  We study quantum corrections to the scalar potential in classically scale
invariant theories, using a manifestly scale invariant regularization. To this
purpose, the subtraction scale $\mu$ of the dimensional regularization is
generated after spontaneous scale symmetry breaking, from a subtraction
function of the fields, $\mu(\phi,\sigma)$. This function is then uniquely
determined from general principles showing that it depends on the dilaton only,
with $\mu(\sigma)\sim \sigma$. The result is a scale invariant one-loop
potential $U$ for a higgs field $\phi$ and dilaton $\sigma$ that contains an
additional {\it finite} quantum correction $\Delta U(\phi,\sigma)$, beyond the
Coleman Weinberg term. $\Delta U$ contains new, non-polynomial effective
operators like $\phi^6/\sigma^2$ whose quantum origin is explained. A flat
direction is maintained at the quantum level, the model has vanishing vacuum
energy and the one-loop correction to the mass of $\phi$ remains small without
tuning (of its self-coupling, etc) beyond the initial, classical tuning (of the
dilaton coupling) that enforces a hierarchy $\langle\sigma\rangle\gg
\langle\phi\rangle$. The approach is useful to models that investigate scale
symmetry at the quantum level.
