  The relaxation mechanism, which solves the electroweak hierarchy problem
without relying on TeV scale new physics, crucially depends on how a
Higgs-dependent back-reaction potential is generated. In this paper, we suggest
a new scenario in which the scalar potential induced by the QCD anomaly is
responsible both for the relaxation mechanism and the Peccei-Quinn mechanism to
solve the strong CP problem. The key idea is to introduce the relaxion and the
QCD axion whose cosmic evolutions become quite different depending on an
inflaton-dependent scalar potential. Our scheme raises the cutoff scale of the
Higgs mass up to 10^7 GeV, and allows reheating temperature higher than the
electroweak scale as would be required for viable cosmology. In addition, the
QCD axion can account for the observed dark matter of the universe as produced
by the conventional misalignment mechanism. We also consider the possibility
that the couplings of the Standard Model depend on the inflaton and become
stronger during inflation. In this case, the relaxation can be implemented with
a sub-Planckian field excursion of the relaxion for a cutoff scale below 10
TeV.
