About propagator and poles in QFT

[Lucien1011]

Hi all, I am studying QFT using John Preskill's notes. I have a question about the propagator and poles.

On page 2.91, at the bottom, he said that there is a s-channel pole, which is the pole of the exact propagator. Then he claimed that by the argument about unitarity in page 2.70, the pole is where the physical mass of the particle sits in.

My question is: the scattering process that he is considering is a 2 body scattering process. Isn't the pole in page 2.70 the mass of the virtual particle? Why can he use the argument on page 2.70 for the actual physical mass of the particle?

Here is the link to the notes I am studying:
http://www.theory.caltech.edu/~preskill/ph205/205Chapter2-Page50-102.pdf

 

[Einj]

The mathematical expression of the propagator is a consquence of the theory you are using (i.e. of the lagrangian of your theory). Consequently the mass that appear in the denominator is that of your theory which is, after the process of renormalization, the physical mass of the particle.
The vituality of the process you are considering appears only in the value of q=p₁+p₂ and it obviously doesn't affect the value of the mass of the propagator.