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 γW⁺W^- and ZW⁺W^- vertices in the context of the standard model, with all three incoming momenta off shell. We show that the γW⁺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^-→W⁺W^- Explicit calculations give rise to expressions for static properties of the W gauge bosons such as the magnetic dipole and electric quadrupole moments, which satisfy the crucial properties of infrared finiteness as well as gauge independence.