  We show that the minimal Weyl-invariant Einstein-Cartan gravity in
combination with the Standard Model of particle physics contains just one extra
scalar degree of freedom (in addition to the graviton and the Standard Model
fields) with the properties of an axion-like particle which can solve the
strong CP-problem. The smallness of this particle's mass as well as of the
cosmological constant is ensured by tiny values of the gauge coupling constants
of the local Lorentz group. The tree value of the Higgs boson mass and that of
Majorana leptons (if added to the Standard Model to solve the neutrino mass,
baryogenesis and dark matter problems) are very small or vanishing, opening the
possibility of their computability in terms of the fundamental parameters of
the theory due to nonperturbative effects.
