Cancelling the vacuum energy and Weyl anomaly in the standard model with dimension-zero scalar fields

The standard model is a remarkably consistent and complete quantum field theory but its coupling to gravity and the Higgs field remain problematic, as reflected in the cosmological constant problem, the Weyl anomaly, and the hierarchy puzzle. We point out that 36 conformally-coupled dimension-zero scalar fields can simultaneously cancel the vacuum energy and both terms in the Weyl anomaly, if the Higgs field is emergent. The cancellation is highly non-trivial: given the standard model gauge group $SU(3)\times SU(2)\times U(1)$, it requires precisely $48$ Weyl fermions, {\it i.e.}, three generations of standard model fermions, including right-handed neutrinos. Due to a large additional gauge symmetry, the new scalars contribute no new local degrees of freedom or particle states. Their only physical state is their vacuum state, in which they possess a scale invariant power spectrum extending to long wavelengths. This suggests a new explanation for the primordial scalar perturbations in cosmology, not requiring inflation. We also discuss how the Higgs field might emerge as a composite object.