Gauge-invariant three-boson vertices in the standard model and the static properties of theW

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 $e^{+}{e}^{-}\to W^{+}{W}^{-}$ 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.