TrkVertexFitters

Author

Nicol.nosp@m.a.Gi.nosp@m.acint.nosp@m.o.Pi.nosp@m.acqua.nosp@m.dio@.nosp@m.cern..nosp@m.ch

Introduction

This package contains the Vertex Fitters in the form of Athena AlgoTools, which are needed for vertex finding applications. The input is typically a bunch of Tracks or TrackParameters, eventually an initial position and a constraint vertex, and the output the fitted vertex. For a description of the finders which uses these tools, please give a look at the InDetPriVxFinderTool package.

Design

Trk::SequentialVertexFitter

An iterative vertex fitter, updating the vertex estimate with a single track at a time. The measurement equation is relinearized with the position of the resulting estimate and the vertex is refit. The iterations are performed until the vertex position improves or the maximal number of iterations is reached. Smoothing (refit of tracks with the knowledge of the vertex position) is then performed on request. The following properties can be set per jobOptions:

• MaxIterations
• MaxShift (in mm).

Trk::AdaptiveVertexFitter

This vertex algorithm is also based on the typical Kalman-Filtering approach, with the difference that the inverse of the covariance matrices of the track parameters of the tracks which enter the fit are reweighted according to the probability of the tracks to be compatible with the vertex to be fit. In this way outliers/tracks which do not belong to the vertex are smoothly rejected.

Since the estimation of the vertex position during the first fit iterations is not particularly good and the compatiblity estimation of the tracks not always reliable, an annealing technique is also implemented, in order to make the rejection of outliers soft in the beginning and harder towards the end of the fit (for this the Annealing Maker class is responsible: as a default the Temperature of this thermodinamical procedure is lowered according to few predefined steps)

For greater modularity the algorithm is divided into 6 modules (please look at the TrkVertexFitterUtils package for these):

• 1. SeedFinder
• 2. LinearizedTrackFactory
• 3. TrackCompatibilityEstimator
• 3b. ImpactPoint3dEstimator
• 4. VertexUpdator
• 5. VertexSmoother
• plus another one, which is responsible for letting the temperature go down
• (the so called "annealing technique")
• 6. AnnealingMaker

This kind of algorithm was implemented for the first time by CMS: for information about the theoretical motivations a good reference is Wolfgang Waltenberger's PhD Thesis and many of the calculations implemented have been extensively shown in theoretical & experimental papers by Fruehwirth, Waltenberger, Strandlie et al.

The following parameters can be set:

• MaxIterations (limit on fit iterations)
• MaxDistToLinPoint (if the distance from the point where the track was linearized to the new fitted vertex is higher than this number in mm, then the track will be relinearized before the next iteration)
• InitialError (initial value of the diagonal weight matrix of the vertex before fit, so the name is really bad, because you have to provide the inverse of the error squared. Should be small enough not to result in biases, but still such that it doesn't create numerical problems)
• onlyzseed (requests seeding the primary vertex only along the z direction, for x and y the value of the beam spot vertex is used)
• DoSmoothing (if true enables smoothing)

Trk::AdaptiveMultiVertexFitter

This class implements a multi vertex fitting algorithm which is adaptive and robust, quite insensitive to the presence of outliers.

The multi-vertex version of the fit is more complicate than the single-vertex version and needs the input to be provided in the form of a vector of already initialized MVFVxCandidate objects. Details of the the objects to provide you find in the fit() and addVtxTofit() functions.

During the multi-vertex fit all the vertices are fit, using the tracks which are contained in their respective vertex candidates. Tracks which are shared among more than one vertex get their weights adjusted dynamically iteration after iteration thanks to a Deterministic Annealing procedure, so that in the end they are dinamically assigned to the vertex they most probably belong to.

Parameters to be set per joboptions:

• MaxIterations
• MaxDistToLinPoint
• InitialError
• DoSmoothing (for these the meaning is the same as for the single-vertex AdaptiveVertexFitter)
• MinWeight (all the tracks which during the fit acquire a value which is lower than this predefined value, are not considered anymore in the fit)

Trk::DummyVertexSmoother

The vertex smoother is used by all the fitter as a final step to improve the Track Parameters of the Tracks with the knowledge of the fitted vertex. The Dummy Vertex Smoother however does not refit trajectories with the knowledge of the vertex. Instead it takes trajectories, extrapolate them to the transverse point of the closest approach to the reconstructed vertex and calculates the perigee parameters of trajectories with respect to that vertex.

Trk::SequentialVertexSmoother

A concrete implementation of the Vertex smoother. Takes the tracks from the VxCandidates and updates them with the knowledge of the reconstructed vertex position. Can be used with any VertexTrackUpdator. The default is KalmanVertexTrackUpdator