  Pecci-Quinn (PQ) symmetry breaking by perturbative dynamics would suffer from
a hierarchy problem, just like the electroweak symmetry breaking in the
standard model. The dynamics of the axion, associated with the PQ symmetry
breaking, would also involve a triviality problem. We provide a paradigm to
resolve those two problems potentially existing in the PQ symmetry breaking
scenario, with keeping successful axion relaxation for the QCD strong CP phase.
The proposed theory includes an axicolor dynamics with the axicolored fermions
partially gauged by the QCD color, and is shown to be governed by an
asymptotically safe (AS) fixed point: quantum scale invariance is built. The AS
axicolor is actually a "walking" dynamics, which dynamically breaks a PQ
symmetry, a part of the chiral symmetry carried by the axicolored fermions. The
PQ scale generation is then triggered by the nonperturbative dimensional
transmutation in the "walking" dynamics. A composite axion emerges as the
assosiated Nambu-Goldstone boson. That is, no hierarchy or triviality problem
is present there. The composite axion can potentially be light due to the
characteristic feature of the AS axicolor ("walking" axicolor), and the mass
can reach the QCD axion limit. The axicolor theta term is unphysical, and can
be rotated away by a residual chiral symmetry. Thus the QCD CP problem can
unambiguously be solved and the axion relaxation is protected by the
established (near) scale invariance during the "walking" regime.
