  We consider a coupling of dilaton gravity to the classically scale-invariant
B-L extended standard model which has been recently proposed as a
phenomenologically viable model realizing the Coleman-Weinberg mechanism of
breakdown of the electroweak symmetry. It is shown in the present model that
without recourse to the Coleman-Weinberg mechanism, the B-L gauge symmetry is
broken in the process of spontaneous symmetry breakdown of scale invariance at
the tree level and as a result the B-L gauge field becomes massive via the
Higgs mechanism. Since the dimensionful parameter is only the Planck mass in
our model, one is forced to pick up very small coupling constants if one wishes
to realize the breaking of the B-L symmetry at TeV scale.
