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Vertex reconstruction with tracks

Vertex reconstruction with tracks. Andrea Dainese INFN Legnaro in collaboration with E.Bruna, E.Crescio, M.Masera, F.Prino. Primary vertex in pp collisions. Primary vertex resolution affects impact param. resolution :

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Vertex reconstruction with tracks

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  1. Vertex reconstructionwith tracks Andrea Dainese INFN Legnaro in collaboration with E.Bruna, E.Crescio, M.Masera, F.Prino ALICE Physics Week, Muenster - 16.02.07 Andrea Dainese

  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: ALICE Physics Week, Muenster - 16.02.07 Andrea Dainese

  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 ALICE Physics Week, Muenster - 16.02.07 Andrea Dainese

  4. Vertex reconstruction with tracksAliVertexerTracks • 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) ALICE Physics Week, Muenster - 16.02.07 Andrea Dainese

  5. y track x vertex need an estimate of the vertex and its cov. matrix 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| < nsd0(pt) sd0(pt) = svtxstrack(pt) from track’s covariance matrix ALICE Physics Week, Muenster - 16.02.07 Andrea Dainese

  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 fAlgo=1 (which gives the best resolution) ALICE Physics Week, Muenster - 16.02.07 Andrea Dainese

  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 track’s cov matrix • The solution that minimizes this c2 is analytic: vertex covariance matrix vertex ALICE Physics Week, Muenster - 16.02.07 Andrea Dainese

  8. Easy to add “beam constraint” • Same procedure as before + constraint: vertex vertex covariance matrix where: ALICE Physics Week, Muenster - 16.02.07 Andrea Dainese

  9. 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)| < 5 mm • VERTEX FINDING, (fAlgo=1) • VERTEX FITTING  vtx1 • 2nd iteration: • TRACKS SELECTION: |d0rf(vtx1)| < n sd0 • VERTEX FINDING , (fAlgo=1) • VERTEX FITTING  vtx2 (final estimate) • n= 3 provides optimal resolution and “good” cov. matrix (pulls ~ 1) ALICE Physics Week, Muenster - 16.02.07 Andrea Dainese

  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) [b*=10m] • AliRoot HEAD (January 16th 2007) • Select triggered events: [ (V0A or V0C) and SPDFO ] ALICE Physics Week, Muenster - 16.02.07 Andrea Dainese

  11. Efficiency • Vertex found if distance to MC vertex in (x,y) is < 1 mm (with beam constraint) ALICE Physics Week, Muenster - 16.02.07 Andrea Dainese

  12. Residuals x z ALICE Physics Week, Muenster - 16.02.07 Andrea Dainese

  13. Resolutions Resolutions VS multiplicity (obtained from gaussian fit of residuals) 3s track-cut 10s track-cut (with beam constraint) ALICE Physics Week, Muenster - 16.02.07 Andrea Dainese

  14. 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) ALICE Physics Week, Muenster - 16.02.07 Andrea Dainese

  15. c2/ndf (with beam constraint) ALICE Physics Week, Muenster - 16.02.07 Andrea Dainese

  16. Efficiency vs zMC SPD: -14 < z < +14 cm ALICE Physics Week, Muenster - 16.02.07 Andrea Dainese

  17. 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 ALICE Physics Week, Muenster - 16.02.07 Andrea Dainese

  18. Performance w/o beam constraint(as in PDC events) without constraint with constraint ALICE Physics Week, Muenster - 16.02.07 Andrea Dainese

  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 TPC&ITS(≥5 pts) ALICE Physics Week, Muenster - 16.02.07 Andrea Dainese

  20. 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 (fAlgo=4)  vtx0 • 1st iteration: • TRACKS SELECTION: |d03D(vtx0)| < 5 mm • VERTEX FINDING, (fAlgo=1) • VERTEX FITTING  vtx1 • 2nd iteration: • TRACKS SELECTION: |d0rf(vtx1)| < n sd0 • VERTEX FINDING , (fAlgo=1) • VERTEX FITTING  vtx2 (final estimate) • n = 3 provides optimal resolution and “good” cov. matrix (pulls ~ 1) ALICE Physics Week, Muenster - 16.02.07 Andrea Dainese

  21. Performance w/o beam constraint(as in PDC events) tracks used for vertex vertex not found tracks in TPC&ITS(≥5 pts) ALICE Physics Week, Muenster - 16.02.07 Andrea Dainese

  22. s of d0 distribution for primaries s [mm] y track x vertex bias! 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! ALICE Physics Week, Muenster - 16.02.07 Andrea Dainese

  23. 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) ALICE Physics Week, Muenster - 16.02.07 Andrea Dainese

  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)| < 3 sd0 • VERTEX FITTING standard procedure one-shot fit OK! ALICE Physics Week, Muenster - 16.02.07 Andrea Dainese

  25. Secondary vertex reconstructionAliVertexerTracks::VertexForSelectedTracks() • Finder+Fitter ➔ errors ➔ heavy flvr cuts on normalized vars • Test on D0Kp vertex: same resolution as V0 vertexer x x z z ALICE Physics Week, Muenster - 16.02.07 Andrea Dainese

  26. 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 (finder+fitter) tested on D0Kp vertex reco • resolution OK; pulls OK; • small problem at low pt: to be fixed • to do: tests with >2-prong decays ALICE Physics Week, Muenster - 16.02.07 Andrea Dainese

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