Why Does Inserting a Mass Width Simulate Higher Order Diagram Effects?

[EL]

When calulating near resonant cross sections one usually inserts a mass width in the denominator of the propagator. This should, at least as I have understood it, correspond to taking the higher order diagrams into account.
What I would like to see is a proof for the equivalence between inserting a mass width and calculating the process to higer orders. Anyone's got a reference to this?

 

[ZapperZ]

When calulating near resonant cross sections one usually inserts a mass width in the denominator of the propagator. This should, at least as I have understood it, correspond to taking the higher order diagrams into account.
What I would like to see is a proof for the equivalence between inserting a mass width and calculating the process to higer orders. Anyone's got a reference to this?

Maybe I understood you incorrectly, but it appears that you're asking for the origin, or at least the perturbation expansion, in the self-energy of the propagator. If this is correct, shouldn't this be something that is covered in a typical QFT text? I would even recommend Mattuck's "Feynman Diagram in Many-Body Problems" (Dover), which has planty of examples of such perturbation expansion.

Zz.

 

[Haelfix]

Usually you add terms like that to the denominator of the propagator when you are treating a particle that has an unstable decay width. So you add the term to smear out its mass function and hence avoid problematic poles.

If you run through the field theoretic calculatiosn carefully you see its simply proportional to contributions from 1 loop self energy diagrams, or you could simply put in numbers from experiment.

Peskin and Shroeder most likely would be your best bet

 

[EL]

I (or really a co-worker) couldn't find it in Peskin & Schroeder. Neither was there a complete investigation in Mand&Shaw.
I will try Mattuck, and aslo check P&S myself.

 

[EL]

To clearify: I want to know if the method of adding those mass widths in the denominator of the propagator is equivalent to calculating the process to higher orders in general, or if it is just an ad hoc method or a method that only works under certian circumstances?

 

[vanesch]

To clearify: I want to know if the method of adding those mass widths in the denominator of the propagator is equivalent to calculating the process to higher orders in general, or if it is just an ad hoc method or a method that only works under certian circumstances?

There IS something about it in P&S, but it is not rigorous although quite suggestive. I don't have the book here handy, but it is close to the application of the optical theorem.

 

[Norman]

There IS something about it in P&S, but it is not rigorous although quite suggestive. I don't have the book here handy, but it is close to the application of the optical theorem.

Page 236 in P&S

 

[EL]

Yeah, there is indeed something about it in P&S.
Thanks!

 

[dextercioby]

I'd suggest Bailin & Love for a nice exposure about "dimensional regularization". It contains the regularization of the 7 "dangerous" diagrams in QCD and Roberto Casalbuoni's lecture notes the application of dimensional regularization to QED.

One loop in both cases, of course.

Daniel.

 

[EL]

I'd suggest Bailin & Love for a nice exposure about "dimensional regularization".Daniel.

Is the title "Dimensional regualrisation"?
Just can find "Introduction to gauge field theory" at the library here.