Error on Number of signal events after background subtraction

[SimN]

Hi,

I subtracted a Chebychev polynomial from a histogram and after that I fit the background subtracted histogram with a gaussian and polynomial.
Before the subtraction I had Nsig = 20947 ± 1105
After the subtraction I had Nsig = 21247 ± 146
If I increment the order of polynomial the error after the subtraction is even smaller Nsig=21096 ± 11

Is there an explanation why I have this difference between the errors before and after the subtraction. Is it logical to see this result ?

My code for the subtraction

  RooRealVar x("x","MM_{(#pi #pi)} GeV/c^{2}",3.04,3.17) ;
  RooDataHist dh("dh","dataset",x,hist4260);
  RooPlot* frame = x.frame(Title("@4.26 GeV :: e^{+}e^{-} -> J/#psi #pi^{+} #pi^{-}")) ;
  dh.plotOn(frame,Name("dh")) ;
  RooRealVar mean1("#mu","mean of gaussians",3.095,3.098);
  RooRealVar sigma1("#sigma","width of gaussians",0.0025,0.006);
  RooGaussian sig1("sig1", "sig1", x, mean1, sigma1);
  RooRealVar a0("a0","a0",-2.,2.) ;
  RooRealVar a1("a1","a1",-2.,2.) ;
  RooRealVar a2("a2","a2",-2.,2.) ;
  RooRealVar a3("a3","a3",-2.,2.) ;
  RooChebychev bkg("bkg","background p.d.f.",x,RooArgList(a0));
  RooRealVar nsig("N_{SIG}","signal events",0,1000000);
  RooRealVar nbkg("N_{BKG}","signal background even0ts",0,100000000);
  RooAddPdf all("all","model",RooArgList(sig1,bkg),RooArgList(nsig,nbkg));
  RooFitResult* r = all.fitTo(dh,Extended(kTRUE),Save()) ;
  all.paramOn(frame,Layout(0.5,0.90,0.55));
  all.plotOn(frame,Components(bkg),LineStyle(kDashed));
  all.plotOn(frame,Name("all"));
  TH1 *hbkg = bkg.createHistogram("hbkg",x,Binning(150,3.04,3.17));
  
    r->Print();

  frame->GetXaxis()->SetTitle("");
  frame->GetXaxis()->SetLabelSize(1);
  frame->GetYaxis()->SetLabelSize(0.05);
  frame->SetMinimum(20000);

  RooPlot *residual= x.frame();
  RooHist *resHist = (RooHist*)frame->pullHist();
  residual->addObject(resHist,"PZ");
  residual->SetMinimum(-11.);
  residual->SetMaximum(+11.);
  residual->GetXaxis()->SetLabelSize(0.1);
  residual->GetXaxis()->SetTitleOffset(0.8);
  residual->GetXaxis()->SetTitleSize(0.15);
  residual->GetYaxis()->SetLabelSize(0.1);
  residual->GetYaxis()->SetNdivisions(110);

  TCanvas *c1 = new TCanvas("c1","Jpsi",1200,1200);
  c1->Divide(2);
  c1->GetPad(1)->SetPad(0.,0.3,1.,1.);
  c1->GetPad(2)->SetPad(0.,0.,1.,0.3);
  c1->GetPad(1)->SetBottomMargin(0);
  c1->GetPad(2)->SetTopMargin(0);
  c1->GetPad(2)->SetBottomMargin(0.25);
  c1->GetPad(2)->SetFillColor(4000);
  c1->cd(1);
  frame->Draw();
  c1->cd(2);
  residual->Draw();

My code for the fit after the subtraction

 TFile *f = new TFile("file4260.root");
  TH1F * h1 = new TH1F("h1","h1",150,3.04,3.17);
  h1 = (TH1F*)f.Get("h4260");

  RooRealVar x1("x1","MM_{(#pi #pi)} GeV/c^{2}",3.04,3.17) ;
  RooDataHist dh1("dh1","dataset",x1,h1);
  RooPlot* frame1 = x1.frame(Title("title")) ;
  dh1.plotOn(frame1,Name("dh1")) ;
  RooRealVar mean11("#mu","mean of gaussians",3.0965,3.0985);
  RooRealVar sigma11("#sigma","width of gaussians",0.002,0.0045);

  RooRealVar a0("a0","a0",-2.,2.) ;
  RooRealVar a1("a1","a1",-2.,2.) ;
  RooRealVar a2("a2","a2",-2.,2.) ;
  RooRealVar a3("a3","a3",-2.,2.) ;

  RooChebychev bkg("bkg","background p.d.f.",x1,RooArgList(a0,a1));

   RooRealVar nbkg("N_{BKG}","signal background even0ts",0,100000000);

  RooGaussian sig11("sig11", "sig11", x1, mean11, sigma11);
  RooRealVar nsig1("N_{SIG}","signal events",0,1000000);

  RooAddPdf all1("all1","model",RooArgList(sig11,bkg),RooArgList(nsig1,nbkg));

  RooFitResult* r1 = all1.fitTo(dh1,Extended(kTRUE),Save()) ;
  all1.paramOn(frame1,Layout(0.5,0.90,0.55));
  all1.plotOn(frame1,Name("all1"));
  all1.plotOn(frame1,Components(bkg),LineStyle(kDashed));
  all1.plotOn(frame1);
  r1->Print();

  RooPlot *residual1= x1.frame();
  RooHist *resHist1 = (RooHist*)frame1->pullHist();
  residual1->addObject(resHist1,"PZ");
  residual1->SetMinimum(-10.);
  residual1->SetMaximum(+10.);
  residual1->GetXaxis()->SetLabelSize(0.1);
  residual1->GetXaxis()->SetTitleOffset(0.8);
  residual1->GetXaxis()->SetTitleSize(0.15);
  residual1->GetYaxis()->SetLabelSize(0.1);
  residual1->GetYaxis()->SetNdivisions(110);

  TCanvas *c1 = new TCanvas("c1","Jpsi",1200,1200);
  c1->Divide(2);
  c1->GetPad(1)->SetPad(0.,0.3,1.,1.);
  c1->GetPad(2)->SetPad(0.,0.,1.,0.3);
  c1->GetPad(1)->SetBottomMargin(0);
  c1->GetPad(2)->SetTopMargin(0);
  c1->GetPad(2)->SetBottomMargin(0.25);
  c1->GetPad(2)->SetFillColor(4000);
  c1->cd(1);
  r1->Draw();
  frame1->Draw();
  c1->cd(2);
  residual1->Draw();

[StephanH]

You seem to have a different number of parameters. There’s an additional a1 in the bottom plot.

I could also imagine that due to the subtraction, the uncertainties of the dataset are not correct because you might need some kind of propagation of errors. RooFit probably only assumes that the data are poisson-distributed.