Single Top Polarization for MadGraph s-channel sample

1. Single Top s-channel


2. Optimal basis, theory

Mahlon and Parke showed in their paper "Improved spin basis for Angular Correlation Studies in Single Top Quark Production at the Tevatron" [hep-ph/9611367] that the spin of the top quark in Single Top s-channel production is correlated with the direction of the d-quark.

First they decompose the top quark momentum into a sum of two massless auxiliary momenta, then write down the matrix elements for a spin up top and a spin down top. They can show that one of them vanishes if the spin of the topquark is chosen

3. Madevent

1. The generated sample

MadGraph process: pp>tb~, QCD=99, QED=99, Model sm.
Chosen decay: t -> b ve e+


2. The used macro

// Load shared library

// Create chain of root trees
  TChain chain("LHEF");
// Create object of class ExRootTreeReader
  ExRootTreeReader *treeReader = new ExRootTreeReader(&chain);
  Long64_t numberOfEntries = treeReader->GetEntries();
// Get pointers to branches used in this analysis
  TClonesArray *branchParticle = treeReader->UseBranch("Particle");
// Book histograms
  TCanvas *MyC = new TCanvas("MyC","Test",1);
  TH1 *histCos = new TH1F("Cos", "s-Channel: Cos(Phi), Optimal Basis", 100, -1, 1);

// Loop over all events
  for(Int_t entry = 0; entry < numberOfEntries; ++entry) {
// Load selected branches with data from specified event
    TLorentzVector vec1;
    TLorentzVector vec2;
    TLorentzVector vec3;
    TLorentzVector vec4;
    if(branchParticle->GetEntries() > 0) {
// Loop
               for (int i=0;i<7;i++) {
      TRootLHEFParticle *particle = (TRootLHEFParticle*) branchParticle->At(i);

    vec1.SetPtEtaPhiE(particle->PT, particle->Eta, particle->Phi, particle->E);
      else if(particle->PID==-11){
    vec2.SetPtEtaPhiE(particle->PT, particle->Eta, particle->Phi, particle->E);
      else if(particle->PID==-1){
    vec3.SetPtEtaPhiE(particle->PT, particle->Eta, particle->Phi, particle->E);
    TVector3 boost1 = -(vec1)->BoostVector();
    TVector3 p = vec2.Vect();
    TVector3 q = vec3.Vect();
    Double_t a = p.Angle(q);
    Double_t  b = TMath::Cos(a);

  // Show resulting histograms

3. The Madevent result


4. ONETOP result

This is the polarization distribution of a sample generated by the ONETOP generator with tevatron setting.


5. References

The madgraph website:
"Improved spin basis for Angular Correlation Studies in Single Top Quark Production at the Tevatron" [hep-ph/9611367] by Mahlon and Parke (see attachment)
-- SarahHeim - 08 Apr 2008
Topic attachments
I Attachment Action Size Date Who Comment
mahlonparkepolarization.pdfpdf mahlonparkepolarization.pdf manage 194.8 K 09 Apr 2008 - 00:00 SarahHeim  
pidschannel.jpgjpg pidschannel.jpg manage 21.5 K 08 Apr 2008 - 22:47 SarahHeim  
s-channel.jpgjpg s-channel.jpg manage 7.2 K 08 Apr 2008 - 23:13 SarahHeim  
schanneloptimalfit.jpgjpg schanneloptimalfit.jpg manage 23.3 K 08 Apr 2008 - 23:08 SarahHeim  
schanneltevatronpaper.jpgjpg schanneltevatronpaper.jpg manage 19.0 K 08 Apr 2008 - 23:10 SarahHeim  
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Topic revision: r31 - 09 Apr 2008, SarahHeim

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