Standard tracking implementation

Interfaces

For flexibility littrack has a set of abstract interfaces for all main track reconstruction tools. They are:

• CbmLitField: access to the magnetic field map.
• CbmLitGeoNavigator: navigation in the detector geometry.
• CbmLitHitToTrackMerger: hit-to-track merging.
• CbmLitMaterialEffects: calculation of the material effects (energy losses and multiple scattering).
• CbmLitTrackExtrapolator: extrapolation of tracks without taking into account material effects.
• CbmLitTrackFinder: finding of tracks.
• CbmLitTrackFitter: fitting of tracks.
• CbmLitTrackPropagator: propagation of tracks taking into account material effects using CbmLitTrackExtrapolator,CbmLitMaterialEffects,CbmLitGeoNavigator.
• CbmLitTrackSelection: selection of tracks.
• CbmLitTrackUpdate: update of track parameters using Kalman Filter.
• CbmLitWeightCalculator: calculation of hit weights.
• CbmLitWeightedHitCalculator: calculation of weighted mean hit.

Each interface has a corresponding type definition in CbmLitPtrTypes.h header.

Concrete algorithm objects are created via tool factory CbmLitToolFactory which implements singleton pattern.

Example of creation of different tracking tools is shown below:

CbmLitToolFactory* factory = CbmLitToolFactory::Instance();
TrackPropagatorPtr propagator = factory->CreateTrackPropagator("lit");
TrackUpdatePtr filter = factory->CreateTrackUpdate("kalman");
TrackFitterPtr fitter = factory->CreateTrackFitter("lit_kalman");
TrackFitterPtr smoother = factory->CreateTrackFitter("kalman_smoother");

Detector layout classes

The detector layout classes are used in the tracking for a simplified description of the detector layout like positions of different detection elements. NOTE that they do not describe detector material which is needed for track propagation. For this TGeo is used.

The detector layout as it is used in the tracking have a certain structure which is shown on the picture below. The detector layout consists of station groups, each station group consists of stations and each station consists of substations. Station groups are detector elements which located far away from each other (for example three TRD stations) or there is an absorber in between (for example MUCH). Stations represents one detector plane. Substations are needed because of the staggered detector structure, i.e. detector modules located on different z positions.

Detector layout

The following classes implement this detector structure:

• CbmLitDetectorLayout
• CbmLitStationGroup
• CbmLitStation
• CbmLitSubstation

The conversion of the Monte-Carlo geometry stored in TGeo format to the CbmLitDetectorLayout format is performed in the CbmLitEnvironment class. It provides a set of functions for conversion of the TRD, MUCH and TOF geometries to the detector layout understandable for tracking. CbmLitEnvironment implements singleton pattern one can access it from any part of the program.

Example of getting different layouts:

CbmLitEnvironment* env = CbmLitEnvironment::Instance();
const CbmLitDetectorLayout& layout = env->GetLayout(); // Returns detector layout for MUCH, TRD or MUCH+TRD depending on the detectors used in the simulation
const CbmLitDetectorLayout& muchLayout = env->GetMuchLayout(); // Returns MUCH layout
const CbmLitDetectorLayout& trdLayout = env->GetTrdLayout(); // Returns TRD layout

Data classes

Data classes provide access to hit, track, track parameters and other information. They optimize for faster and more convenient dynamic access unlike CBMROOT data classes mainly optimize for storage.

• CbmLitHit - base class for hits
• CbmLitStripHit - strip like hit
• CbmLitPixelHit - pixel like hit
• CbmLitTrackParam - track parameters and its covariance matrix
• CbmLitTrack - track
• CbmLitFitNode - fit node stores predicted, updated and smoothed track parameters during track fit for each station

Track propagation

The track propagation algorithm estimates the trajectory and its errors in a covariance matrix while taking into account three physics effects which influence the trajectory, i.e. energy loss, multiple scattering and the influence of a magnetic field.

All track propagation algorithms has to implement CbmLitTrackPropagator interface. Track propagation algorithm is decomposed in three main components: track extrapolation which has to implement CbmLitTrackExtrapolator interface, material effects calculator which has to implement CbmLitMaterialEffects interface and geometry navigator which has to implement CbmLitGeoNavigator interface.

The extrapolation of the trajectory is done according to the equation of motion. If the track passes a magnetic field the equation of motion for a charged particle is solved applying the 4th order Runge-Kutta method and the transport matrix is calculated by integrating the derivatives along the so called zero trajectory (implemented in CbmLitRK4TrackExtrapolator class). If passing a field free region a straight line is used for extrapolation and the transport matrix calculation (implemented in CbmLitLineTrackExtrapolator class). CbmLitCleverTrackExtrapolator class automatically determines what type of track extrapolation to use (CbmLitRK4TrackExtrapolator or CbmLitLineTrackExtrapolator) depending on the presence of the magnetic field.

The influence of the material on the track momentum is taken into account by calculating the expected average energy loss due to ionization (Bethe-Bloch formula) and bremsstrahlung (Bethe-Heitler formula). The influence on the error, i.e. the covariance matrix due to multiple scattering is included by adding process noise in the track propagation. Here, a gaussian approximation using the Highland formula is used to estimate the average scattering angle. The implementation of the material effects calculation is done in the CbmLitMaterialEffectsImp.

In order to include material effects correctly in the track propagation algorithm one needs to identify which materials in the complex detector geometry have been traversed by the particle. The track length has to be calculated, material properties need to be known etc. This is done by the geometry navigation algorithm which finds intersection points with detector elements in a certain interval (z1 , z2 ) along a straight line. The implementation of the navigation is based on the ROOT geometry package TGeo in the CbmLitTGeoNavigator.

Track fit

All track fitter algorithms has to implement CbmLitTrackFitter interface. Kalman filter based track fitting algorithms may use track propagation within CbmLitTrackPropagator interface and Kalman filter update within CbmLitTrackUpdate interface.

Currently all implemented track fitter algorithms are based on Kalman filter method:

• CbmLitTrackFitterImp - standard Kalman filter impelemtation
• CbmLitKalmanSmoother - standard Kalman smoother implementation
• CbmLitTrackFitterIter - iterative Kalman Filter consisting of forward and backward track fit and outliers removing.
• CbmLitTrackFitterWeight - iterative Kalman filter using weight calculation. Similar to DAF but can use different weight functions.

Track finding

UNDER CONSTRUCTION

Track selection

All track selection algorithms implement CbmLitTrackSelection interface. The input to the track selection is an array of tracks which algorithm has to classify as "good" or "bad".

Several base track selection algorithms have been implemented:

• CbmLitTrackSelectionCuts - cut based track selection (chi square, momentum, number of hits etc.);
• CbmLitTrackSelectionEmpty - does no track selection, implemented for convenience;
• CbmLitTrackSelectionSameSeed - selects the best track for each subset of tracks with the same previous track index;
• CbmLitTrackSelectionSharedHits - removes clone and ghost tracks sorting by quality and checking of shared hits;
• CbmLitTrackSelectionShortTracks - removes short track which have a longer track with the same set of hits;
• CbmLitQualitySort - sorts track array by a quality criterion based on chi square and number of hits in track.

Detector specific track selection combines basic algorithms with different parameters:

• CbmLitTrackSelectionMuch - performs final track selection in MUCH tracking;
• CbmLitTrackSelectionTrd - performs final track selection in TRD tracking.