Weyl's scale invariance for the standard model, renormalizability and the zero cosmological constant

Abstract

We introduce Weyl's local scale invariance into the standard model (SM) with an extra scalar σ. The total symmetry group of the system is , where the last three subgroups are the usual SM gauge group, while is Weyl's local scale invariance group with its gauge field called Weylon. The extra scalar φ ≡ −MP ln(κσ) with the Planck mass MP and κ ≡ 1/MP plays a role of a Stückelberg-type compensator, breaking the symmetry at the tree level. Our potential of a Higgs doublet Φ and the compensator φ is V = λ(Φ†Φ)2 − μM2P(Φ†Φ) e−2κφ + ξMP4 e−4κφ. Even after the SU(2) breaking, this system yields a vanishing cosmological constant Rμν = 0, thanks to the identity 4V ≡ −MP(∂V/∂φ) + Φ(∂V/∂Φ) + Φ†(∂V/∂Φ†), because of local scale invariance. The cancellation condition for the trace anomaly out of quantum fluctuations is also given. Scale invariance dictates that the only possible new divergent terms be of the form and . These results provide the strong indication that this theory is most likely renormalizable, and the classical-level zero-cosmological constant mechanism will continue to be maintained at the quantum level.