In Gauge Theories of the Strong, Weak, and Electromagnetic Interactions, C. Quigg explains how the process $$\nu \overline{\nu} \rightarrow W^+ W^-$$ violates unitarity at high energy unless we add the $$Z^0$$ boson to the EW theory (see sections 6.2 and 6.3).
I have some difficulty with Quigg's proof that the t-channel diagram (with a leptonic mediator) cancels the s-channel amplitude (mediated by $$Z^0$$) at high energy. The problem comes from equations 6.3.37 and 6.3.39 (see below) where the sign of the s-channel amplitude changes, apparently for no reason. I've been trying the proof myself and I obtain equation 6.3.37, but I cannot get to 6.3.39 (although I understand why the term $$S^\mu S^\nu$$ vanishes). Here $$q_1,q_2$$ are the 4-momenta of the incoming neutrinos, $$S$$ is the momentum of the $$Z$$ boson, $$k_+,k_-$$ are the 4-momenta of the outgoing $$W$$ bosons and $$\epsilon_\pm^*$$ are their polarization 4-vectors (in the high energy limit the longitudinal mode dominates: $$\epsilon_\pm^*\simeq k_\pm/M_z$$).
Could it be a typo? Obviously, the sign makes all the difference here since we want $$\mathcal{M}_s$$ to cancel $$\mathcal{M}_t$$. Also, I noticed that different references use different signs for the Feynman rules of the EW vertices, could that be part of the problem?