Friday 21 August 2020

quantum field theory - Peskin Schroeder $phi^4$ mass renormalization



In Peskin Schroeder, section 10.2, the contributions to $M^2(p^2)$ of order $\lambda^2$ are calculated. They respective Feynman diagrams are given: enter image description here


why is this diagram NOT included?


enter image description here



Answer



Just before their statement that the first non-zero corrections to the $\phi^4$-propagator are those you indicated, they compute the one-loop corrections, using on-shell renormalization conditions, and find out that they are zero:


The one-loop result


It seems that for the $\mathcal{O}(\lambda^2)$ (two-loop) corrections, one should indeed consider not only the diagram you pointed out but another one with a counterterm insertion, which cancels it due to the above one-loop result in the considered scheme. Schematically:


The full two-loop sum


Where the fourth diagram corresponds to the one you drew and the fifth term is the $\mathcal{O}(\lambda^2)$ contribution with the counterterm insertion.


No comments:

Post a Comment

Understanding Stagnation point in pitot fluid

What is stagnation point in fluid mechanics. At the open end of the pitot tube the velocity of the fluid becomes zero.But that should result...