Small bias in zrec (“pulled towards z=0”)

Larger bias observed in vertex with SPD (see talk by F.Prino)

It was due to bug in the SPD geometry, introduced in September, now corrected

However, for large z there can be acceptance-induced bias

AliVertexerTracks


New development: possibility to remove (add) tracksOne-shot fit procedure

Select tracks with kITSrefit and 5 or 6 ITS clusters

Prpogate them to diamond centre (vtxmean)

TRACKS SELECTION: |d0r(vtxmean)| < 3 d0

VERTEX FITTING

standard procedure one-shot fitOK!


Efficiencies vs zMC

VertexerZ(all events)

VertexerTracks(triggered events)

even

ts w

ith v

erte

x / a

ll ev

ents

even

ts w

ith v

erte

x / t

rigge

red

even

ts

Documents

ALICE Physics Forum, CERN - 07.03.07 Andrea Dainese 1 Vertex reconstruction in ALICE Andrea Dainese in collaboration with E.Bruna, E.Crescio, S.Gorbunov,