I'm studying Peskin & Schroeder's An Introduction to Quantum Field Theory, specifically the section about the quantization of the Glashow-Weinberg-Salam model of the electroweak gauge theory where they analyze the $e^+e^-\to W^+W^-$ reaction (section 21.2, page 750 in my edition). They affirm, if I read that right, that the various cancellations of "badly behaved" terms in the high-energy limit are required by the Ward identity of the gauge theory. I'm trying to show why it is so, but I'm stuck at the beginning since I'm not even sure how is the Ward identity written in the electroweak gauge theory. Judging from their sketch of a proof of the Goldstone boson equivalence theorem, I assumed that the identity would be the good old $k_\mu\mathcal{M}^\mu=0$, obtained from a matrix element $\mathcal{M}$ by replacing the polarization vector of one of the two final $W$ bosons with its momentum. I tried to calculate it, e.g. in the massless-electron limit, when the initial electron is left-handed, adding together the diagrams

Diagram with an internal photon Diagram with an internal Z0 boson Diagram with an internal neutrino,

and replacing a polarization vector as I said above, but that didn't give me zero. So, either I messed something up during the calculation (I tried with Mathematica, too, without success...), or I'm thinking of the wrong identity to prove. Is my procedure correct?



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