Difference between revisions of "Lmd eta three pion hlu"
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<td>[[file:CompareThetaPim etaprime eta.png |thumb|left|300px]]</td> | <td>[[file:CompareThetaPim etaprime eta.png |thumb|left|300px]]</td> | ||
<td>[[file:ComparePhiPim etaprime eta.png |thumb|left|300px]]</td> | <td>[[file:ComparePhiPim etaprime eta.png |thumb|left|300px]]</td> | ||
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| + | </table> | ||
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| + | <table> | ||
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| + | <td>[[file:CompareEBeam eta three pion.png |thumb|left|300px]]</td> | ||
| + | </tr> | ||
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| + | <td>[[file:CompareMomentumProton eta three pion.png |thumb|left|300px]]</td> | ||
| + | <td>[[file:CompareThetaProton eta three pion.png |thumb|left|300px]]</td> | ||
| + | <td>[[file:ComparePhiProton eta three pion.png |thumb|left|300px]]</td> | ||
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| + | </tr> | ||
| + | <tr> | ||
| + | <td>[[file:CompareMomentumPip eta three pion.png |thumb|left|300px]]</td> | ||
| + | <td>[[file:CompareThetaPip eta three pion.png |thumb|left|300px]]</td> | ||
| + | <td>[[file:ComparePhiPip eta three pion.png |thumb|left|300px]]</td> | ||
| + | </tr> | ||
| + | <tr> | ||
| + | <td>[[file:CompareMomentumPim eta three pion.png |thumb|left|300px]]</td> | ||
| + | <td>[[file:CompareThetaPim eta three pion.png |thumb|left|300px]]</td> | ||
| + | <td>[[file:ComparePhiPim eta three pion.png |thumb|left|300px]]</td> | ||
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Revision as of 12:35, 10 April 2014
Statistics
Fit missing mass of proton
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:
Test of the formula
10M events of Gaussian distribution were generated for a histograms:
side-band subtracted and plot together with the function:
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
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
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
