Single Top Polarization for MadGraph s-channel sample

0. Abstract

The polarization distribution for a Single top s-channel sample, generated by MadEvent was analyzed. The distribution doesn't show the expected 100 % polarization, which leads to the conclusion that MadEvent does not simulate the polarization of the Single Top s-channel quarks correctly.

1. Single Top s-channel

s-channel.jpg

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 they 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 parallel to the direction of the d quark.
Thus we expect the top quarks produced in the s-channel to be 100% polarized.

3. ONETOP result

This is the polarization distribution of a sample generated by the ONETOP generator with tevatron setting. Here the expected 100% polarization can be seen.

schanneltevatronpaper.jpg

4. Madevent

1. The generated sample

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

pidschannel.jpg

2. The used macro

{
// Load shared library
  gSystem->Load("../ExRootAnalysis/ExRootAnalysis/lib/libExRootAnalysis.so");
  gSystem->Load("libPhysics");

// Create chain of root trees
  TChain chain("LHEF");
  chain.Add("pptbbar_unweighted_events.root");
  
// 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);
  gStyle->SetOptStat(0);
  TH1 *histCos = new TH1F("Cos", "s-Channel: Cos(Phi), Optimal Basis", 100, -1, 1);
  
  histCos->GetXaxis()->SetTitle("Cos(Phi)");
  histCos->GetXaxis()->SetLabelSize(0.05);
  histCos->GetYaxis()->SetLabelSize(0.05);
  histCos->GetXaxis()->SetTitleSize(0.05);
  histCos->SetMinimum(0);

// Loop over all events
  for(Int_t entry = 0; entry < numberOfEntries; ++entry) {
 
// Load selected branches with data from specified event
    treeReader->ReadEntry(entry);
    
    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);

      if(particle->PID==6){
    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();
    vec2->Boost(boost1);
    vec3->Boost(boost1);
    TVector3 p = vec2.Vect();
    TVector3 q = vec3.Vect();
    Double_t a = p.Angle(q);
    Double_t  b = TMath::Cos(a);
    
    histCos->Fill(b);
            }
  }

  // Show resulting histograms
    histCos->Draw();
}

3. The Madevent result for pp>tb~

In the polarization distribution we do not see the expected 100% polarization.

schanneloptimalfit.jpg

4. Why don't we see the full polarization?

The problem is that Madevent uses approximations, e.g. the masses of the light quarks are assumed to be zero. The higher the energy, the better are the approximations.
So if we don't use pdfs but the partons themselves and change the energies of the incoming beam we can see this effect.

We get:

energy of incoming partons (GeV) degree of polarization
200 0.73 +/- 0.02
500 0.93 +/- 0.02
2000 0.99 +/- 0.02

Histogram for 2000 GeV partons:

madeventschannel2000.jpg

5. Madevent approximations

For an incoming beam of 200 GeV and a minimum PT of 100 GeV for the bottom quark, we get D = 0.90 +/- 0.02. So it can be assumed that Madevent doesn't give the expected 100 % polarization because it makes approximations while producing events (e.g. the bottom quark being massless).

5. References

1. The madgraph website: http://madgraph.hep.uiuc.edu/
2. "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 - 07 May 2008
Topic attachments
I Attachment Action Size Date WhoSorted ascending Comment
HEP9611367.pdfpdf HEP9611367.pdf manage 194 K 09 Apr 2008 - 00:05 SarahHeim  
madeventschannel2000.jpgjpg madeventschannel2000.jpg manage 22 K 07 May 2008 - 21:59 SarahHeim  
pidschannel.jpgjpg pidschannel.jpg manage 21 K 08 Apr 2008 - 22:47 SarahHeim  
s-channel.jpgjpg s-channel.jpg manage 7 K 08 Apr 2008 - 23:13 SarahHeim  
schanneloptimalfit.jpgjpg schanneloptimalfit.jpg manage 23 K 08 Apr 2008 - 23:08 SarahHeim  
schanneltevatronpaper.jpgjpg schanneltevatronpaper.jpg manage 18 K 08 Apr 2008 - 23:10 SarahHeim  
Topic revision: r47 - 08 May 2008, SarahHeim
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