I would like to understand how experimentalists search for new physics at the LHC. Lets imagine I want to use the LHC data to put a bound on the coupling of some new physics effective operator, say, for example a flavor changing Yukawa interaction of the form $t_R c_LH$ (top-charm-Higgs).
What I have understood up to now is the following (correct me if I'm wrong): one must first look at the interesting channels that involve these new interactions e.g. $p p \to t \bar t$ followed by the new decay $t\to Hc$. Next, assume the new effective coupling is such that the Branching ratio lies within the current experimental uncertaintes $Br(t\to Hc)\sim 1\%$. Then you have to simulate (with Monte Carlo) the relevant processes, count the number of expected events (after subtracting the SM background) and finally compare it to the real Data. This should give an upper bound on the effective coupling.
Can someone give me a detailed description of these type of LHC searches? I am particularly interested in understanding the role of the MC simulations (MadGraph, Pythia, etc). Thanks!