  We show, using the large $N$ limit, that there is a non--trivial scale
invariant action for four dimensional scalar field theory. We investigate the
possibility that the scalar sector of the standard model of particle physics
has such a scale invariant action, with scale invariance being spontaneously
broken by the vacuum expectation value of the scalar. This leads to a
prediction for the mass of the lightest massive scalar particle (the Higgs
particle) to be $5.4$ Tev.
