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

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

Jul 2011

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2011cqgra..28n5014n&link_type=abstract

Classical and Quantum Gravity, Volume 28, Issue 14, pp. 145014 (2011).

Mathematics

Logic

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Scientific paper

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 {(diffeomorphisms)} \times {\widetilde{U}}\hspace{1.084pt}(1) \times SU(3)\times SU(2) \times U(1), where the last three subgroups are the usual SM gauge group, while {\widetilde{U}}\hspace{1.084pt}(1) is Weyl's local scale invariance group with its gauge field called Weylon. The extra scalar phiv ≡ -MP ln(κσ) with the Planck mass MP and κ ≡ 1/MP plays a role of a Stückelberg-type compensator, breaking the {\widetilde{U}}\hspace{1.084pt}(1) symmetry at the tree level. Our potential of a Higgs doublet Φ and the compensator phiv is V = λ(Φ†Φ)2 - μM2P(Φ†Φ) e-2κphiv + ξMP4 e-4κphiv. Even after the SU(2) breaking, this system yields a vanishing cosmological constant Rμν = 0, thanks to the identity 4V ≡ -MP(∂V/∂phiv) + 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 e ({\widetilde{R}}\hspace{1.084pt}_{\mu \nu \rho }{}^{\sigma })^2, e ({\widetilde{R}}\hspace{1.084pt}_{(\mu \nu )})^2 and e {\widetilde{R}}\hspace{1.084pt}^2. 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.

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