Why is there an additional prefactor in equation (12.52) of Peskin's QFT book?

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Thread starter thatboi
Start date Apr 2, 2023
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Peskin Qft

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Apr 2, 2023

thatboi

Hey all,
I am currently having trouble understanding equation (12.52) in Peskin's QFT book. Specifically the term for external leg corrections, in which they tack on an additional prefactor of ##(-ig)##. Normally with external leg prefactors, we don't see the coupling constant multiplied onto the field renormalization counterterm so why is such a prefactor included here?
Thanks.