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.
