  Spontaneous breaking of quantum scale invariance may provide a solution to
the hierarchy and cosmological constant problems. In a scale-invariant
regularization, we compute the two-loop potential of a higgs-like scalar $\phi$
in theories in which scale symmetry is broken only spontaneously by the dilaton
($\sigma$). Its vev $\langle\sigma\rangle$ generates the DR subtraction scale
($\mu\sim\langle\sigma\rangle$), which avoids the explicit scale symmetry
breaking by traditional regularizations (where $\mu$=fixed scale). The two-loop
potential contains effective operators of non-polynomial nature as well as new
corrections, beyond those obtained with explicit breaking ($\mu$=fixed scale).
These operators have the form: $\phi^6/\sigma^2$, $\phi^8/\sigma^4$, etc, which
generate an infinite series of higher dimensional polynomial operators upon
expansion about $\langle\sigma\rangle\gg \langle\phi\rangle$, where such
hierarchy is arranged by {\it one} initial, classical tuning. These operators
emerge at the quantum level from evanescent interactions ($\propto\epsilon$)
between $\sigma$ and $\phi$ that vanish in $d=4$ but are demanded by classical
scale invariance in $d=4-2\epsilon$. The Callan-Symanzik equation of the
two-loop potential is respected and the two-loop beta functions of the
couplings differ from those of the same theory regularized with $\mu=$fixed
scale. Therefore the running of the couplings enables one to distinguish
between spontaneous and explicit scale symmetry breaking.
