Can some one explain the fake factor method in a general sense? I am trying to learn the fake factor method but I am having trouble understanding the concepts. I know it is a method to check the rate at which hadron jets from proton - proton collision are mistaken as leptons in say the ATLAS detector.
http://www.hep.upenn.edu/~johnda/Papers/vC/FakeFactor.pdf
This is the article that I am currently using to inform my self.
In the page 156 we have that fake factor equals the numerator/denominator. I understand the numerator is the full selection process is a criteria to determine what are leptons. So the fake factor is a extrapolation method to compare the ratio of leptons misidentified as in the main signal region to the misidentified denominator jets in a controlled region. I do not understand what they mean by denominator or how the fake factor works ?
Page 155 the article says
"The control region is defined in order to select the background being estimated. The type of
background considered with the fake factor method arises from particle misidentification. To collect
this type background more efficiently, the particle selection in the signal region is replaced with
a particle selection for which the misidentification rate is higher. This alternative particle selection
criteria is referred to as the “denominator selection” or the “denominator definition”; particles passing
this criteria are referred to as “denominator objects” or simply “denominators”. "
So when they say that in page 156 that "The fake factor relates background which is misidentified as denominators, to background which is
misidentified as passing the full particle selection in the signal region." what is meant by denominator misidentified as denominators?
 A: To estimate the fake objects in your signal region, a control region is used. This control region (CR) should be highly dominated by these fakes but otherwise similar to the signal region (SR). Typically you invert the lepton identification criterium. While in the SR you use leptons fulfiling the "Tight" identification working point (WP), in the control region you may use all objects not fulfilling the "Tight" WP and thus enrich the CR in fakes.
Then, Yield + shape of the fakes are calculated in this region, typically via Data - MC prediction.
Now you need a transfer factor (fake-factor, extrapolation factor) from the CR to the SR. This transfer factor is defined by the ratio between events fulfiling the 'Tight' WP and those failing the 'Tight' WP in your fake CR.
So overall you have four regions:

*

*blinded signal region (Tight leptons)

*control region (not tight leptons)

*fake control region (Tight leptons but e.g. transverse mass>20 GeV)

*fake control region (not tight leptons but e.g. transverse mass>20 GeV)

In 3)+4) you measure the transfer factor to go from 2) to 1). Similar to widely used ABCD methods.
