Vertex reconstruction with tracks

1
Vertex reconstructionwith tracks

• Andrea Dainese
• INFN Legnaro
• in collaboration with
• E.Bruna, E.Crescio, M.Masera, F.Prino

2
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

3
Barrel Tracking Vertex Recons.

• ITS local reconstruction (? RecPoints)
• Vertex (x,y,z) from SPD tracklets
• Compute diamond transverse profile, as mean and
  RMS of vertices in high-multiplicity events of
  each LHC fill
• Repeat zvtx with SPD starting from mean (x,y)
• important, to have zvtx for all events (even with
  one tracklet), w/o bias
• Barrel Tracking
• Vertex with tracks, using info on diamond profile
• final (x,y) resolution better than diamond RMS
  for ALL events

1st pass on subsample
2nd pass full statistics
4
Vertex reconstruction with tracks
AliVertexerTracks

• Three main tasks implemented
• TRACKS SELECTION
• reject secondary tracks
• VERTEX FINDING
• give first estimate of vtx position
• VERTEX FITTING
• give optimal estimate of the position of the
  vertex
• give vertex covariance matrix
• give a c2 (vertex quality)

5
Tracks Selection

• Idea use primary tracks for vertex
  reconstruction
• Only tracks with 5 or 6 points in ITS
• Select primary tracks on the basis of their d0
• Cut d0 lt n?sd0(pt)
• sd0(pt) svtx ? strack(pt)

from tracks covariance matrix
6
Vertex Finder

• Aim get a first estimate of the vertex position
  in (x,y) to be used as a starting point for
  vertex fitter
• 3(2) different algorithms available (dev. by
  E.Bruna, F.Prino)
• fAlgo 1 or 2 ? approximate tracks as straight
  lines and calculate the minimum-distance point
  among all the tracks at once, with or without
  weighting the tracks
• fAlgo 3 ? average among DCA points of all
  possible pairs of tracks treated as Helices
• fAlgo 4 or 5 ? average among DCA points of all
  possible pairs of tracks approximated as straight
  lines , with or without weighting the tracks
• Default fAlgo1 (which gives the best resolution)

7
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 tracks cov matrix
• The solution that minimizes this c2 is analytic

vertex covariance matrix
vertex
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Easy to add beam constraint

• Same procedure as before constraint

vertex
vertex covariance matrix
where
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Primary vertex reco with tracksAliVertexerTracks
FindPrimaryVertex(AliESD esd)

• Primary vertex reconstruction iterative
  procedure
• Select tracks with kITSrefit and 5 or 6 ITS
  clusters
• 1st iteration
• TRACKS SELECTION d03D(vtx0) lt 5 mm
• VERTEX FINDING, (fAlgo1)
• VERTEX FITTING ? vtx1
• 2nd iteration
• TRACKS SELECTION d0rf(vtx1) lt n ? sd0
• VERTEX FINDING , (fAlgo1)
• VERTEX FITTING ? vtx2 (final estimate)
• n 3 provides optimal resolution and good cov.
  matrix (pulls 1)

10
Test sample

• 14000 pp 14 TeV events (PYTHIA min bias)
• thanks Jan Fiete!
• MC vertex (0,0,0) with ss (50 mm, 50 mm, 5.3
  cm) b10m
• AliRoot HEAD (January 16th 2007)
• Select triggered events (V0A or V0C) and SPDFO
  

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Efficiency

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

(with beam constraint)
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Residuals
x
z
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Resolutions

• Resolutions VS multiplicity (obtained from
  gaussian fit of residuals)

3s track-cut
10s track-cut
(with beam constraint)
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Pulls

• Pulls VS multiplicity (pull s of residual/error
  distribution distributions are well fitted by a
  Gaussian)

3s track-cut
10s track-cut
(with beam constraint)
15
c2/ndf
(with beam constraint)
16
Efficiency vs zMC
SPD -14 lt z lt 14 cm
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Residuals vs zMC

• Small bias in zrec (pulled towards z0)
• 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

18
Performance w/o beam constraint(as in PDC events)
without constraint
with constraint
19
Performance w/o beam constraint(as in PDC events)
problem spotted with event display
scanning (Y.Foka, M.Tadel)
tracks used for vertex
vertex not found
tracks in TPCITS(5 pts)
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Primary vertex reco with tracksAliVertexerTracks
FindPrimaryVertex(AliESD esd)

• Primary vertex reconstruction iterative
  procedure
• Select tracks with kITSrefit and 5 or 6 ITS
  clusters
• 0th iteration
• VERTEX FINDING, using track pairs (fAlgo4) ?
  vtx0
• 1st iteration
• TRACKS SELECTION d03D(vtx0) lt 5 mm
• VERTEX FINDING, (fAlgo1)
• VERTEX FITTING ? vtx1
• 2nd iteration
• TRACKS SELECTION d0rf(vtx1) lt n ? sd0
• VERTEX FINDING , (fAlgo1)
• VERTEX FITTING ? vtx2 (final estimate)
• n 3 provides optimal resolution and good cov.
  matrix (pulls 1)

21
Performance w/o beam constraint(as in PDC events)
tracks used for vertex
vertex not found
tracks in TPCITS(5 pts)
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New development possibility to remove (add)
tracks

• Why remove tracks?
• systematic underestimate of d0 of tracks used for
  vertex fit

? primary vertex has to be reconstructed for
each D/B candidate excluding its
daughters time-consuming!
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New development possibility to remove (add)
tracks

• Shortcut
• fit weighted mean over tracks
• can calculate ri and Wi and subtract them from
  rvtx and V
• need to know position at which track i was
  propagated
• this is the position given by the finder, which
  depends also on track i
• problem ...
• Solution propagate tracks at the position of the
  beam constraint and run fitter without finder
• removing a track i from the vertex will give
  mathematically the same vertex that would be
  obtained re-reconstructing the vertex with the
  tracks but i
• Need to check the performance of the vertexer
  with fit only (no finder)

24
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) lt 3 ? sd0
• VERTEX FITTING

standard procedure
one-shot fit
OK!
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Secondary vertex reconstruction
AliVertexerTracksVertexForSelectedTracks()

• FinderFitter ? errors ? heavy flvr cuts on
  normalized vars
• Test on D0?Kp vertex same resolution as V0
  vertexer

x
x
z
z
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Conclusions

• Algorithm for primary vertex reco with tracks
• selection, finder, fitter
• Use beam constraint to reject secondaries and
  improve resolution
• NEW if beam constraint available (will be the
  case with data reco), can remove/add track(s) on
  the fly
• NEW same algorithm (finderfitter) tested on
  D0?Kp vertex reco
• resolution OK pulls OK
• small problem at low pt to be fixed
• to do tests with gt2-prong decays