1. Vertex reconstruction in ALICE
Andrea Dainese
in collaboration with
E.Bruna, E.Crescio, S.Gorbunov, I.Kisel,
S.Masciocchi, M.Masera, F.Prino
alieve, M.Tadel
ALICE Physics Forum, CERN Andrea Dainese

2. Outline Interaction 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
ALICE Physics Forum, CERN Andrea Dainese

3. Primary vertex in pp collisions
Primary 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:
pp 14TeV nominal (ALICE)
pp 14 (0.9)TeV initial
Pb-Pb
3.75 mm
3.75 (3.75) mm
0.55 (10) m
(+displacement)
10 (10) m
0.5 m
12 (150) mm
50 (198) mm
11 mm
~1034 (30) cm-2s-1
~1030 ( ) cm-2s-1
~1027 cm-2s-1
ALICE Physics Forum, CERN Andrea Dainese

4. Algorithms for vertex reco
AliITSVertexerZ: z from SPD tracklets
PROS: almost 100% efficient in triggered events;
CONS: only z; with large beam offsets has problems (loss of precision and accuracy);
AliITSVertexer3D: xyz from SPD tracklets
PROS: 3D; no problem with beam offset;
CONS: not 100% efficient; cannot account for curvature;
AliVertexerTracks: xyz from tracks
PROS: most precise (curvature known); gives cov matrix and c2;
CONS: can be done only after tracking;
Optimal performance by exploiting the pros of the different algorithms during event reconstruction (next slide)
ALICE Physics Forum, CERN Andrea Dainese

5. Barrel Tracking & Vertex Recons.
Vertex (x,y,z) from SPD tracklets (AliITSVertexer3D)
only z with AliITSVertexerZ when AliITSVertexer3D fails
Barrel Tracking
Compute diamond transverse profile, as mean and RMS of vertices in high-multiplicity events of each “LHC fill” ➔ stored in OCDB
Repeat step 1)
important, to have zvtx for all events (even with one tracklet)
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
on subsample
1st pass
2nd pass
full statistics
ALICE Physics Forum, CERN Andrea Dainese

6. AliITSVertexerZ – the method
F.Prino, Münster
Build “tracklets” from SPD Clusters
associate 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 mm (200 in pp) bin size
define a z window (2 mm wide) around the “peak”
Calculate vertex position and error
Zv = 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
Layer 2
Layer 1
Beam axis
ALICE Physics Forum, CERN Andrea Dainese

7. AliITSVertexer3D – the method
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
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)
Get a first estimate of the vertex from selected tracklets
same vertex finder algorithm used with tracks (AliVertexerTracks)
Re-build tracklets
Selection 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
small DCA (<1 mm) between the two tracklets
Tracklet intersection close to the estimated vertex (Dr < 0.5 cm)
Tracklet intersection in the diamond region (Dz < 0.5 cm)
Calculate the vertex using the selected tracklets
F.Prino, Münster
ALICE Physics Forum, CERN Andrea Dainese

8. Vertexing with SPD: Efficiency
pp 14 TeV events (PYTHIA minimum bias)
MC vertex: (0,0,0) with ss = (50 mm, 50 mm, 5.3 cm) [b*=10m]
No trigger selection
Efficiency = events with vertex / all events
Vertexer3D requires at least 2 selected tracklets
Events with just one tracklet are ≈10%
SPD
pp14TeV B = 0.5 T
SPD
pp14TeV B = 0 Z 3D
kPyMb
84%
75%
Non diffr.
98%
90% Z 3D
kPyMb
84%
77%
Non diffr.
98%
92%
ALICE Physics Forum, CERN Andrea Dainese

9. Vertexing with SPD: Resolutions
pp14TeV B = 0.5 T
SPD
pp14TeV B = 0
Resolution improved for both vertexers in last weeks
New procedure for VertexerZ
Cut optimization and improved track selection for Vertexer3D
Everything working with B=0
better resolution in (x,y) because tracks are straight
ALICE Physics Forum, CERN Andrea Dainese

10. 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 resolution
with large offset
due to geom. effect
ALICE Physics Forum, CERN Andrea Dainese

11. Barrel Tracking & Vertex Recons.
Vertex (x,y,z) from SPD tracklets (AliITSVertexer3D)
only z with AliITSVertexerZ when AliITSVertexer3D fails
Barrel Tracking
Compute diamond transverse profile, as mean and RMS of vertices in high-multiplicity events of each “LHC fill” ➔ stored in OCDB
Repeat step 1)
important, to have zvtx for all events (even with one tracklet)
Vertex with tracks (AliVertexerTracks), using info on diamond profile, taken from OCDB
final (x,y) resolution better than
diamond RMS for ALL events
on subsample
1st pass
2nd pass
full statistics
ALICE Physics Forum, CERN Andrea Dainese

12. AliVertexerTracks Three main “tasks” implemented: TRACKS SELECTION
reject secondary tracks
VERTEX FINDING
give first estimate of vertex position
method: 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 vertex
give vertex covariance matrix
give a c2 (vertex quality)
ALICE Physics Forum, CERN Andrea Dainese

13. 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 c2 is written as the sum of the single track c2s 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 c2 is analytic:
vertex
covariance
matrix
vertex
ALICE Physics Forum, CERN Andrea Dainese

14. Easy to add “beam constraint”
Same procedure as before + constraint:
vertex
vertex
covariance
matrix
where:
ALICE Physics Forum, CERN Andrea Dainese

15. VertexerTracks – the method
Primary vertex reconstruction: iterative procedure
Input: interaction diamond (vtx0)
Select tracks with kITSrefit and 5 or 6 ITS clusters
1st iteration:
TRACK SELECTION: |d0rf(vtx0)| < 15  sd0
VERTEX FINDING
VERTEX FITTING  vtx1
2nd iteration:
TRACK SELECTION: |d0rf(vtx1)| < 3  sd0
VERTEX FITTING  vtx2 (final estimate)
ALICE Physics Forum, CERN Andrea Dainese

16. VertexerTracks: Efficiency
pp 14 TeV events (PYTHIA minimum bias)
MC vertex: (0,0,0) with ss = (50 mm, 50 mm, 5.3 cm) [b*=10m]
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)
ALICE Physics Forum, CERN Andrea Dainese

17. VertexerTracks: Resolutions & Pulls
res: from gaussian fit of residuals distribution
pulls: from gaussian fit of residual/error distribution
3s track-cut
3s track-cut
(with beam constraint; not yet in PDC, but soon)
ALICE Physics Forum, CERN Andrea Dainese

18. VertexerTracks: c2/ndf
ALICE Physics Forum, CERN Andrea Dainese

19. 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()
ALICE Physics Forum, CERN Andrea Dainese

20. VertexerTracks w/o beam constraint (importance of event display)
problem spotted
with event display scanning
(Y.Foka, M.Tadel)
tracks used for vertex
“bad”
vertices
vertex
not found
tracks in TPC&ITS(≥5 pts)
ALICE Physics Forum, CERN Andrea Dainese

21. VertexerTracks w/o beam constraint (importance of event display)
Ladies and Gentlemen, (in)famous event #24 !
before
after
vertex
not found
ALICE Physics Forum, CERN Andrea Dainese

22. VertexerTracks - pp 0.9 TeV B = 0 s = (198mm,198mm,7.9cm) -
B = 0.5 T
pp0.9TeV
B = 0
SPD
barrel
ALICE Physics Forum, CERN Andrea Dainese

23. Secondary vertex reconstruction AliVertexerTracks::VertexForSelectedTracks()
Finder+Fitter ➔ errors ➔ heavy flvr cuts on normalized vars
Test on D0Kp vertex: same resolution as V0 vertexer
Test on D+Kpp in progress (E.Bruna, F.Prino) x z
resolution [mm] x z
pull
Münster
ALICE Physics Forum, CERN Andrea Dainese

24. Implementation of a new vertexing package (Gorbunov, Kisel, Masciocchi)
Vertexing package based on the Kalman filter
S. Gorbunov and I. Kisel, CBM-SOFT-note , CBM-SOFT-note
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 D0Kp as a benchmark
ALICE Physics Forum, CERN Andrea Dainese

25. New vertexing package - resolutions and pulls on D0 vertex -
resolution [mm]
Preliminary,
Work in progress z z
pull
resolution [mm]
ALICE Physics Forum, CERN Andrea Dainese

26. Summary
3 complementary (not alternative) vertex reconstruction methods: all used during event reconstruction
AliITSVertexerZ: z from SPD tracklets
PROS: almost 100% efficient in triggered events; error provided;
AliITSVertexer3D: xyz from SPD tracklets
PROS: 3D; no problem with beam offset;
AliVertexerTracks: xyz from tracks
PROS: most precise (curvature known); gives cov matrix and c2; allows fast removal of tracks from fit;
being tested for heavy-flavour vertexing (D0, D+,...): good peformance
Kalman-filter vertex fitter on the way
ALICE Physics Forum, CERN Andrea Dainese

27. EXTRA SLIDES
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28. VertexerZ: average of residuals
Unbiased!
The small bias (≈5 mm) 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 of AliITSVertexerZ.cxx
ALICE Physics Forum, CERN Andrea Dainese

29. Vertexer3D: average of residuals
No apparent bias
ALICE Physics Forum, CERN Andrea Dainese

30. 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 mm
The bias is introduced by the SPD chip thickness
Bug found and fixed by L. Gaudichet on February 5th 2007
ALICE Physics Forum, CERN Andrea Dainese

31. VertexerZ and beam offset (I)
Beam offset up to 1 cm assumed unknown
Efficiency not affected
Resolution dramatically worsens with increasing beam offset
ALICE Physics Forum, CERN Andrea Dainese

32. 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
ALICE Physics Forum, CERN Andrea Dainese

33. Vertexer3D and beam offset
Beam offset up to 1 cm assumed unknown
Performance maintained
ALICE Physics Forum, CERN Andrea Dainese

34. Pile-up
Expected 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
ALICE Physics Forum, CERN Andrea Dainese

35. VertexerTracks: Efficiency for triggered events
pp 14 TeV events (PYTHIA minimum bias)
MC vertex: (0,0,0) with ss = (50 mm, 50 mm, 5.3 cm) [b*=10m]
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
minimum bias
triggered
(with beam constraint)
ALICE Physics Forum, CERN Andrea Dainese

36. Performance w/o beam constraint (as in PDC events)
with constraint
without constraint
ALICE Physics Forum, CERN Andrea Dainese

37. Residuals vs zMC AliVertexerTracks
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
ALICE Physics Forum, CERN Andrea Dainese

38. New development: possibility to remove (add) tracks
One-shot fit procedure
Select tracks with kITSrefit and 5 or 6 ITS clusters
Prpogate them to diamond centre (vtxmean)
TRACKS SELECTION: |d0rf(vtxmean)| < 3  sd0
VERTEX FITTING
standard procedure
one-shot fit
OK!
ALICE Physics Forum, CERN Andrea Dainese

39. Efficiencies vs zMC VertexerZ VertexerTracks (all events)
events with vertex / triggered events
events with vertex / all events
VertexerZ
(all events)
VertexerTracks
(triggered events)
ALICE Physics Forum, CERN Andrea Dainese