I am new to Roofit, so I am very sorry for the basic question. I am doing an extended likelihood fit S+B (model: Nssgn(x,…) + Nbbkg(x,…)), and I obtain the signal yield Ns and other parameters. After this, I can plot also the NLL and the profiled NLL vs those POIs.
However, I cannot figure out how can I do if, instead of Ns, I want to put as POI the cross-section (which is related to Ns by means of the luminosity ) … and then plot the NLL as function of this new POI (or derived?).
I am building the S+B model with RooAddPdf, and this allows easily to perform the extended likelihood fit and obtain Ns, but I cannot find how to obtain what I need.
You can express your model in term of Ns, the number of signal events, that will be a RooRealVar object, or you can express in term of the cross section, defining then Ns = Lint * sigma where Lint is the integrated luminosity (a parameter of your model, which will be constant or defined using a Gaussian constraint to describe its uncertainty and sigma will be the parameter of interest of the model.
You can do this creating a RooProduct object defining Ns and pass it as parameter of your pdf as before. For example:
RooRealVar sigma("crossSection","crossSection",value, vmin, vmax);
RooRealVar lumi("Luminosity","Integrated luminosity",lumiValue); // assume is a constant parameter (no uncertainty)
RooProduct Ns("Ns","Number of signal events",RooArgSet(sigma,lumi));