Get normalization factor of the plotted PDF

[iaosiiuv]

Dear experts,

I would like to know how many events Roofit used to renormalize the PDF when plotted, or I want to get directly the normalization factor. I don’t know how to get this information, and I explain below the case I am dealing with, which is not trivial.

I have a simple TDCPV example, using a RooBCPGenDecay to model the signal, and a simple gaussian for the background. I combined them using RooAddPdf:

# Background PDF
mgBkg = r.RooRealVar("mgBkgB", "mg", 0)
sgBkg = r.RooRealVar("sgBkg1", "sg2", 4.3)
bkgPDF = r.RooGaussian("bkgPDF", "gauss", dt, mgBkg, sgBkg)

# BCPGenDecay model
BCPGenDecayPDF = r.RooBCPGenDecay("BCPGenDecayPDF", "BCPGenDecayPDF", dt, q, tau, dm, w, Agen, Sgen, dw, effR, signalRes, r.RooBCPGenDecay.DoubleSided)

# Combined PDF
combinedPDF = r.RooAddPdf("combinedPDF", "combinedPDF", r.RooArgList(BCPGenDecayPDF, bkgPDF), r.RooArgList(fsig))

Now, I generate from this combination 100000 events, which depend on the flavor q (a category, B0 or B0bar):

nevents = 100000
data_set = combinedPDF.generate(r.RooArgSet(dt, q), nevents)

and then I only plot the B0 category:

frame = dt.frame(nbins)
data_set.plotOn(frame, Cut="q==q::B0", MarkerColor=r.kBlue)
combinedPDF.plotOn(frame, Slice=(q, "B0"), Components="BCPGenDecayPDF", LineStyle=r.kDashed, LineColor=r.kGreen)
combinedPDF.plotOn(frame, Slice=(q, "B0"), Components="bkgPDF", LineStyle=r.kDashed, LineColor=r.kRed)

Now, the renormalization used by the Slice method of plotOn is trivial for the gaussian background component, but not for the CP asymmetry part.

For the background component, which doesn’t depend on the flavor, I get the correct normalization value with:

q.setLabel("B0")
xlim = (dt.getMin(), dt.getMax())
x = np.linspace(*xlim, 10000)
for i in range(len(x)):
     var.setVal(x[i])
     bkgPDF.getVal(var)*norm

with

norm = n_expected_events_for_bkgPDF * bin_width / bkgPDF_integral
     = (n_B0_events * (1 - f_sig))  * bin_width / 1
     = (nevents/2 * (1 - f_sig))    * bin_width / 1

This was tested and works wonderfully.

For BCPGenDecayPDF, this is not trivial, as we don’t have

n_expected_events_for_BCPGenDecayPDF = nevents/2 * f_sig

The dependencies on the miss-tagging w, the asymmetry parameters A and S or the misstag rate dw makes n_expected_events_for_BCPGenDecayPDF go a bit higher or lower. All those parameters are fixed before using the same method to get the correct values for the gaussian background, and somehow it is always a bit off by a factor between 0.8 and 1.1 from my tests.

I tried to get information on normalization using combinedPDF.getComponents(), or I tried to get information of the RooPlot output when I plot BCPGenDecayPDF (plot.getHist(plot.nameOf(1)) returns a null pointer, or plot.getFitRangeNEvt() returns 10000) without any success.

Any suggestions on how to get this correct normalization factor?

Best regards

[moneta]

@jonas can probably help you on this

[iaosiiuv]

Small update: I managed to correctly get the correct number for n_expected_events_for_BCPGenDecayPDF, which is:

n_expected_events_for_BCPGenDecayPDF = n_true_B0_events - n_expected_events_for_bkgPDF

with n_true_B0_events equal to the number of B0 events actually generated in the data_set. It differs from the n_B0_events defined in my first post, which is the theoretical number of B0 generated (without CP asymmetry) equal to nevents/2.

This solution gives in the end the correct normalization factor. It works because the background component doesn’t depend on the CP asymmetry.

For more complex examples, I still don’t know how I can get the normalization (or just the integral) of the plotted function by plotOn.