I have studied QFT from Peskin and Schroeder and from a few other books and lectures and I think I understand the procedure of renormalizing various parameters in the Lagrangian like mass, coupling constant, field strength etc. And in $\phi^4$ theory I did repeat the calculations by myself and in other theories too I have tried a bit and everything was straight forward. But the real problem I faced when I was trying to calculate a decay amplitude (the question is not specific to decay only) and I am going to explain the question step by step below.
Suppose I am calculating the process $ A \to B + C $ up to 1-loop order, then:
At tree level what are the values of the masses and various parameters used ? Are they the parameters of the Lagrangian directly replaced by the experimental values ? Or even in the tree level calculations we consider the 1-loop correction to the masses and wave functions ?
In the 1-loop diagram calculation, if we consider the external legs corrected by the wave function renormalization, then are we not going to more than one loop already ? What I mean is, consider the diagram:
How is it a 1-loop diagram if we consider the renormalization of the external legs ?