The effective potential for the conformal factor in the standard model and beyond

Abstract

There is a general mechanism by which certain matter fields coupled to gravity can generate a nontrivial effective potential for the conformal factor of the metric. It is based on a nonstandard regularization method, with the cutoff being defined independently of the conformal factor. This mechanism produces a coupling of the matter fields to a dilaton, and a complicated interaction between matter, dilaton and metric. When it is applied to the standard model, it gives an effective potential which can be used to predict the top and Higgs masses. If the purely gravitational contribution to the potential is added, the mass of the dilaton is of the order of Planck's mass and the large hierarchy between the Planck and Fermi scales appears to be due to the smallness of the Higgs-dilaton coupling.