Gauge invariant three-boson vertices in the Standard Model and the static properties of the W


We use the S-matrix pinch technique to derive to one loop-order gauge independent $\gamma W^{+} W^{-} $ and Z $W^{+} W^{-}$ vertices in the context of the Standard Model,with all three incoming momenta off-shell. We show that the $\gamma W^{+} W^{-}$ vertex so constructed is related to the gauge-independent W self-energy,derived by Degrassi and Sirlin,by a very simple QED-like Ward identity.The same results are obtained by the pinch technique applied directly to the process $e^{+}e^{-} \rightarrow W^{+}W^{-}$. Explicit calculations give rise to expressions for the static properties of the W gauge bosons like magnetic dipole and electric quadruple moments which being gauge independent satisfy such crucial properties as infrared finiteness and perturbative unitarity

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