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 and graviton fields are 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, i.e., three generations of standard model fermions, including right-handed neutrinos. The dimension-zero scalars have a four-derivative Lagrangian, usually taken to imply vacuum instability. However, using the Euclidean inner product natural in the context of our recent proposal arXiv:2109.06204, we find no negative norm or negative energy states. Hence the vacuum is stable. Moreover, the scalars possess a scale invariant power spectrum extending to long wavelengths, suggesting a new explanation for the primordial scalar perturbations in cosmology, without the need for inflation. These intriguing results, spanning a vast range of scales, suggest dimension-zero scalars may play a key role in fundamental physics. We discuss how the Higgs and graviton fields might emerge in this context.