Difference between revisions of "Lmd eta three pion hlu"

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−
==More==
+
==old==
 +
===Statistics===
 +
====Fit missing mass of proton====
 +
<table>
 +
<tr>
 +
<td>
 +
[[File:Linear background fit g11.png|thumb|left|400px|fit missing mass of proton with linear background from g11 data. ~1.3M events]]
 +
</td>
 +
<td>
 +
[[File:Linear background fit g12.png|thumb|left|400px|fit missing mass of proton with linear background from g12 data. ~1.5M events]]
 +
</td>
 +
 
 +
</tr>
 +
</table>
 +
 
 +
===More===
 +
[[File:Eta and eta prime two pion.pdf]]
 +
===Form of side-band subtraction histograms===
 +
Question: Suppose there is an original function (e.g. Gaussian), what is the form of the function after bin-by-bin side-band subtraction
 +
 
 +
Answer: Suppose the function is y=f(x). The side-band subtraction makes a new function:
 +
 
 +
[[File:formula.gif]]
 +
 
 +
====Test of the formula====
 +
10M events of Gaussian distribution were generated for a histograms:
 +
 
 +
[[File:standard_gaussian_fit.png]]
 +
 
 +
side-band subtracted and plot together with the function:
 +
 
 +
[[File:side_band_subtracted_standard_gaussian_fit.png]]
 +
 
 +
source code:
 +
<pre>
 +
test(){
 +
  const float NEvent=1e7;
 +
  const int NBin=50;
 +
  const float Low=-5;
 +
  const float High=5;
 +
  const float BinWidth=(High-Low)/NBin;
 +
  TH1D* h1=new TH1D("test","test",NBin,Low,High);
 +
  h1->FillRandom("gaus",NEvent);
 +
  TH1D* h2=h1->Clone("subtracted");
 +
  for(int i=2;i<100;i++){
 +
    float middle=h1->GetBinContent(i);
 +
    float left=h1->GetBinContent(i-1);
 +
    float right=h1->GetBinContent(i+1);
 +
    float result=middle-(left+right)/2.0;
 +
    float error=sqrt(middle+left/2.0+right/2.0);
 +
    h2->SetBinContent(i,result);
 +
    h2->SetBinError(i,error);
 +
  }
 +
 
 +
  TF1* func=new TF1("fit","-[3]*[3]/2*(-gaus(0)/[2]/[2]+(x-[1])*(x-[1])*gaus(0)/([2]**4))");
 +
 
 +
  func->FixParameter(2,1);
 +
  func->FixParameter(0,NEvent/sqrt(2*3.1416)/1*BinWidth);
 +
  func->FixParameter(1,0);
 +
  func->FixParameter(3,BinWidth);
 +
 
 +
  h2->Fit("fit");
 +
  TCanvas* c1=new TCanvas("c1","c1",696,474);
 +
  h2->Draw();
 +
  TCanvas* c2=new TCanvas("c2","c2",696,474);
 +
  h1->Fit("gaus");
 +
  h1->Draw();
 +
}
 +
 
 +
 
 +
</pre>
 +
 
 +
==== Test with larg bin width ====
 +
 
 +
<table>
 +
<tr>
 +
<td>[[File:Side band subtracted standard gaussian fit 1sigma.png|thumb|left|300px|fit of side-band subtracted Gaussian. bin width:1, Sigma: 1 Original magnitude: 3.98942e+02; fitted magnitude: 3.31002e+02]]</td>
 +
<td>[[File:Side band subtracted standard gaussian fit 0.5sigma.png|thumb|left|300px|fit of side-band subtracted Gaussian. bin width:0.5, Sigma: 1 Original magnitude: 1.99471e+02; fitted magnitude: 1.91370e+02]]</td>
 +
<td>[[File:Side band subtracted standard gaussian fit 2sigma.png|thumb|left|300px|fit of side-band subtracted Gaussian. bin width:2, Sigma: 1 Original magnitude: 7.97884e+02; fitted magnitude: 2.49810e+02]]</td>
 +
</tr>
 +
</table>
 +
 
 +
<pre>
 +
test(){
 +
  const float NEvent=1e3;
 +
  const int NBin=5;
 +
  const float Low=-5;
 +
  const float High=5;
 +
  const float BinWidth=(High-Low)/NBin;
 +
  TRandom3 random(0);
 +
  TH1D* h1=new TH1D("test","test",NBin,Low,High);
 +
  h1->FillRandom("gaus",NEvent);
 +
  TH1D* h2=h1->Clone("subtracted");
 +
  for(int i=2;i<100;i++){
 +
    float middle=h1->GetBinContent(i);
 +
    float left=h1->GetBinContent(i-1);
 +
    float right=h1->GetBinContent(i+1);
 +
    float result=middle-(left+right)/2.0;
 +
    float error=sqrt(middle+left/2.0+right/2.0);
 +
    h2->SetBinContent(i,result);
 +
    h2->SetBinError(i,error);
 +
  }
 +
 
 +
  TF1* funcFix=new TF1("fit_fix","-[3]*[3]/2*(-gaus(0)/[2]/[2]+(x-[1])*(x-[1])*ga\
 +
us(0)/([2]**4))");
 +
 
 +
  funcFix->FixParameter(2,1);
 +
  funcFix->FixParameter(0,NEvent/sqrt(2*3.1416)/1*BinWidth);
 +
  funcFix->FixParameter(1,0);
 +
  funcFix->FixParameter(3,BinWidth);
 +
  funcFix->SetLineColor(kRed);
 +
  h2->Fit("fit_fix");
 +
  TF1* func=new TF1("fit","-[3]*[3]/2*(-gaus(0)/[2]/[2]+(x-[1])*(x-[1])*gaus(0)/(\
 +
[2]**4))");
 +
 
 +
  func->FixParameter(2,1);
 +
  //  func->FixParameter(0,NEvent/sqrt(2*3.1416)/1*BinWidth);
 +
  func->FixParameter(1,0);
 +
  func->FixParameter(3,BinWidth);
 +
  func->SetLineColor(kBlue);
 +
  h2->Fit("fit","+");
 +
  TCanvas* c1=new TCanvas("c1","c1",696,474);
 +
  h2->Draw();
 +
  TCanvas* c2=new TCanvas("c2","c2",696,474);
 +
  h1->Fit("gaus");
 +
  h1->Draw();
 +
}
 +
 
 +
</pre>
 +
 
 +
===Test with background===
 +
<table>
 +
<tr>
 +
<td>[[File:Fit standard guassian background.png|thumb|left|300px|fit of standard Gaussian with second-order polynomial background.]]</td>
 +
<td>[[File:Side band subtracted standard gaussian fit 2sigma background.png|thumb|left|300px|fit of side-band subtracted Gaussian. bin width:0.5, Sigma: 1 Original magnitude: 1.99471e+04; fitted magnitude: 1.98083e+04]]</td>
 +
</tr>
 +
</table>
 +
 
 +
<pre>
 +
test(){
 +
  const float NEvent=1e5;
 +
  const float NSignal=1e5;
 +
  const int NBin=20;
 +
  const float Low=-5;
 +
  const float High=5;
 +
  const float BinWidth=(High-Low)/NBin;
 +
  TRandom3 random(0);
 +
  TH1D* h1=new TH1D("test","test",NBin,Low,High);
 +
  h1->FillRandom("pol2",NEvent);
 +
  h1->FillRandom("gaus",NSignal);
 +
  TH1D* h2=h1->Clone("subtracted");
 +
  for(int i=2;i<100;i++){
 +
    float middle=h1->GetBinContent(i);
 +
    float left=h1->GetBinContent(i-1);
 +
    float right=h1->GetBinContent(i+1);
 +
    float result=middle-(left+right)/2.0;
 +
    float error=sqrt(middle+left/2.0+right/2.0);
 +
    h2->SetBinContent(i,result);
 +
    h2->SetBinError(i,error);
 +
  }
 +
 
 +
  TF1* funcFix=new TF1("fit_fix","-[3]*[3]/2*(-gaus(0)/[2]/[2]+(x-[1])*(x-[1])*gaus(0)/([2]**4))");
 +
 
 +
  funcFix->FixParameter(2,1);
 +
  funcFix->FixParameter(0,NSignal/sqrt(2*3.1416)/1*BinWidth);
 +
  funcFix->FixParameter(1,0);
 +
  funcFix->FixParameter(3,BinWidth);
 +
  funcFix->SetLineColor(kRed);
 +
  h2->Fit("fit_fix");
 +
  TF1* func=new TF1("fit","-[3]*[3]/2*(-gaus(0)/[2]/[2]+(x-[1])*(x-[1])*gaus(0)/([2]**4))");
 +
 
 +
  func->FixParameter(2,1);
 +
  //  func->FixParameter(0,NEvent/sqrt(2*3.1416)/1*BinWidth);
 +
  func->FixParameter(1,0);
 +
  func->FixParameter(3,BinWidth);
 +
  func->SetLineColor(kBlue);
 +
  h2->Fit("fit","+");
 +
 
 +
  TCanvas* c2=new TCanvas("c2","c2",696,474);
 +
  h2->Draw();
 +
  TCanvas* c1=new TCanvas("c1","c1",696,474);
 +
  TF1* signal_back=new TF1("signal_back","gaus(0)+pol2(2)");
 +
  signal_back->SetParameters(NEvent/sqrt(2*3.1416)/1*BinWidth,0.0,1.0,0.0,0.0,0.0);
 +
  h1->Fit("signal_back");
 +
  h1->Draw();
 +
}
 +
</pre>
 +
 
 +
==== apply on the data ====
 +
bin width=1MeV yield/error:0.16384 limit:1.81985
 +
 
 +
bin width=2MeV yield/error:-1.69772 limit:0.491618
 +
 
 +
bin width=3MeV yield/error:-2.48978 limit:0.321244
 +
=== Compare data and simu ===
 +
==== eta prime====
 +
<table>
 +
<tr>
 +
<td>[[file:CompareEBeam etaprime eta.png ‎|thumb|left|300px|compare beam energy between data (red) and simulation (blue)]]</td>
 +
</tr>
 +
<tr>
 +
<td>[[file:CompareMomentumProton etaprime eta.png ‎|thumb|left|300px|compare momentum of proton between data (red) and simulation (blue)]]</td>
 +
<td>[[file:CompareThetaProton etaprime eta.png ‎|thumb|left|300px|compare polar angle of proton between data (red) and simulation (blue)]]</td>
 +
<td>[[file:ComparePhiProton etaprime eta.png ‎|thumb|left|300px|compare azimuthal angle between data (red) and simulation (blue)]]</td>
 +
 
 +
</tr>
 +
<tr>
 +
<td>[[file:CompareMomentumPip etaprime eta.png ‎|thumb|left|300px|compare momentum of pi+ between data (red) and simulation (blue)]]</td>
 +
<td>[[file:CompareThetaPip etaprime eta.png ‎|thumb|left|300px|compare polar angle of pi+ between data (red) and simulation (blue)]]</td>
 +
<td>[[file:ComparePhiPip etaprime eta.png ‎|thumb|left|300px|compare azimuthal angle of pi+ between data (red) and simulation (blue)]]</td>
 +
</tr>
 +
<tr>
 +
<td>[[file:CompareMomentumPim etaprime eta.png ‎|thumb|left|300px|compare momentum of pi- between data (red) and simulation (blue)]]</td>
 +
<td>[[file:CompareThetaPim etaprime eta.png ‎|thumb|left|300px|compare polar angle of pi- between data (red) and simulation (blue)]]</td>
 +
<td>[[file:ComparePhiPim etaprime eta.png ‎|thumb|left|300px|compare azimuthal angle between data (red) and simulation (blue)]]</td>
 +
</tr>
 +
 
 +
</table>
 +
 
 +
==== eta====
 +
<table>
 +
<tr>
 +
<td>[[file:CompareEBeam eta three pion.png ‎|thumb|left|300px|compare beam energy between data (red) and simulation (blue)]]</td>
 +
</tr>
 +
<tr>
 +
<td>[[file:CompareMomentumProton eta three pion.png ‎|thumb|left|300px|compare momentum of proton between data (red) and simulation (blue)]]</td>
 +
<td>[[file:CompareThetaProton eta three pion.png ‎|thumb|left|300px|compare polar angle of proton between data (red) and simulation (blue)]]</td>
 +
<td>[[file:ComparePhiProton eta three pion.png ‎|thumb|left|300px|compare azimuthal angle of proton between data (red) and simulation (blue)]]</td>
 +
 
 +
</tr>
 +
<tr>
 +
<td>[[file:CompareMomentumPip eta three pion.png ‎|thumb|left|300px|compare momentum of pi+ between data (red) and simulation (blue)]]</td>
 +
<td>[[file:CompareThetaPip eta three pion.png ‎|thumb|left|300px|compare polar angle of pi+ between data (red) and simulation (blue)]]</td>
 +
<td>[[file:ComparePhiPip eta three pion.png ‎|thumb|left|300px|compare azimuthal angle of pi+ between data (red) and simulation (blue)]]</td>
 +
</tr>
 +
<tr>
 +
<td>[[file:CompareMomentumPim eta three pion.png ‎|thumb|left|300px|compare momentum of pi- between data (red) and simulation (blue)]]</td>
 +
<td>[[file:CompareThetaPim eta three pion.png ‎|thumb|left|300px|compare polar angle of pi- between data (red) and simulation (blue)]]</td>
 +
<td>[[file:ComparePhiPim eta three pion.png ‎|thumb|left|300px|compare azimuthal angle of pi- between data (red) and simulation (blue)]]</td>
 +
</tr>
 +
 
 +
</table>
 +
 
 +
===Feldman-Cousin Method===
 +
[[File:Feldman cousin upper limit.png]]
 +
==Revive==
 +
===channel===
 +
&gamma; p &rarr; p &pi;+&pi;-&pi;+&pi;-
 +
 
 +
selecting p &eta; prime production and &eta; prime decay to &pi;+&pi;-&eta;
 +
 
 +
<table>
 +
<tr>
 +
<td>[[File:Mm p before cut.png|thumb|left|300px|before selecting &eta; prime]]</td>
 +
<td>[[File:Mm p after cut.png|thumb|left|300px|after selecting &eta; prime. A mistake makes the selection too too tight]]</td>
 +
</tr>
 +
</table>
 +
===Production channels===
 +
<table>
 +
<tr>
 +
<td>[[File:Mm2vsmmppipi.png|thumb|left|300px|Missing mass square vs. missing mass of p＆pi;+&pi;-]]</td>
 +
<td>[[File:Mm ppippim.png|thumb|left|300px|Fit &eta; in spectrum of missing mass of p＆pi;+&pi;- and yield 6349]]</td>
 +
</tr>
 +
</table>
 +
 
 +
===With or Without photon===
 +
<table>
 +
<tr>
 +
<td>[[File:Mpvsmmpppipi.png|thumb|left|300px|Missing momentum vs. missing mass of p＆pi;+&pi;- after selecting missing mass around zero]]</td>
 +
<td>[[File:Im pippim.png|thumb|left|300px|Invariant mass of &pi;+&pi;- after requiring missing momentum smaller than 50 MeV]]</td>
 +
</tr>
 +
</table>
 +
===Upper Limit===
 +
<table>
 +
<tr>
 +
<td>[[File:Fit im pippim.png|thumb|left|300px|Fit of invariant mass of &pi;+&pi;- around &eta; and yield upper limit of 1.64 with statistical uncertainty of bin at 5.12 and fitted yield -12.5]]</td>
 +
</tr>
 +
</table>
 +
 
 +
Therefore, the upper limit is 1.64/6349*0.28(fraction of all charged mode)=7.0e-5
  
 
==reference==
 
==reference==
 +
[http://fr.arxiv.org/pdf/hep-ex/0411030v2 upper limit of eta with KLOE detector]

Latest revision as of 16:31, 30 October 2015

old

Statistics

Fit missing mass of proton

Error creating thumbnail: File missing
fit missing mass of proton with linear background from g11 data. ~1.3M events
Error creating thumbnail: File missing
fit missing mass of proton with linear background from g12 data. ~1.5M events

More

File:Eta and eta prime two pion.pdf

Form of side-band subtraction histograms

Question: Suppose there is an original function (e.g. Gaussian), what is the form of the function after bin-by-bin side-band subtraction

Answer: Suppose the function is y=f(x). The side-band subtraction makes a new function:

Formula.gif

Test of the formula

10M events of Gaussian distribution were generated for a histograms:

Standard gaussian fit.png

side-band subtracted and plot together with the function:

Side band subtracted standard gaussian fit.png

source code: 

test(){
  const float NEvent=1e7;
  const int NBin=50;
  const float Low=-5;
  const float High=5;
  const float BinWidth=(High-Low)/NBin;
  TH1D* h1=new TH1D("test","test",NBin,Low,High);
  h1->FillRandom("gaus",NEvent);
  TH1D* h2=h1->Clone("subtracted");
  for(int i=2;i<100;i++){
    float middle=h1->GetBinContent(i);
    float left=h1->GetBinContent(i-1);
    float right=h1->GetBinContent(i+1);
    float result=middle-(left+right)/2.0;
    float error=sqrt(middle+left/2.0+right/2.0);
    h2->SetBinContent(i,result);
    h2->SetBinError(i,error);
  }

  TF1* func=new TF1("fit","-[3]*[3]/2*(-gaus(0)/[2]/[2]+(x-[1])*(x-[1])*gaus(0)/([2]**4))");

  func->FixParameter(2,1);
  func->FixParameter(0,NEvent/sqrt(2*3.1416)/1*BinWidth);
  func->FixParameter(1,0);
  func->FixParameter(3,BinWidth);

  h2->Fit("fit");
  TCanvas* c1=new TCanvas("c1","c1",696,474);
  h2->Draw();
  TCanvas* c2=new TCanvas("c2","c2",696,474);
  h1->Fit("gaus");
  h1->Draw();
}

Test with larg bin width

Error creating thumbnail: File missing
fit of side-band subtracted Gaussian. bin width:1, Sigma: 1 Original magnitude: 3.98942e+02; fitted magnitude: 3.31002e+02
Error creating thumbnail: File missing
fit of side-band subtracted Gaussian. bin width:0.5, Sigma: 1 Original magnitude: 1.99471e+02; fitted magnitude: 1.91370e+02
Error creating thumbnail: File missing
fit of side-band subtracted Gaussian. bin width:2, Sigma: 1 Original magnitude: 7.97884e+02; fitted magnitude: 2.49810e+02
 
test(){
  const float NEvent=1e3;
  const int NBin=5;
  const float Low=-5;
  const float High=5;
  const float BinWidth=(High-Low)/NBin;
  TRandom3 random(0);
  TH1D* h1=new TH1D("test","test",NBin,Low,High);
  h1->FillRandom("gaus",NEvent);
  TH1D* h2=h1->Clone("subtracted");
  for(int i=2;i<100;i++){
    float middle=h1->GetBinContent(i);
    float left=h1->GetBinContent(i-1);
    float right=h1->GetBinContent(i+1);
    float result=middle-(left+right)/2.0;
    float error=sqrt(middle+left/2.0+right/2.0);
    h2->SetBinContent(i,result);
    h2->SetBinError(i,error);
  }

  TF1* funcFix=new TF1("fit_fix","-[3]*[3]/2*(-gaus(0)/[2]/[2]+(x-[1])*(x-[1])*ga\
us(0)/([2]**4))");

  funcFix->FixParameter(2,1);
  funcFix->FixParameter(0,NEvent/sqrt(2*3.1416)/1*BinWidth);
  funcFix->FixParameter(1,0);
  funcFix->FixParameter(3,BinWidth);
  funcFix->SetLineColor(kRed);
  h2->Fit("fit_fix");
  TF1* func=new TF1("fit","-[3]*[3]/2*(-gaus(0)/[2]/[2]+(x-[1])*(x-[1])*gaus(0)/(\
[2]**4))");

  func->FixParameter(2,1);
  //  func->FixParameter(0,NEvent/sqrt(2*3.1416)/1*BinWidth);
  func->FixParameter(1,0);
  func->FixParameter(3,BinWidth);
  func->SetLineColor(kBlue);
  h2->Fit("fit","+");
  TCanvas* c1=new TCanvas("c1","c1",696,474);
  h2->Draw();
  TCanvas* c2=new TCanvas("c2","c2",696,474);
  h1->Fit("gaus");
  h1->Draw();
}

Test with background

Error creating thumbnail: File missing
fit of standard Gaussian with second-order polynomial background.
Error creating thumbnail: File missing
fit of side-band subtracted Gaussian. bin width:0.5, Sigma: 1 Original magnitude: 1.99471e+04; fitted magnitude: 1.98083e+04
 
test(){
  const float NEvent=1e5;
  const float NSignal=1e5;
  const int NBin=20;
  const float Low=-5;
  const float High=5;
  const float BinWidth=(High-Low)/NBin;
  TRandom3 random(0);
  TH1D* h1=new TH1D("test","test",NBin,Low,High);
  h1->FillRandom("pol2",NEvent);
  h1->FillRandom("gaus",NSignal);
  TH1D* h2=h1->Clone("subtracted");
  for(int i=2;i<100;i++){
    float middle=h1->GetBinContent(i);
    float left=h1->GetBinContent(i-1);
    float right=h1->GetBinContent(i+1);
    float result=middle-(left+right)/2.0;
    float error=sqrt(middle+left/2.0+right/2.0);
    h2->SetBinContent(i,result);
    h2->SetBinError(i,error);
  }

  TF1* funcFix=new TF1("fit_fix","-[3]*[3]/2*(-gaus(0)/[2]/[2]+(x-[1])*(x-[1])*gaus(0)/([2]**4))");

  funcFix->FixParameter(2,1);
  funcFix->FixParameter(0,NSignal/sqrt(2*3.1416)/1*BinWidth);
  funcFix->FixParameter(1,0);
  funcFix->FixParameter(3,BinWidth);
  funcFix->SetLineColor(kRed);
  h2->Fit("fit_fix");
  TF1* func=new TF1("fit","-[3]*[3]/2*(-gaus(0)/[2]/[2]+(x-[1])*(x-[1])*gaus(0)/([2]**4))");

  func->FixParameter(2,1);
  //  func->FixParameter(0,NEvent/sqrt(2*3.1416)/1*BinWidth);
  func->FixParameter(1,0);
  func->FixParameter(3,BinWidth);
  func->SetLineColor(kBlue);
  h2->Fit("fit","+");

  TCanvas* c2=new TCanvas("c2","c2",696,474);
  h2->Draw();
  TCanvas* c1=new TCanvas("c1","c1",696,474);
  TF1* signal_back=new TF1("signal_back","gaus(0)+pol2(2)");
  signal_back->SetParameters(NEvent/sqrt(2*3.1416)/1*BinWidth,0.0,1.0,0.0,0.0,0.0);
  h1->Fit("signal_back");
  h1->Draw();
}

apply on the data

bin width=1MeV yield/error:0.16384 limit:1.81985

bin width=2MeV yield/error:-1.69772 limit:0.491618

bin width=3MeV yield/error:-2.48978 limit:0.321244

Compare data and simu

eta prime

Error creating thumbnail: File missing
compare beam energy between data (red) and simulation (blue)
Error creating thumbnail: File missing
compare momentum of proton between data (red) and simulation (blue)
Error creating thumbnail: File missing
compare polar angle of proton between data (red) and simulation (blue)
Error creating thumbnail: File missing
compare azimuthal angle between data (red) and simulation (blue)
Error creating thumbnail: File missing
compare momentum of pi+ between data (red) and simulation (blue)
Error creating thumbnail: File missing
compare polar angle of pi+ between data (red) and simulation (blue)
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compare azimuthal angle of pi+ between data (red) and simulation (blue)
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compare momentum of pi- between data (red) and simulation (blue)
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compare polar angle of pi- between data (red) and simulation (blue)
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compare azimuthal angle between data (red) and simulation (blue)

eta

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compare beam energy between data (red) and simulation (blue)
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compare momentum of proton between data (red) and simulation (blue)
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compare polar angle of proton between data (red) and simulation (blue)
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compare azimuthal angle of proton between data (red) and simulation (blue)
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compare momentum of pi+ between data (red) and simulation (blue)
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compare polar angle of pi+ between data (red) and simulation (blue)
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compare azimuthal angle of pi+ between data (red) and simulation (blue)
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compare momentum of pi- between data (red) and simulation (blue)
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compare polar angle of pi- between data (red) and simulation (blue)
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compare azimuthal angle of pi- between data (red) and simulation (blue)

Feldman-Cousin Method

Feldman cousin upper limit.png

Revive

channel

γ p → p π+π-π+π-

selecting p η prime production and η prime decay to π+π-η

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before selecting η prime
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after selecting η prime. A mistake makes the selection too too tight

Production channels

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Missing mass square vs. missing mass of p＆pi;+π-
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Fit η in spectrum of missing mass of p＆pi;+π- and yield 6349

With or Without photon

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Missing momentum vs. missing mass of p＆pi;+π- after selecting missing mass around zero
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Invariant mass of π+π- after requiring missing momentum smaller than 50 MeV

Upper Limit

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Fit of invariant mass of π+π- around η and yield upper limit of 1.64 with statistical uncertainty of bin at 5.12 and fitted yield -12.5

Therefore, the upper limit is 1.64/6349*0.28(fraction of all charged mode)=7.0e-5

reference

upper limit of eta with KLOE detector

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