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Secondary Vertex reconstruction for the D +

Secondary Vertex reconstruction for the D +. Elena Bruna University of Torino. ALICE Physics Week Erice, Dec. 6 th 2005. Outline. Three different methods to find the secondary vertex for D + → K - π + π + Comparison between the methods  find the candidate for the D + analysis

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Secondary Vertex reconstruction for the D +

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  1. Secondary Vertex reconstruction for the D+ Elena Bruna University of Torino ALICE Physics Week Erice, Dec. 6th 2005

  2. Outline • Three different methods to find the secondary vertex for D+→ K-π+π+ • Comparison between the methods  find the candidate for the D+ analysis • Tuning of the cuts on the tracks used to “feed” the vertexer • Future plans Elena Bruna

  3. Originally developed to find the primary vertex in p-p Based on the Straight Line Approximation of a track (helix) Main steps The method receives N (N=3 in our case) tracks as input Each track is approximated by a straight line in the vicinity of the primary vertex An estimation of the secondary vertex from each pair of tracks is obtained evaluating the crossing point between the 2 straight lines The coordinates of secondary vertex are determined averaging among all the track pairs: Straight Line Vertex finder Elena Bruna

  4. Add a cut on the distance of closest approach (DCA) between the two straight lines A pair of tracks is not used for the vertex estimation if their distance of closest approach is > fDCAcut Use a weighted mean of the 2 DCA points In order to take into account the errors on the tracks parameters Use the track as helix, without the straight line approximation Calculate a parameter representing the dispersion of the vertices given by the track pairs (fSigma) Improvements on the Straight Line Vertex Finder Elena Bruna

  5. 1. DCA cut effect fDCAcut = 1.5 mm fDCAcut = 0.7 mm RMS=179 μm RMS=178 μm Finder- MC (mm) Finder- MC (mm) RMS=182 μm RMS=181 μm Finder- MC (mm) Finder- MC (mm) RMS=165 μm RMS=163 μm Finder- MC (mm) Finder- MC (mm) No DCAcut X coord RMS=179 μm Finder- MC (mm) Y coord RMS=183 μm Finder- MC (mm) Z coord RMS=166 μm Elena Bruna Finder- MC (mm)

  6. 2. Weighted mean effect Weighted mean RMS=179 μm Finder- MC (mm) Improved resolution on Z RMS=183 μm Finder- MC (mm) RMS=160 μm Finder- MC (mm) Arithmetic mean X coord RMS=179 μm Finder- MC (mm) Y coord RMS=183 μm Finder- MC (mm) Z coord RMS=166 μm Elena Bruna Finder- MC (mm)

  7. 3. Results from the helix finder Helix Finder RMS=169 μm Helix finder has better resolution and also a lower number of overflows and underflows (≈400 instead of ≈650) Finder- MC (mm) RMS=171 μm Finder- MC (mm) RMS=162 μm Finder- MC (mm) Straight Line Finder X coord RMS=179 μm Finder- MC (mm) Y coord RMS=183 μm Finder- MC (mm) Z coord RMS=166 μm Elena Bruna Finder- MC (mm)

  8. Same distribution for Helix and Straight Line finder 4. Vertices dispersions The DCA cut reduces the dispersion Dispersion fSigma = standard deviation of the 3 vertex estimations obtained from each track pair Str. Line Finder Str. Line with DCA cut Helix Finder with DCA cut fSigma (cm) Elena Bruna

  9. New secondary vertex finder d Straight Line Approximation used → analytic method Vertex coordinates (x0,y0,z0) from minimization of: Where:d1,d2,d3are the distances (weighted with the errors on the tracks) of the vertex from the 3 tracks: P1 (x1,y1,z1) σx = σy Vertex (x0,y0,z0) Elena Bruna

  10. Resolution of the vertex finder RMS x RMS y At high Pt of D+ (Pt>5-6 GeV/c), the RMS in the bending planeincreases, instead of going down to ~15µm (spatial pixel resolution) as expected. RMS z Conclusion New method improves RMS of ~40μm for PtD+ ~ 2GeV/c for x, y and z with respect to previous Helix vertex finder based on DCA of pairs of tracks. Elena Bruna

  11. Resolution at high Pt /1 Checks with events only made of pions show that the RMS on the bending plane: • Decreases down to 50 µm if the 3 tracks have Pt ~ 2 GeV/c • Reaches a value of ~20 µm (in agreement with spatial pixel resolution) if the 3 tracks have Pt =100 GeV/c 3 pion vertex:RMS in the bending plane vs. Pt Elena Bruna

  12. Resolution at high Pt /2 y y x’ y’ rotated x x In the signal events, as the Pt of the D+ increases, the “daughters” become more and more co-linear, resulting in a worse resolution along the D+ direction. π+ π+ K- bending plane D+ Elena Bruna

  13. Resolution in the rotated frame Along the Pt of the D+ (x’ coord.) Orthogonal to the Pt of the D+ (y’ coord.) → Along the Pt of the D+: as Pt increases (for Pt>5-6 GeV/c) the angles between the decay tracks become smaller: in this coordinate the RMS increases → Orthogonal to the Pt of the D+: the RMS decreases as expected Elena Bruna

  14. Vertices dispersions/1 Δx = XVertex FOUND – XVertex MC Δx < 1000 μm 1000<Δx <3000 μm 3000<Δx <5000 μm Δx > 5000 μm fSigma bigger for bad vertices fSigma (cm) Elena Bruna

  15. Vertices dispersions/2 Cut on fSigma (for X coordinate) Vertices taken / Vertices Tot (“True” vertices) “Fake” vertices (tracks coming from 3 different D+ vertices) RMS x (μm) Mean x (μm) • fSigma < 0.7 cm cuts ~1% of the events and gives a RMS of 130 μm • fSigma < 0.5 cm cuts ~6% of the events and gives a RMS of 110 μm Elena Bruna

  16. The Straight Line vertex finder: DCA cut: negligible effect on the RMS of the residual distributions, slightly reduced number of overflows and underflows The use of a weighted mean: improves Z resolution by ≈6 mm Cutting on the dispersion fSigma: removes the events for which the VertexFinder misses the true vertex by more than 1 mm and improves the resolution Conclusions on the finders • The Helix vertex finder: • Has better resolution w.r.t. Straight Line finder (by approximately 10 mm) • Has less overflows and underflows w.r.t. Straight Line finder • DRAWBACK: the DCA between helices is obtained by minimization • DCA cut, weighted mean and fSigma cut: improve the resolution • The Minimum Distance vertex finder: • Has better resolution w.r.t. Helix finder (by approximately 30 mm) • Has less overflows and underflows w.r.t. previous finders • Is an analytic method • Weighted mean and fSigma cut: improve the resolution • Is presently THE candidate for first D+ analysis • A cut on fSigma has to be tuned (it can be done at analysis level) Elena Bruna

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