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Interaction vertex reconstruction in pp collisions

This presentation discusses the reconstruction of interaction vertices in pp collisions, focusing on the use of primary vertex position for physics analyses. It covers the z-coordinate reconstruction from pixel layers and 3D reconstruction with tracks. The expected resolutions, vertex finding algorithm, and optimization of the algorithm are also discussed.

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Interaction vertex reconstruction in pp collisions

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  1. Interaction vertex reconstruction in pp collisions Andrea Dainese - Padova Massimo Masera - Torino ALICE Performance Week - January 20-24, 2003 Andrea Dainese

  2. Contents • Motivation • use of primary vertex position for physics analyses • LHC • beams and interaction point • z coordinate reconstruction from pixel layers (M.Masera) • estimate of expected resolution • results • 3D reconstruction with tracks (A.D. and M.Masera) • estimate of expected resolution • vertex finding algorithm • vertex fitting algorithm • optimization of the algorithm • results ALICE Performance Week - January 20-24, 2003 Andrea Dainese

  3. 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 • reconstruction of flight-line in space • Crucial in open charm (d0~100 mm) and open beauty (d0~500 mm) detection • Relevant (but less critical) for strange hadrons track d0(rf) in the direction  to the track ALICE Performance Week - January 20-24, 2003 Andrea Dainese

  4. 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 s) z coordinate has to be measured in Pb-Pb and in pp • Position of the beam in (x,y) given by the machine with very high precision (stable for a long time) • 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 Performance Week - January 20-24, 2003 Andrea Dainese

  5. 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 SPD1 and SPD2  straight line in (z,r) (tracklet) • at r = 0, estimate of zvtx • if N tracklets are used, resolution  1/N (+ background / misallignments) • N  dNch/dy • The expected resolution can be estimated as: ALICE Performance Week - January 20-24, 2003 Andrea Dainese

  6. SPD2 r = 7 cm x/X0 = 1% (r2 ,z2) (r1 ,z1) r = 4 cm x/X0 = 1% SPD1 r = 3 cm x/X0 = 0.3% PIPE BEAM (0 ,z0) z “Back-of-the-envelope” calculation • Exercise: estimate zvtx resolution from SPD geometry/resolution 2 clusters 1 tracklet Estimate of zvtx: z0 = 7/3 z1 - 4/3 z2 [error on r and correlation of errors in the two layers neglected] Estimated error:(z0)= 7/3 (z1)  4/3 (z2) 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 Performance Week - January 20-24, 2003 Andrea Dainese

  7. zRMS L RMS … 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 (a=p/2, p=pT) • In central Pb-Pb (HIJING): <b c pT>  400 MeV • If the particle flyes for a distance L, the hit on the next layer will have: • For the PIPE+SPD1+SPD2 system we have: SPD1 SCATTERING(z) = (r1 -rPIPE) RMSPIPE SPD2 SCATTERING(z) = (r2 -rPIPE) RMSPIPE (r2 -r1) RMSSPD1 ALICE Performance Week - January 20-24, 2003 Andrea Dainese

  8. If the particle has a generic polar angle a: • 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 zRMS zRMS/sin  sSCATTERING(z) sSCATTERING(z)/(sin a)3/2 • Average value of 1/(sin a)3/2 for particles that hit both SPD layers is 1.8 • We have: • SPD1: s(z) = 120 mm  30 mm = 125 mm • SPD2: s(z) = 120 mm  200 mm = 240 mm Error on z with 1 tracklet: s(z) = 430 mm ALICE Performance Week - January 20-24, 2003 Andrea Dainese

  9. In Pb-Pb (6000) # of good tracklets (two clusters from the same track) ~ 8000 • In pp the multiplicity is lower by a factor ~1000 s(zvtx) worse by a factor ~30 Catania results for ion-ion 5.5 m @ 6000 ALICE Performance Week - January 20-24, 2003 Andrea Dainese

  10. zvtx from pixels: results • Same method as in Pb-Pb (adapted to pp by M. Masera) s(z) = 155 mm ALICE Performance Week - January 20-24, 2003 Andrea Dainese

  11. 3D reconstruction with tracks • Track reconstruction in TPC+ITS • track seeding uses the position of the primary vertex: • (x, y) from beam position (resolution ~ 150 mm) • z from pixels information (resolution ~ 150 mm) • Vertex reconstruction in 2 steps: • VERTEX FINDING: using DCA for track pairs (M.Masera) • VERTEX FITTING: (inspired by CMS and ATLAS methods) • give optimal estimate of the position of the vertex • give vertex covariance matrix • give a c2 ALICE Performance Week - January 20-24, 2003 Andrea Dainese

  12. Expected resolutions • Average # rec. tracks = 7 (average on events with # > 1) • Average pT of rec. tracks = 0.6 GeV/c • Resolutions of track position parameters @ 0.6 GeV/c: • s(d0(rf))  100 mm [ d0(rf) is  to the track! ] • s(d0(z))  240 mm ALICE Performance Week - January 20-24, 2003 Andrea Dainese

  13. 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: • propagate tracks to vertex nominal position • calculate DCA (in space) for each possible pair of tracks (using straight line approximation) • get estimate of xvtx and yvtx from mean of results from all pairs ALICE Performance Week - January 20-24, 2003 Andrea Dainese

  14. Results ALICE Performance Week - January 20-24, 2003 Andrea Dainese

  15. Vertex Fitting Algorithm • Inspiration: CMS Note 1997/051 • Tracks are propagated to the point given by the vertex finder (at the moment nominal position used) • A c2 is written as the sum of the single track c2s w.r.t. a generic vertex position rvtx: where Wi is track “covariance matrix in global ref. frame” • The solution that minimizes this c2 is analytic: covariance matrix vertex ALICE Performance Week - January 20-24, 2003 Andrea Dainese

  16. Tuning of the algorithm • Inspiration: ATLAS TRT TDR • Criterion used to reject mismeasured and secondary tracks from the fit: cut on the maximum contribution to the c2 ci2 < c2max • if c2max is too low too many tracks are rejected and we loose resolution • if c2max 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 Performance Week - January 20-24, 2003 Andrea Dainese

  17. Results: resolutions s(y) = 55 mm s(x) = 55 mm s(z) = 90 mm ALICE Performance Week - January 20-24, 2003 Andrea Dainese

  18. Resolution “per track” ALICE Performance Week - January 20-24, 2003 Andrea Dainese

  19. Results: pulls The covariance matrix of the vertex describes correctly the resolutions ALICE Performance Week - January 20-24, 2003 Andrea Dainese

  20. Results: reduced c2 ALICE Performance Week - January 20-24, 2003 Andrea Dainese

  21. Resolution VS # tracks ALICE Performance Week - January 20-24, 2003 Andrea Dainese

  22. Resolutions VS multiplicity ALICE Performance Week - January 20-24, 2003 Andrea Dainese

  23. Comparisons and Probability <mult> of events with charm ALICE Performance Week - January 20-24, 2003 Andrea Dainese

  24. Impact on impact parameter resolution as in Pb-Pb pp with charm pp min. bias “Delicate” analyses may be helped by some “wisdom”… ALICE Performance Week - January 20-24, 2003 Andrea Dainese

  25. y x y x • Vertex position will be: • well measured to thrust • poorly measured || to thrust Event topology and vertex reconstruction • In the bending plane, each track gives information only on the position of the vertex in the direction normal to the track • In pp collisions, many (most) events have jets • Particles can be produced along an axis: 2-JET topology, THRUST ALICE Performance Week - January 20-24, 2003 Andrea Dainese

  26. Event Thrust [in (x,y) plane] • Definition: • thrust= [all vectors in (x,y) plane] • = is the thrust axis “axis which maximizes projected momenta” ALICE Performance Week - January 20-24, 2003 Andrea Dainese

  27. y D0K-p+ x D0 w.r.t. thrust axis pT < 1 GeV/c 1 < pT < 2 GeV/c 2 < pT < 3 GeV/c 3 < pT < 5 GeV/c 5 < pT < 10 GeV/c pT > 10 GeV/c ALICE Performance Week - January 20-24, 2003 Andrea Dainese

  28. Reference frame matters! • The primary vertex should be reconstructed in the reference frame indicated by the thrust: reference frame rotated of angle f around z axis, being f the angle between the thrust axis and the x axis yT = coordinate  to the thrust, better resolution xT = coordinate || to the thrust, worse resolution • In the global ALICE frame: xvtx = xvtxT cos f – yvtxT sin f s2(xvtx) = s2(xvtxT) cos2f + s2(yvtxT) sin2f = = 0.5  [s2(xvtxT) + s2(yvtxT)] ALICE Performance Week - January 20-24, 2003 Andrea Dainese

  29. Results with Thrust Axis In the thrust frame the two coordinates have different resolutions Improvement when using thrust frame: ~ 25 % ALICE Performance Week - January 20-24, 2003 Andrea Dainese

  30. y1 y0 y2 D0 is “lucky” • In D0 detection strategy the impact parameters of K and p are combined in: P = d0K d0p • Definition of d0 is such that for the “good” signal topology the sign of P is negative (the two d0s have opp. signs) • The impact of the error on vertex position is worse when the pT of the decay products is high • Let’s consider a high pT (~ 5 GeV/c) D0 and calculate the resolution on P ALICE Performance Week - January 20-24, 2003 Andrea Dainese

  31. Tentative Classes Design • AliITSVertex • data members: position (3 #s), covariance matrix 3x3 (6 #s), c2 (1 #), # tracks used (1 #) • one object per event; objects stored in a file (which file?) • AliITSVertexer • mother class: some common methods and deal with I/O; idea • inherited classes: • AliITSVertexerIons: (x,y,z) from pixels in Ion-Ion (Catania) • AliITSVertexerPPTracklets: z from pixels in pp • AliITSVertexerPPTracks: (x,y,z) from tracks in pp • AliITSVertexerFast: (x,y,z) with smearing of true position using resolutions • Status: AliITSVertex, AliITSVertexer ready; others on the way; committed hopefully early next week ALICE Performance Week - January 20-24, 2003 Andrea Dainese

  32. Conclusions • In pp collisions at LHC with L = 1029 cm-2s-1 the position of the interaction vertex has to be reconstructed in 3D • Method used in Pb-Pb for z reconstruction with pixels (before tracking) adapted to pp • Complete algorithm for 3D vertex reconstruction with tracks implemented • results: s(xvtx, yvtx, zvtx)  (55, 55, 90) mm • use of thrust reference frame allows optimal determination of vertex position in the bending plane • To do: • optimize and study stability of vertex finding algorithm • implement classes in AliRoot • report in Internal Note and PPR ch. 5 ALICE Performance Week - January 20-24, 2003 Andrea Dainese

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