1 Vertex Finding in AliVertexerTracks E. Bruna (TO), E. Crescio (TO), A. Dainese (LNL), M. Masera (TO), F. Prino (TO)

2 Vertex Finding GOALS:  First estimation of vertex position to be passed to the fitter  Calculation of dispersion  (AliVertex::GetDispersion() ) of tracks around the found vertex can be used to select good secondary vertices Five algorithms for vertex finding implemented in AliVertexerTracks  Can be selected with AliVertexerTracks::SetFinderAlgorithm fAlgo=1 or 2  approximate tracks as straight lines and calculate the minimum- distance point among all the tracks at once 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  Default fAlgo=1 (which gives the best resolution, see next slides)

3 StrLinVertexFinder (fAlgo= 4,5) Approximate tracks as straight lines (analytical method)  See next slide Build all possible pairs of tracks  Calculate the point of minimum distance (DCA) of the 2 lines Reject tracks with DCA > fDCAcut  Calculate the “intersection” point of the 2 tracks on the DCA segment Possibility to use (fAlgo=4) or not (fAlgo=5) track parameter errors as wieghts Calculate the vertex position as the average of the “intersections” of all pairs of tracks Calculate the dispersion as the standard deviation of the “intersection” points around the found vertex track 1 track 2 track 3 DCA 13 DCA 12 DCA 23 “intersection” points

4 d (μm) B=0.5 T p T = 0.5 GeV/c Decay dist (μm) Straight Line Approximation d (μm) = distance between the secondary vertex and the tangent line Primary vertex Secondary vertex track Straight Line Approximation d (μm) P T (GeV/c) B=0.5 T Decay dist = 300  m Geometrical calculation of the “error” introduced by approximating the track (helix) with a straight line close to the primary vertex.  Good approximation: error is negligible w.r.t. tracks r  d 0 resolution (≈ 100  m for 0.5 GeV/c tracks)

5 HelixVertexFinder (fAlgo=3) Same algorithm (based on DCA of track pairs) as StrLinVertexFinder  Tracks treated as helices DCA calculation no more analytical, but based on minimization –Sometimes does not converge (“GetDCA stopped at not a minimum” error) Reject tracks with DCA > fDCAcut  Tracks propagated to the DCA points  “Intersection” points calculated from DCA track points after propagation Possible improvement on vertex precision and accuracy track 1 track 2 track 3 DCA 13 DCA 12 DCA 23 “intersection” points Track DCA distribution from pp events

6 StrLinVertexFinderMinDist (fAlgo=1,2) Calculate the point of minimum distance from tracks  Tracks approximated as straight lines (analytical method)  Minimize the quantity D 2 =d 1 2 +d 2 2 +d 3 2 where:  All tracks at once, no pairing  Errors  x,  y and  z used for fAlgo=1 and not for fAlgo=2 The dispersion  is given by: Secondary Vertex d1d1 track 1 d2d2 track 2 d3d3 track 3

7 RMS x RMS z RMS y Comparing the VertexFinders (I) Case of 3 charged body ( D +  K  ) decay vertex reconstruction The method based on the minimization of the distance from all tracks at once (fAlgo=1) provides the best resolution

8 Comparing the VertexFinders (II) Different finder algorithms maintained because of different features that can be exploited StrLinVertexFinder (fAlgo=4,5) and HelixVertexFinder (fAlgo=3)  Possibility of track selection based on DCA  Useful for rejection of displaced secondary tracks (mainly from strange particles) in primary vertex calculation when no information on the (x,y) beam position in the LHC fill is available StrLinVertexFinderMinDist (fAlgo=1)  Better resolution  better vertex determination  Better calculation of track dispersion, useful for secondary vertex selection (see next slides)

9 D mesons in ALICE central barrel No dedicated trigger in the central barrel  extract the signal from Minimum Bias events  Large combinatorial background (benchmark study with dN ch /dy = 6000 in central Pb-Pb ) SELECTION STRATEGY: invariant-mass analysis of fully- reconstructed topologies originating from displaced vertices  build pairs/triplets/quadruplets of tracks with correct combination of charge signs and large impact parameters  particle identification to tag the decay products  calculate the vertex (DCA point) of the tracks  good pointing of reconstructed D momentum to the primary vertex

10 D mesons: hadronic decays MesonFinal state # charged bodies Branching Ratio D0D0 K-K- 2 3.8% K-K- 4 Total7.48% Non resonant1.74% D 0  K -      K -       6.2% D+D+ K-K- 3 Total9.2% Non resonant8.8% D +  Kbar 0* (892)    K -     1.29% D +  Kbar 0* (1430)    K -     2.33% Ds+Ds+ K+K-K+K- 3 Total4.3% D s +  K + Kbar 0*  K + K -   2.0% D s +    K + K -   1.8% Most promising channels for exclusive charmed meson reconstruction

11 Vertex finder: D +  K  bending plane x y K-K- π+π+ π+π+ D+D+ y’ x’ rotated x y

12 Vertex finder: D s  KK  D s  KK  D +  K  Better resolution for D+ due to larger average momentum of daughter tracks R. Silvestri, E. Bruna

13 Vertex finder: D 0  K  4 body decay vertex For comparison pT integrated resolutions for 3 body decays: xreco-xtrue [cm] zreco-ztrue [cm] yreco-ytrue [cm] RMSxRMSyRMSz D +  K  D s  KK  D 0  K  R. Romita, G. Bruno

14 ZOOM Vertex selection: D +  K  BLACK: signal (K  from D+) RED: BKG (K  combinatorics) σ MAX (cm) Accepted triplets with σ < σ MAX σ MAX (cm) Vertex quality selection based on track dispersion ( AliVertex::GetDispersion() ) around the found vertex  Distribution of track dispersion for K  triplets from D+ decay (signal) and combinatorial triplets (background)  Fraction of selected signal and background triplets as a function of the cut on track dispersion (  ). BLACK: signal (K  from D+) RED: BKG (K  combinatorics) BLACK: signal (K  from D+) RED: BKG (K  combinatorics)

15 Decay vertices in AliVertexerTracks AliVertexerTracks::VertexForSelectedTracks is the method for secondary vertex determination  Arguments (NEW version presently under test): 1.TObjArray (or TTree) of AliESDtracks 2.Bool_t optUseFitter: if kFALSE the fitting step is not performed and the vertex given by the finder is used 3.Bool_t optPropagate: if kTRUE after the fitter tracks are propagated to the found vertex.  Track selection: PrepareTracks = just propagate tracks to the x, y of the primary vertex No rejection of tracks based on impact parameter (assume that user macro already did the selection)

16 Summary on heavy flavour vertices AliVertexerTracks used for D +  K  reconstruction in PbPb and pp  Vertex position is obtained with a resolution ~ 100  m  A “quality” parameter (the dispersion) is calculated and is used for vertex selection  See Elena Bruna’s PhD thesis for more details Ongoing studies on:  D 0  K   D s  KK    J/   e + e - (G.Bruno)  Next step: include kinematical constraint for the resonant decay chains (e.g. D s  KK 0*  KK  or D s   KK  ) Need (especially in pp) to remove the candidate secondary tracks from the primary vertex determination  See Andrea’s talk about the fitter