1. CHEP2003, La Jolla, San Diego, March 24-28 P.Vanlaer, IIHE-ULB Brussels 1 Vertex reconstruction framework and its implementation for CMS Outline Introduction Vertex fitting Vertex finding R.Frühwirth, W.Waltenberger, HEPHY-Vienna T.Speer, K.Prokofiev, Zürich University P.Vanlaer, IIHE-Brussels University CHEP 2003, La Jolla, San Diego, March 24-28

2. P.Vanlaer, IIHE-ULB Brussels 2 Vertex reconstruction can be decomposed in: Vertex finding given a set of tracks, separate it into clusters of compatible tracks, i.e. vertex candidates inclusively: not related to a particular decay channel search for secondary vertices in a jet exclusively: find best match with a decay channel general solution: requires generation of combinations, selection of topologies and kinematic constraints work in progress, not described here Vertex fitting find the 3D point most compatible with a set of tracks constrain track parameters with vertex Introduction

3. CHEP2003, La Jolla, San Diego, March 24-28 P.Vanlaer, IIHE-ULB Brussels 3 Problem is complex can’t guess what the optimal algorithms will be there is probably not 1 optimal algorithm but several, each optimized for a specific task Math is complex but localized in a few places ease development by providing mathematical toolkit Performance evaluation is not easy comparison with Monte-Carlo truth not trivial vertex are high level reconstructed objects, i.e. made out of reconstructed tracks disentangle effects from track and vertex reconstructions Problem is very generic once tracks are given a good case for code re-use  we need a flexible framework for the development and evaluation of algorithms Motivation for a framework

4. CHEP2003, La Jolla, San Diego, March 24-28 P.Vanlaer, IIHE-ULB Brussels 4 Vertex fitting

5. CHEP2003, La Jolla, San Diego, March 24-28 P.Vanlaer, IIHE-ULB Brussels 5 Problem definition 1 RecVertex = 3D point most compatible with input tracks Bunch of tracks Vertex fitting Principle: minimization problem Find x which minimizes a function F[x – f(p i )], p i parameters of track i Example: f(p i ) = x i p.c.a. to vertex F =  i=1 N (x-x i ) T C i -1 (x-x i ) usual total  2 Algorithms may differ by: choice of track parametrization p i (and function f(p i ) ) form of function F to minimize

6. CHEP2003, La Jolla, San Diego, March 24-28 P.Vanlaer, IIHE-ULB Brussels 6 All parametrizations needed are supported provided by a concrete class: LinearizedTrack computed on demand by helper classes cached for performance conversions from 1 parametrization into another also supported 2 parametrizations used in ORCA: (x, y, z) at p.c.a. to vertex (previous picture) V.Karimäki, CMS Note 1997/051 5 parameters at perigee (q/p T, ,  p, signed d 0, z p ) P.Billoir et al., NIM A311(1992) 139 R.Frühwirth et al., Computer Physics Comm. 96 (1991) 189 Track parametrizations

7. CHEP2003, La Jolla, San Diego, March 24-28 P.Vanlaer, IIHE-ULB Brussels 7 LinearizedTrack : why this name? f(p i ) must be linearized in vicinity of true vertex 2 linearizations used in ORCA: straight line track approximation, constant track error matrix used with p.c.a. parametrization helix track approximation, linear error propagation used with perigee parametrization Jacobians for error propagation also provided by LinearizedTrack helix model formally much more precise both models valid in our p T range (> 0.7 GeV/c) requires first guess of vertex position = linearization point abstract LinearizationPointFinder class 3 implementations in ORCA (1 non-robust, 2 robust) based on crossing points of high p T track pairs Linearization

8. CHEP2003, La Jolla, San Diego, March 24-28 P.Vanlaer, IIHE-ULB Brussels 8 Iterations arise naturally: 1) when linearization point too far from fitted vertex 2) when function F has no explicit minimum To solve case 2), tracks should be allowed to contribute to vertex fit with weights  1 see robust algorithms in Wolfgang Waltenberger’s talk weight = function of distance between track and current vertex evolves during iteration the same LinearizedTrack can contribute with  weights to different vertices  concrete VertexTrack class: knows its LinearizedTrack, current vertex and weight Memory management of LinearizedTrack and VertexTrack by reference-counting mechanism (ref.-counting pointers) Iterative vertex fitting

9. CHEP2003, La Jolla, San Diego, March 24-28 P.Vanlaer, IIHE-ULB Brussels 9 Error matrices of track parameters p i are uncorrelated VertexTrack s can be added 1 after another to vertex update of vertex, in Kalman language abstract VertexUpdator 1 implementation per track parametrization VertexUpdator uses VertexTrackCompatibilityEstimator to increment vertex fit  2 also, 1 implementation per parametrization can be used during vertex finding to test compatibility One more component: VertexSmoother : computes track parameters constrained with vertex position stores them in VertexTrack currently, implementation only for perigee parametrization Kalman fitting formalism

10. CHEP2003, La Jolla, San Diego, March 24-28 P.Vanlaer, IIHE-ULB Brussels 10 Vertex finding

11. CHEP2003, La Jolla, San Diego, March 24-28 P.Vanlaer, IIHE-ULB Brussels 11 Vertex finding class framework still in an early stage… Users use an implementation of a VertexReconstructor Decomposition of VertexReconstructor still evolves while features common to new algorithms emerge Current decomposition: 1) initial track selection: Filter operates on each element of RecTrack container; boolean result: track accepted or rejected 2) VertexSeedGenerator finds clusters of compatible tracks 3) and one of the VertexFitter s to fit each cluster into a vertex CombinationGenerator, in ORCA statistical toolkit I.e. for exclusive vertex finding …but performance analysis framework is well advanced Vertex finding framework

12. CHEP2003, La Jolla, San Diego, March 24-28 P.Vanlaer, IIHE-ULB Brussels 12 Analysis of performance PV finding efficiency SV finding efficiency PV track purity SV track purity 1-fake rate Total “score” …for these algorithms We want to evaluate, in b-jets, 50 GeV,   1.4… PV track assignment efficiency SV track assignment efficiency

13. CHEP2003, La Jolla, San Diego, March 24-28 P.Vanlaer, IIHE-ULB Brussels 13 Comparison with MC truth Selected simulated verticesReconstructed vertices Association VertexAssociator by tracks uses TrackAssociator by distance

14. CHEP2003, La Jolla, San Diego, March 24-28 P.Vanlaer, IIHE-ULB Brussels 14 For each performance figure, 1 estimator class Examples: VertexFindingEfficiencyEstimator VertexTrackAssignmentPurityEstimator updated each event These are all combined into a standard performance test: VertexRecoPerformanceTest which reports results for each estimator, and a total Score Score is a user-defined function of the different estimators Example: S = Eff.PV^a * Eff.SV^b * Purity PV^c * Purity SV^d * (1-Fake Rate)^e Evaluation of performance

15. CHEP2003, La Jolla, San Diego, March 24-28 P.Vanlaer, IIHE-ULB Brussels 15 Vertex fast simulation VertexFastSim package Fully controlled input to vertex reconstruction Configurable event generator number and position of vertices number and momentum vector of prongs Very simple track reconstruction Gaussian smearing; configurable resolutions fraction of non-Gaussian tails configurable What for? Test statistical consistency of vertex fitters Compare vertex finders for standard events  speed-up development and debugging  software release tests independent of full track reconstruction Future: interface to FAMOS (see Stephan Wynhoff’s talk) for more realistic yet fast track reconstruction

16. CHEP2003, La Jolla, San Diego, March 24-28 P.Vanlaer, IIHE-ULB Brussels 16 Tuning of vertex finding algorithms Idea: automatic search of parameter value which maximizes algorithm Score for a given event sample Abstract TunableVertexReconstructor class: wrapper around the algorithm to tune TunableVertexReconstructor::setParameter(float value) TunableVertexReconstructor::initialRange() Concrete FineTuner1D class: maximization algorithm divides initialRange() in N bins makes N clones of TunableVertexReconstructor with different parameter values, by setParameter(float value) computes Score for each zooms in or shifts range until parameter precision reached

17. CHEP2003, La Jolla, San Diego, March 24-28 P.Vanlaer, IIHE-ULB Brussels 17 Conclusions We have developed an efficient class framework for the development of vertex fitting algorithms We have developed a friendly environment to evaluate and tune vertex finding algorithms A first version of the class framework for vertex finding algorithms is present improving while more algorithms get prototyped Now, time for implementations and results… (next talk)

18. CHEP2003, La Jolla, San Diego, March 24-28 P.Vanlaer, IIHE-ULB Brussels 18 Backup slides

19. CHEP2003, La Jolla, San Diego, March 24-28 P.Vanlaer, IIHE-ULB Brussels 19 Problem definition Impact parameter resolutions d 0 in tt (full), W+c (dashed), W+u,d,s,g (dotted) impact parameter of secondary tracks << 1 mm  (z 0 ) [  m]  (d 0 ) [  m] W+u,d,s,g tt d 0 (cm) |d 0 | < 1 mm  (d 0 ) = f(p T,  ) p T = 1 GeV/c: 0.1  0.2 mm high p T : 10  20  m  (z 0 ) = f(p T,  ) p T = 1 GeV/c: 0.1  1 mm high p T : 20  100  m Primary and secondary tracks not well separated Reconstruction in 3D; global optimization

20. CHEP2003, La Jolla, San Diego, March 24-28 P.Vanlaer, IIHE-ULB Brussels 20 Vertex fitting framework UML diagrams:

21. CHEP2003, La Jolla, San Diego, March 24-28 P.Vanlaer, IIHE-ULB Brussels 21 VertexFastSim framework

22. CHEP2003, La Jolla, San Diego, March 24-28 P.Vanlaer, IIHE-ULB Brussels 22 Vertex finding tuning framework

23. CHEP2003, La Jolla, San Diego, March 24-28 P.Vanlaer, IIHE-ULB Brussels 23 Evaluation of vertex reconstruction performance Analysis (cont.) Performance estimator classes (1 for each performance figure) Divided into: vertex finding performance estimators vertex track assignment performance estimators Examples (see reference manual): VertexFindingEfficiencyEstimator VertexTrackAssignmentPurityEstimator You have to provide them with the Monte-Carlo truth, and the associators that you want them to use VertexAssociationToolsFactory provides 1 VertexAssociator and 1 TrackAssociator that are consistent with each other type of associators configurable in.orcarc

24. CHEP2003, La Jolla, San Diego, March 24-28 P.Vanlaer, IIHE-ULB Brussels 24 Analysis (cont.) These are all combined into a standard performance test: VertexRecoPerformanceTest simulated vertices separated into primary and secondary vertices performance evaluated for each type separately only reconstructible simulated vertices considered  2 tracks reconstructed vertex association by tracks, successful if purity of RecVertex  50% associated simulated vertices: Efficiency unassociated reconstructed vertices: Fake rate irrespective of primary or secondary track association: by hits (default) specify by pulls if no hits used to evaluate purity and track assignment efficiency