### Feynman Rules: R-Xi Gauge and MSSM

11Jul07

This is just a quick note to share two reference I’ve found useful for looking up Feynman rules in a pinch. The first reference is for the $R_\xi$-gauge Feynman rules for the Standard Model and the second is for the MSSM Feynman rules in $\xi = 1$.

Standard Model $R_\xi$-gauge Feynman rules

The canonical reference for these Feynman rules is usually Cheng and Li’s Gauge Theory of Elementary Particle Physics. This is a fantastic book to read after a rigorous first QFT course. However, the $R_\xi$-gauge Feynman rules in the back of the book are incomplete: they do not include the rules for Higgs-scalar W-scalar W vertices. (By scalar Ws I mean the Higgs goldstone bosons that are eaten by the W bosons.) These are straightforward to calculate and add in as an erratum sticky note, but I’ve found another nice reference in a new book by Burgess and Moore.

Their book, The Standard Model: A Primer, is intended for an introductory QFT course that connects to Standard Model from the very start. I believe the intended audience are first-year postgraduate courses in phenomenology with a mixed theorist-experimentalist audience. What I find very nice about the book are the last two appendices which provide a complete set of $R_\xi$-gauge Feynman rules for the Standard Model and a guide for converting between the +— and -+++ metric conventions. (Unfortunately the book uses the -+++ GR/East Coast’ convention, rather than the +— Particle/West Coast’ convention that I’m used to.)

I’m not sure about the effectiveness of the book as a primary text for a proper QFT course, but I think it would certainly be a nice reference to compliment phenomenological courses.

MSSM Feynman Rules

Also, for those who want a nice reference for MSSM Feynman rules, I’d like to highlight J. Rosiek’s Complete set of Feynman rules for the MSSM, Phys. Rev. D41 (1990) 3464 (erratum hep-ph/9511250).

Please note that both the Phys. Rev. D and the arXiv versions are outdated, and the most updated paper can be found on the author’s webspace: http://www.fuw.edu.pl/ rosiek/physics/prd41.html .

Happy calculating!