Standard Model gauge couplings from gauge-dilatation symmetry breaking
Abstract
We argue that there is a spontaneously broken rotational symmetry between space-time coordinates and gauge theoretical phases. The dilatonic mode acts as the massive Higgs boson, whose vacuum expectation value determines the gauge couplings. This mechanism requires that the quadratic divergences, or tadpoles of the three gauge-theory couplings, unify at a certain scale. We verify this statement, and find that this occurs at u ~ 4x107 GeV. The tadpole cancellation condition, together with the dilaton self-energy, fixes the value of the unified tadpole coefficient to be 1/[4 ln(cut/u)]. The observed values of the coupling constants at u then implies cut ~ 4x1018 GeV, which is close to the value of the reduced Planck mass MRPl=MPl/sqrt(8 pi)=2.4 x 1018 GeV. In other words, by assuming a cutoff at MPl or MRPl, we are able to obtain predictions for the gauge couplings which agree with the true values to within a few percent. It turns out that this symmetry breaking can only take place if mass is generated with the aid of some other means such as electroweak symmetry breaking. Assuming dynamical symmetry breaking originating at MRPl, we obtain Mchi ~ 109 GeV, which is not unreasonable but somewhat higher than u. The cancellation of an anomaly in the dilaton self-energy requires that the number of fermionic generations equals three.