Non--trivial Fixed Point in Four Dimensional Scalar Field Theory and the Higgs Mass

Abstract

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.