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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
Belle Weekly MeetingApril 14th 200311
• 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
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