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:

  1. 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 ?

  2. 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:

enter image description here

How is it a 1-loop diagram if we consider the renormalization of the external legs ?

  • $\begingroup$ The amputated diagram is one-loop. It's just terminology to call the entire diagram then "one-loop". $\endgroup$
    – ACuriousMind
    Commented Jul 4, 2015 at 9:56
  • $\begingroup$ @ACuriousMind so are you saying that I should still treat the above diagram one loop ? Does that mean even at tree level calculation I should dress-up the external legs ? $\endgroup$
    – quanta
    Commented Jul 4, 2015 at 10:08


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