Planck and Electroweak Scales Emerging from Conformal Gravity

We show that both the Planck and electroweak mass scales can be generated from conformal gravity via the Coleman-Weinberg mechanism of dimensional transmutation. At the first step, the Planck scale is generated via the Coleman-Weinberg mechanism in the sector of conformal gravity, which means that radiative corrections associated with gravitons induce spontaneous symmetry breakdown of a local conformal symmetry. At the second step, the vacuum expectation value of a scalar field is transmitted to the sector of the standard model via a potential involving the conformally invariant part and the contribution from the Coleman-Weinberg mechanism, thereby generating the electroweak scale. The huge hierarchy between the two scales can be explained in terms of a very tiny coupling constant between the scalar and the Higgs field in a consistent way.