Divergent Diagrams in the Standard Model

[Geonaut]

It is my understanding that the task of enumerating all of the divergent diagrams in a quantum field theory can be reduced to analyzing a hand full of diagrams (well, at the moment I know that this is at least true for QED and phi^4 theory), and that all other divergent diagrams are divergent because they contain at least one of these said hand full of diagrams as a subdiagram.

When I bought Peskin I had assumed/hoped that all of the basic information regarding this topic would be included, but that doesn't seem to be the case. The said hand full of diagrams are provided for QED and phi^4 theory, but I don't see this information for electroweak theory or QCD. In fact, I don't see this very important information, that is, a catalog of these said diagrams for every theory within the Standard model along with the exact evaluated corresponding amplitudes, within any document that I've come across thus far via google searches or book sifting.

I think that this information should be readily available and easy to find for anyone that wants to learn about the Standard Model as renormalization is a great cause of curiosity and confusion in modern physics, and so I think it would be nice if we could at least provide a portion of that catalog here if not all of it. If this is too much to do explicitly on a single page then hopefully it is reasonable to do through various links. Of course, the said task is most likely too big for one contributor on physicsforums, but I think several small contributions can quickly add up so I'm hoping that this is seen as a reasonable proposition.

What I have so far is:

1. "An Introduction to Quantum Field Theory by Michael E. Peskin and Daniel V. Schroeder, page 317-319" - QED divergent diagrams

2. "An Introduction to Quantum Field Theory by Michael E. Peskin and Daniel V. Schroeder, page 323-325" - Phi^4 theory divergent diagrams

(Note: For reference #1, no amplitudes are provided, just the drawn diagrams and corresponding superficial degree of divergence. For reference #2, the amplitudes are provided, but they are not exact.)

However, anyone without access to the required book will unfortunately not be able to see this information (a reality that we should keep in mind when adding to this thread), but it's a start . I'll continue to look for more sources when I find the time, and add them here.

Thanks for reading!

 

[AndyW]

Dear fellow physicist,

Thank you for bringing up this important topic of divergent diagrams in quantum field theory. As you have correctly pointed out, the task of enumerating all of these diagrams can be reduced to a handful of diagrams, and it is crucial to have this information readily available for anyone interested in studying the Standard Model.

I would like to add to your list of references the book "Quantum Field Theory" by Mark Srednicki, where the author provides a thorough analysis of divergent diagrams in QED, phi^4 theory, and electroweak theory. The book also includes the corresponding amplitudes for these diagrams.

In addition, the website of the Particle Data Group (PDG) also has a section on renormalization and divergent diagrams, which includes a list of references and links to various resources on this topic.

I completely agree with your suggestion of creating a catalog of these diagrams for all theories within the Standard Model. It would be a valuable resource for students and researchers alike. I am willing to contribute to this effort and I hope others will join in as well.

Thank you for bringing attention to this issue and I look forward to seeing this catalog grow.