Gauge Invariant three 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 non–conserved currents to the case of three boson vertices. We outline in detail how effective gauge invariant three boson vertices can be constructed, with all three incoming momenta {\it off–shell}. Explicit closed expressions for the vertices $\gamma W^{-}{W}^{+}$, $Z{W}^{-}{W}^{+}$, 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 sole 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.