Secondary Vertex Secondary Vertex reconstruction for the reconstruction for the DD++

Elena Bruna

University of Torino

ALICE Physics Week Erice, Dec. 6th 2005

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OutlineOutline

•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

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Straight Line Vertex finderStraight Line Vertex finder

• Originally developed to find the primary vertex in p-p Based on the Straight Line Approximation of a track

(helix)

• Main steps1. The method receives N (N=3 in our case) tracks as input2. Each track is approximated by a straight line in the

vicinity of the primary vertex3. 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:

ij

ijpairs

found xN

x1

ij

ijpairs

found yN

y1

ijij

pairsfound z

Nz

1

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Improvements on the Straight Improvements on the Straight Line Vertex FinderLine 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 parameters3. 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)

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1. DCA cut effect1. DCA cut effect

X coord

Y coord

Z coord

RMS=179 μm

RMS=183 μm

RMS=166 μm

No DCAcut

Finder- MC (m)

Finder- MC (m)

Finder- MC (m)

RMS=179 μm

RMS=182 μm

RMS=165 μm

fDCAcut = 1.5 mm

Finder- MC (m)

Finder- MC (m)

Finder- MC (m)

RMS=178 μm

RMS=181 μm

RMS=163 μm

fDCAcut = 0.7 mm

Finder- MC (m)

Finder- MC (m)

Finder- MC (m)

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Weighted mean

RMS=179 μm

RMS=183 μm

RMS=160 μm

Finder- MC (m)

Finder- MC (m)

Finder- MC (m)

2. Weighted mean effect2. 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)

Finder- MC (m)

Finder- MC (m)

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RMS=169 μm

RMS=171 μm

RMS=162 μm

Helix Finder

Finder- MC (m)

Finder- MC (m)

Finder- MC (m)

3. Results from the helix finder3. Results from the helix finder

X coord

Y coord

Z coord

RMS=179 μm

RMS=183 μm

RMS=166 μm

Straight Line Finder

Helix finderhas better resolutionand also a lower number of overflows and underflows (≈400 instead of ≈650)

Finder- MC (m)

Finder- MC (m)

Finder- MC (m)

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4. Vertices dispersions4. 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

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New secondary vertex finder New secondary vertex finder

23

22

21

2 dddD

Straight Line Approximation used → analytic method

Vertex coordinates (x0,y0,z0) from minimization of:

Where: d1,d2,d3 are the distances (weighted with the errors on the tracks) of the vertex from the 3 tracks:

2

01

2

01

2

0121

zyx

zzyyxxd

P1 (x1,y1,z1)

Vertex (x0,y0,z0)

dσx = σy

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RMS x

RMS z

RMS y

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.

At high Pt of D+ (Pt>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 Resolution of the vertex finder

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Resolution at high PResolution at high Pt t /1/1Checks 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. Pt3 pion vertex: RMS in the bending plane vs. Pt

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bending plane

Resolution at high PResolution at high Ptt /2 /2

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.

x

y

K-

π+

π+

D+

y’

x’

rotated

x

y

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Resolution in the rotated frameResolution 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

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Vertices dispersions/1Vertices dispersions/1

23

22

21 dddfSigma

fSigma (cm)

Δx = XVertex FOUND – XVertex MC

Δx < 1000 μm

1000<Δx <3000 μm

3000<Δx <5000 μm

Δx > 5000 μm

fSigma bigger for bad vertices

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Vertices dispersions/2Vertices dispersions/2Cut on fSigma (for X coordinate)

RM

S x

(μ

m)

Mea

n 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)

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Conclusions on the findersConclusions 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♥ Is presently THE candidateTHE 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