GAUGE-INVARIANT 3-BOSON VERTICES AND THEIR WARD IDENTITIES IN THE STANDARD MODEL

In the context of the standard model we extend the S-matrix pinch technique for nonconserved currents to the case of three-boson vertices. We outline in detail how effective gauge-invariant three-boson vertices can be constructed, with an three incoming momenta off shell. Explicit closed expressions for the vertices gamma W-W+, ZW(-)W(+), and chi W-W+ are reported. The three-boson vertices so constructed satisfy naive QED-like Ward identities which relate them to the gauge-invariant gauge boson self-energies previously constructed by the same method. The derivation of the aforementioned Ward identities relies on the sob requirement of complete gauge invariance of the S-matrix element considered; in particular, no knowledge of the explicit closed form of the three-boson vertices involved is necessary. The validity of one of these Ward identities is demonstrated explicitly; through a detailed diagrammatic one-loop analysis, in the context of three different gauges.