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

why is this diagram NOT included?

enter image description here


1 Answer 1


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.


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