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

Elena Bruna 2Outline 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 Straight Line Vertex finder Originally developed to find the primary vertex in p-p  Based on the Straight Line Approximation of a track (helix) Main steps 1.The method receives N (N=3 in our case) tracks as input 2.Each track is approximated by a straight line in the vicinity of the primary vertex 3.An estimation of the secondary vertex from each pair of tracks is obtained evaluating the crossing point between the 2 straight lines 4.The coordinates of secondary vertex are determined averaging among all the track pairs:

Elena Bruna 4 Improvements on the Straight Line Vertex Finder 1.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 2.Use a weighted mean of the 2 DCA points In order to take into account the errors on the tracks parameters 3.Use the track as helix, without the straight line approximation 4.Calculate a parameter representing the dispersion of the vertices given by the track pairs (fSigma)

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

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

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

Elena Bruna 8 4. Vertices dispersions Same distribution for Helix and Straight Line finder The DCA cut reduces the dispersion fSigma (cm) 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

Elena Bruna 9 New secondary vertex finder Straight Line Approximation used → analytic method Vertex coordinates (x 0,y 0,z 0 ) from minimization of: Where: d 1,d 2,d 3 are the distances (weighted with the errors on the tracks) of the vertex from the 3 tracks: P 1 (x 1,y 1,z 1 ) Vertex (x 0,y 0,z 0 ) d σ x = σ y

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

Elena Bruna 11 Resolution at high P t /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 P t ~ 2 GeV/c Reaches a value of ~20 µm (in agreement with spatial pixel resolution) if the 3 tracks have P t =100 GeV/c 3 pion vertex: RMS in the bending plane vs. P t

Elena Bruna 12 bending plane Resolution at high P t /2 In the signal events, as the P t of the D + increases, the “daughters” become more and more co-linear, resulting in a worse resolution along the D + direction. x y K-K- π+π+ π+π+ D+D+ y’ x’ rotated x y

Elena Bruna 13 Resolution in the rotated frame Along the P t of the D + (x’ coord.)Orthogonal to the P t of the D + (y’ coord.) → Along the P t of the D + : as P t increases (for P t >5-6 GeV/c) the angles between the decay tracks become smaller: in this coordinate the RMS increases → Orthogonal to the P t of the D + : the RMS decreases as expected

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

Elena Bruna 15 Vertices dispersions/2 Cut on fSigma (for X coordinate) RMS x (μm) Mean x (μm) Vertices taken / Vertices Tot (“True” vertices) 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 “Fake” vertices (tracks coming from 3 different D + vertices)

Elena Bruna 16 Conclusions on the finders The Helix vertex finder: ♦ Has better resolution w.r.t. Straight Line finder (by approximately 10  m) ♦ 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  m) ♥ Has less overflows and underflows w.r.t. previous finders ♥ Is an analytic method ♥ Weighted mean and fSigma cut: improve the resolution THE candidate ♥ Is presently THE candidate for first D + analysis A cut on fSigma has to be tuned (it can be done at analysis level) 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  m ♣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