  We elaborate on the structure of the graviton-gauge-gauge vertex in the
electroweak theory, obtained by the insertion of the complete energy-momentum
tensor ($T$) on 2-point functions of neutral gauge currents ($VV'$). The vertex
defines the leading contribution to the effective action which accounts for the
conformal anomaly and related interaction between the Standard Model and
gravity. The energy momentum tensor is derived from the curved spacetime
Lagrangian in the linearized gravitational limit, and with the inclusion of the
term of improvement of a conformally coupled Higgs sector. As in the previous
cases of QED and QCD, we find that the conformal anomaly induces an effective
massless scalar interaction between gravity and the neutral currents in each
gauge invariant component of the vertex. This is described by the exchange of
an anomaly pole. We show that for a spontaneously broken theory the anomaly can
be entirely attributed to the poles only for a conformally coupled Higgs
scalar. In the exchange of a graviton, the trace part of the corresponding
interaction can be interpreted as due to an effective dilaton, using a local
version of the effective action. We discuss the implications of the anomalous
Ward identity for the $TVV'$ correlator for the structure of the gauge/gauge/
effective dilaton vertex in the effective action. The analogy between these
effective interactions and those related to the radion in theories with large
extra dimensions is pointed out.
