Standard Model in Weyl conformal geometry
  We study the Standard Model (SM) in Weyl conformal geometry. This embedding
is natural and truly minimal {\it with no new fields} required beyond the SM
spectrum and Weyl geometry. The action inherits a gauged scale symmetry $D(1)$
(known as Weyl gauge symmetry) from the underlying geometry. The associated
Weyl quadratic gravity undergoes spontaneous breaking of $D(1)$ by a geometric
Stueckelberg mechanism in which the Weyl gauge field ($\omega_\mu$) acquires
mass by "absorbing" the spin-zero mode ($\phi_0$) of the $\tilde R^2$ term in
the action. This mode also generates the Planck scale and the cosmological
constant. The Einstein-Proca action of $\omega_\mu$ emerges in the broken
phase. In the presence of the SM, this mechanism receives corrections (from the
Higgs) and it can induce electroweak (EW) symmetry breaking. The EW scale is
proportional to the vev of the Stueckelberg field ($\phi_0$). The Higgs field
($\sigma$) has direct couplings to the Weyl gauge field, and its mass may be
protected at quantum level by the D(1) symmetry. The SM fermions can acquire
couplings to $\omega_\mu$ only in the special case of a non-vanishing kinetic
mixing of the gauge fields of $D(1)\times U(1)_Y$. If this mixing is indeed
present, part of $Z$ boson mass is not due to the Higgs mechanism, but to its
mixing with massive $\omega_\mu$. Precision measurements of $Z$ mass then set
lower bounds on the mass of $\omega_\mu$ which can be light (few TeV). In the
early Universe the Higgs field can have a {\it geometric} origin, by Weyl
vector fusion, and the Stueckelberg-Higgs potential can drive inflation. The
dependence of the tensor-to-scalar ratio $r$ on the spectral index $n_s$ is
similar to that in Starobinsky inflation but shifted to lower $r$ by the Higgs
non-minimal coupling to Weyl geometry.
