ROBUSTIFICATIONof the

Belle Vertex Fitter

April 14th 2003 Johannes RindhauserHephy Vienna

Belle Weekly Meeting

(AdaptiveVtxFitter)

2

Overview

• Vertex Fitting

• Robustification

New class made: AdaptiveVtxFitter

• Results (comparison of kvertexfitter and AdaptiveVtxFitter)

ROBUSTIFICATION of the Belle Vertex Fitter

Belle Weekly MeetingApril 14th 20032

• Vertex Finding: find decay vertices

• Vertex Fitting: determine their position with high accuracy

Introduction: Vertex Reconstruction

ROBUSTIFICATION of the Belle Vertex Fitter

Belle Weekly MeetingApril 14th 20033

• Identification of vertices

• Assignment of tracks to vertices

• Possible estimation of vertex position

Eg. Finding through fitting:• fit all tracks to common vertex• discard incompatible tracks• discarded tracks: secondary vertex search

Vertex Finding

ROBUSTIFICATION of the Belle Vertex Fitter

Belle Weekly MeetingApril 14th 20034

• Estimation of Vertex position and track parameters

• Result: tracks are more precise due to vertex constraint

Vertex Fitting

ROBUSTIFICATION of the Belle Vertex Fitter

Belle Weekly MeetingApril 14th 20035

Ingredients

• Trackmodel: parameters at vertex measurement space

• Minimization Ansatz• Normal Least Squares Method (global)• Kalman Filter (local)• Belle: Constraint Ansatz (global)

ROBUSTIFICATION of the Belle Vertex Fitter

Belle Weekly MeetingApril 14th 20036

• Error of tracks greater than expected ( covariance matrix)

• Problems using LSM or Constraint Ansatz Outliers are not recognized and used as normal (good) tracks

Outliers bias the vertex position!

Problem: Outlier

ROBUSTIFICATION of the Belle Vertex Fitter

Belle Weekly MeetingApril 14th 20037

• Genuine Outlier: track is from particle, but with larger error than expected (eg. -electrons, multiple scattering)

• Corrupted track: partially wrong associated hits (other track, detector noise)

• Outlier: background track or track from secondary vertex

Outlier Types

ROBUSTIFICATION of the Belle Vertex Fitter

Belle Weekly MeetingApril 14th 20038

• ROBUSTIFICATION: making fit (vertex estimate) less sensitive to outliers

• One possible solution: adaptive fitter– Assigns weights to tracks according to its

• Result:– Outliers get larger downweighted– Bias on vertex estimate reduced

SOLUTION to handle OUTLIER

ROBUSTIFICATION of the Belle Vertex Fitter

Belle Weekly MeetingApril 14th 20039

Weighting

• Weight calculation for track k:

• Where is calculated for every track and is a cut value. T is the temperature.

ROBUSTIFICATION of the Belle Vertex Fitter

Belle Weekly MeetingApril 14th 200310

Weighting: Plot

=4

ROBUSTIFICATION of the Belle Vertex Fitter

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• Fully programmed: Extension of the kvertexfitter

• Comparison between AdaptiveVtxFitter and kvertexfitter in special testenvironment:– Controlled Gaussian smearing of the tracks– Detailed study of fitter possible

AdaptiveVtxFitter

ROBUSTIFICATION of the Belle Vertex Fitter

Belle Weekly MeetingApril 14th 200312

z-Shift:

• Use all tracks of ‘Mdst_charged’ (6prong)

• Shift 1 track (eg. B decay vertex)

Outlier Production

ROBUSTIFICATION of the Belle Vertex Fitter

Belle Weekly MeetingApril 14th 200313

z

AdaptiveVtxFitter vs. kvertexfitter

ROBUSTIFICATION of the Belle Vertex Fitter

Belle Weekly MeetingApril 14th 200314

No shift200 um shift

No significant differenceAdaptiveVtxFitter

reduces vertex bias

kvertexfitter 500 um shift AdaptiveVtxFitter

AdaptiveVtxFitter reduces vertex bias

andkeeps RMS small

AdaptiveVtxFitter vs. kvertexfitter

T=1

0

20

40

60

80

100

0 200 400 600

z-shift

vert

ex z

-dev

iati

on

normal fit

adaptive-cut 5.99

adaptive-cut 9.21

adaptive-cut 13.8

ROBUSTIFICATION of the Belle Vertex Fitter

Belle Weekly MeetingApril 14th 200315

0

5

10

15

20

0 200 400 600

z-shift

vert

ex z

-dev

iati

on

normal fit

adaptive-cut 5.99

adaptive-cut 9.21

adaptive-cut 13.8

Plot of vertex z-deviation with respect to z-shift

AdaptiveVtxFitter vs. kvertexfitter

ROBUSTIFICATION of the Belle Vertex Fitter

Belle Weekly MeetingApril 14th 200316

Table (m)

z-shift

normalFit

chiSqCut=5.99 (5% cut)

chiSqCut=9.21 (1% cut)

chiSqCut=13.8 (0.1% cut)

10,00 1,50 1,5 1,4 1,5

20,00 3,10 3,1 3,1 3,1

50,00 8,30 7,6 7,8 7,9

100,00 16,50 11 12,3 14,3

200,00 32,70 6,8 8 12,2

500,00 81,90 3,4 3 2,4

Outlook: Deterministic Annealing

• Starting with high temperature• Cooling down (T1, T2, …. )• Tuned for specific event topology

Result:• Avoiding suboptimal solutions (local

minima) more accurate vertex position

ROBUSTIFICATION of the Belle Vertex Fitter

Belle Weekly MeetingApril 14th 200317

Outlook: Physics Analysis

To be done: Tuning (T resp. annealing scheme, ) on specific event topologies:

• Test on the B0_bar decay vertex of the “golden mode” B0 J/s

• Test on B0 D*+ D*- decay

ROBUSTIFICATION of the Belle Vertex Fitter

Belle Weekly MeetingApril 14th 200318

Work on Robust Fitter

• Literature:– Comp.Phys.Comm. 120, 197 (1999)– J.Phys.G: Nucl. Part. Phys. 29 (2003) 561-

574

• Mathematical Support:– R. Frühwirth (Hephy Vienna)

ROBUSTIFICATION of the Belle Vertex Fitter

Belle Weekly MeetingApril 14th 200319

THE END

April 14th 2003 Johannes RindhauserHephy Vienna

Belle Weekly Meeting