Best function for fiting the trigger efficiency turn-on curve with Roofit

[Sumankkundu]

Can anyone please suggest the best function to fit the trigger efficiency turn-on curve with Roofit?
Thanks in advance.

[Axel]

That depends on the trigger, the objects you trigger on, etc. It’s impossible to answer that in a general way.

[Sumankkundu]

Thanks for reply.
Here I have plotting efficiency for HLT_DiPFJetAve(60,80,140,200…500) as a function of HT2(average of two leading Jet). Already, I have the turn-on histogram which I want to fit with a suitable function for calculate the turn-on value for each trigger.

[Axel]

That question cannot be answered in a general way. When I said “that depends on the trigger, the objects you trigger on” what I really meant is that this is specific to the detector, the algorithms, the trigger parameter values, etc - that’s why we won’t be able to give you “the trigger efficiency turn-on curve”.

You probably want to talk to other people from your experiment having done similar fits.

[Sumankkundu]

yes, Something like that.
Trigger_efficiency.pdf (44.8 KB)
I like to fit those histograms. I have found some example like https://root.cern.ch/doc/master/rf703__effpdfprod_8C.html.

That’s why I have put those queries here.

Cheers,

[Axel]

Well - that usually just works for toys like in the tutorial, but in there we use: RooFormulaVar eff("eff", "0.5*(TMath::Erf((t-1)/0.5)+1)", t);

[Wile_E_Coyote]

You can try different available “continuous probability distributions”. e.g.:

{
  new TCanvas("c", "distributions");
  c->Divide(1, 2);
  c->cd(1);
  gPad->SetGrid(1, 1);
  // https://en.wikipedia.org/wiki/Cauchy_distribution
  TF1 *f_cauchy = new TF1("f_cauchy", "TMath::ATan((x - [0]) / [1]) / TMath::Pi() + 0.5", 0., 200.); // CDF
  f_cauchy->SetParNames("median", "gamma");
  f_cauchy->SetParameters(85., 4.);
  f_cauchy->Draw();
  c->cd(2);
  gPad->SetGrid(1, 1);
  // https://en.wikipedia.org/wiki/Normal_distribution
  TF1 *f_gaus = new TF1("f_gaus", "0.5 * (1.0 + TMath::Erf((x - [0]) / [1] / TMath::Sqrt2()))", 0., 800.); // CDF
  f_gaus->SetParNames("mean", "sigma");
  f_gaus->SetParameters(320., 20.);
  f_gaus->Draw();
  c->cd(0);
}