Fake rate in Particle Physics What is exactly the meaning of "fake rate" in experimental particle physics? 
NB: detailed explanations are deeply appreciated. And I already searched on google, my goal is to cross-check my understanding and get some more details.
 A: Say you are interested in a process with a distinctive final state X. But that a group of different processes may give a final state Y that the detector will identify as X. Then the rate of such misindentifications is the fake rate for Y with respect to X. What is important in the definition is that the particles in Y shall be different from the particles in X, thus the former faking the latter. 
Thus here is first a counter-example: there is $H\to\gamma\gamma$ but we can also have $pp\to\gamma\gamma$ through the box diagram.

This does not enter the fake rate as we have exactly the same particles produced at the quark level.
Here is, on the contrary, a non-exhaustive list of examples, with as much details as I can remember (I could search for references if you are interested):
Gluon-initiated jets may fake light-quark initiated jets. The fake rate is about 1/3 from the top of my head.
The jet in $H\to W + \text{jet}$ may fake one of the lepton in $H\to WW \to l\nu l\nu$:


*

*the decay of a $\pi^0$ may produce a $\gamma$ in the jet, that would then gives an electron (photon conversion); 

*some heavy-flavour hadrons have semi-leptonic decays (i.e. leptons and hadrons in the final state); and then 

*a proton could be mistaken as an electron. 


In this case the fake rate is actually rather low but the cross-section of production of $W + \text{jet}$ is about 3 orders of magnitude higher than the prompt production of $WW$ (where prompt means the process one is interested in here), thus making the fakes an issue.
Prompt photon production is the production of one, or two $\gamma$ at the quark level (good you asked that other question a short while ago, so that I don't need to explain that!). $\pi^0\to 2\gamma$ or $\eta\to 2\gamma$ can fake one prompt photon (the Lorentz boost makes the two photons so parallel that the detector can't discriminate them) whereas $\omega\to\pi^0\gamma$ may doubly fake it. The fake rate is orders of magnitude larger than the prompt photon rate.
There may be others I did not think of but those are among the most studied. @ZeroTheHero was right to focus on fakes of electrons because this is one of the most important one in LHC physics, since it is involved in the Higgs search. But the term is more general, as I hope, is conveyed by this answer.
From here, the next step would be to study the cuts used to remove fakes, and the statistical methods used to subtract the background of those fakes. An example of cuts are the isolated photon cross-sections: events are selected with a photon, such that the hadronic energy inside a cone centred on the photon momentum is below some small threshold. A pair of photons produced by the decay of a $\pi^0$ would be surrounded by all the other hadrons of the jet the $\pi^0$ is part of. Therefore isolating photons in such a way cuts the background of fakes, allowing the measurement of prompt photons, which would be hopeless otherwise.
