Vertex fitting and finding in ROOT

Introduction

The following algorithms for constrained vertex fitting and finding are implemented within the d0root_analysis CVS ROOT-package.

VertexGlobalFitter

Implements a constrained vertex fit of a set tracks. The input is a list of GTracks and the output is an object of the class Vertex containing the position of the vertex and the re-fitted vertex-constrained tracks.

The fit consist of the minimization of a chi2 of 2 terms:

The ROOT algorithm is mathematically equivalent to the Kalman Filter algorithm implemented in the framework, but consist of a Global fit of position and momenta at the same time, instead of the recursive Kalman Filter/Smoother formalism.

Both charged and neutral tracks can be fitted.

Documentation

Example of Vertex fit
       
  VertexGlobalFitter* vFitter = new VertexGlobalFitter;
  vFitter->fit(listOfTracks);
  if(vFitter->status()) {
    Vertex* fittedVertex = new Vertex(* (Vertex*) vFitter->vertex());
  }

PrimaryVertexGlobalFinder

Finds the hard-scatter primary vertex of an event.
The input is the list of all reconstructed GTracks and the nominal beam position and the output is an object of the class Vertex.

It implements the following pattern recognition algorithm:

  1. Cluster tracks in z using a simple-cone track-jet algorithm of infinite radius in the transverse plane and 1cm radius in z.

  2. Select the highest multiplicity track-cluster (this assumes the hard-scatter vertex is the highest multiplicity vertex).

  3. Select tracks with pt> 0.5GeV/c, 11 or more hits and transverse DCA significance with respect to the nominal beam position smaller than 3. The beam spot error is assumed to be 30um in the transverse plane and 25cm in z

  4. Fit tracks to a common vertex using the VertexGlobalFitter algorithm.

  5. If the highest chi2 contribution of a track to the vertex is greater than 10, the track is excluded from the fit and step 4-5 are repeated until the chi2 contribution of all tracks to the vertex is smaller than 10.

    Example of Primary Vertex reconstruction
           
    
  /// define beam spot position 
  TVector3 IP(-0.025,-0.053,0.0);

  /// instantiate vertex finder 
  PrimaryVertexGlobalFinder* pvFinder = new PrimaryVertexGlobalFinder;
  pvFinder->SetIPposition(IP);

  /// read tracks 
  TObjArray tracks; _readEvent.readGTracks(tracks,"401");

  /// find primary vertex 
  pvFinder->FindVertex(tracks);

  /// get primary vertex and its attached tracks 
  Vertex* PV = vFinder->GetVertex();
  TObjArray PVtracks = PV->Particles();

    V0Finder

    Search for 2-track vertices assuming different mass hypothesis and kinematic cuts for K0, Lambda and Psi reconstruction. The V0Finder can be constructed by specifying a list of cuts/options or by using any of the default SetCut methods as the following examples show:

    Example of K0 finding specifying the list of cuts
           
      /// Instantiate Primary Vertex finder 
  TVector3 IP(-0.025,-0.053,0.0); //beam spot
  PrimaryVertexGlobalFinder* pvFinder = new PrimaryVertexGlobalFinder;
  pvFinder->SetIPposition(IP);

  /// Instantiate V0Finder 
  float cuts[12] = {11,    //hits
		    0.3,   // track pT
		    0.0,   // min. dca
		    999.9, // max. dca
		    0.0,   // min dca significance
		    0.13956995, // mass track 1
		    0.13956995, // mass track 2
		    100,   // vertex chi2
		    0.9999,// vertex collinearity angle
		    0.0,   // vertex min. decay lenght
		    0.15,  // min. vertex mass
		    1.4   // max. vertex mass
  };
  V0Finder* K0Finder = new V0Finder(cuts);

  /// read tracks and find the primary vertex 
  TObjArray tracks; _readEvent.readGTracks(tracks,"401");
  pvFinder->FindVertex(tracks);
  Vertex* PV = vFinder->GetVertex();

  /// find K0s   
  K0Finder->SetPrimaryVertex(PV);
  K0Finder->Find(tracks);
  TObjArray K0s = K0Finder->GetVertices();
    Example of Psi finding using default constructor
           
       /// Instantiate Primary Vertex finder 
   TVector3 IP(-0.025,-0.053,0.0); //beam spot
   PrimaryVertexGlobalFinder* pvFinder = new PrimaryVertexGlobalFinder;
   pvFinder->SetIPposition(IP);

   /// Instantiate V0Finder 
   V0Finder* psiFinder = new V0Finder;
   psiFinder->SetJPsiCuts();

   /// read tracks and find the primary vertex 
   TObjArray tracks; _readEvent.readGTracks(tracks,"401");
   pvFinder->FindVertex(tracks);
   Vertex* PV = vFinder->GetVertex();

   /// find J/Psi's   
   psiFinder->SetPrimaryVertex(PV);
   psiFinder->Find(tracks);
   TObjArray JPsis = psiFinder->GetVertices();

    SecondaryVertexGlobalFinder

    Finds inclusive secondary vertices in jets for b-tagging.

    BjpsiXFinder

    Algorithm to search for B --> J/Psi + X vertex decays.

    It starts finding a JPsi vertex candidate using the V0Finder algorithm and, according to the X decay mode specified in the constructor, attaches additional tracks using different mass hypothesis and kinematic selections.

    Example of B -> JPsi + K finding
           
          BjpsiXFinder* BFinder = new BjpsiXFinder;
      BFinder->SetJPsi(jpsiVertex); //previously found with V0Finder
 
      BFinder->Input(tracks); 
      BFinder->FindX("K"); // X = K

      TObjArray Bs = BFinder->GetVertices();

    In addition to vertex fitting and finding algorithms, Track-Jet finding algorithms and flavor tagging methods are provided:

    TrackJetFinder

    Finds track-jets using a 3D cone (D0note 3919) or Kt jet algorithm.
    The input is a list of reconstructed GTracks and the output is a list of objects of the class ParticleCollection.
    Several methods for kinematic cuts are provided in the constructor.

    Example of track-jet finding and jet-charge tagging
           
      /// Instantiate 0.7 cone jet Finder 
  SimpleConeJetFinder* jetFinder = new SimpleConeJetFinder(0.7);
    
  /// read tracks 
  TObjArray tracks; _readEvent.readGTracks(tracks,"401");

  /// find jets 
  TObjArray jets;
  jetFinder->Input(selectedTracks);
  jetFinder->FindJets(jets);

  /// get jet-charge of found jets
  float kappa = 0.5;

  for(int i=0; i <  jets.GetEntries(); i++) {
    ParticleCollection* jet = (ParticleCollection*) jets[i];
    double jch = jet->JetCharge(kappa);
  }

    Example code: B lifetime

           
       TH1F*  h_life = new TH1F("h_life","",100,-0.3,0.3);

   float correctionFactor = 0.73

   /// Instantiate Vertex finders 
   TVector3 IP(-0.025,-0.053,0.0); //beam spot
   PrimaryVertexGlobalFinder* pvFinder = new PrimaryVertexGlobalFinder;
   pvFinder->SetIPposition(IP);
   V0Finder* psiFinder = new V0Finder;
   psiFinder->SetJPsiCuts();


   /// Loop over events 
   int nentries = _readEvent.GetEntries();
   for (int ii=0; ii < nentries; ii++) {
     if(!_readEvent.GetEntry(ii)) continue;

      /// read tracks matched to muons using Gavin's method 
      TObjArray muonTracks;
      TObjArray muList; _readEvent.readTrackMuons_p10(muList,"501");
      for(int y=0; y < muons.GetEntries(); y++) {
        Muon* mu = (Muon*) muons[y];
        Track* trk = (Track*) mu->GetTrack();
        if(trk) {
	  //remove duplicated
	  if(!trk->MatchId(muonTracks)) muonTracks.Add(trk);
        }
      }

      /// Find Primary Vertex
      pvFinder->FindVertex(tracks);
      Vertex* PV = vFinder->GetVertex();

      /// Find J/Psi's   
      psiFinder->SetPrimaryVertex(PV);
      psiFinder->Find(tracks);
      TObjArray JPsis = psiFinder->GetVertices();

      /// compute lifetime   
      for(int i=0; i < JPsis.GetEntries(); i++) {
        Vertex* vtx = (Vertex*) JPsis[i];
        if(vtx->chi2 < 10 && vtx->Pt() > 4.0) { 
          float lifetime = vtx->Lifetime2(PV,3.09688)/correctionFactor;
          h_life->Fill(lifetime);
        }
      }

      psiFinder->Clear();
      _readEvent.Clear();
   } //entries

    Instructions

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    p11 Results


    di-muon Invariant mass (opposite sign charged tracks)


    di-muon Invariant mass (opposite sign charged tracks)


    Invariant mass (same sign charged tracks)


    Lifetime (correction factor = 0.73)


    Lifetime for different PV multiplicities


    B -> JPsi K candidates

    Performance plots.

    FAQ

    Is it easy to modify my d0root code to run on TMB files instead of TMB-Trees? Is there an example macro that does that?

    I think that in a nutshell, what you need to do is:

    • add "Regd0rootPkg" to your OBJECTS file
    • add "RCP root = " (or however you want to refer
      to this RCP file) to your framework RCP file, and include the corresponding name in the framework RCP file's "Packages" line.

    Then, in your analysis (which must be called from a framework package called after the d0rootPkg conversion), simply "read" the information
    from the ReadEvent instance. You obtain this instance using FwkReadEvent::instance()
    A minimal CVS package that does just that is d0root_test (but I suppose that d0root_example would do equally well -- both provide examples of how
    to convert both from TMB/DST and from TMBTree).
    You will probably want to tailor d0rootPkg.rcp, as it affects the level of corrections applied to objects etc. I hope its accompanying documentation is sufficient.
    Frank Filthaut

    Last updated: 05-18-2004
    Ariel Schwartzman