A manifestly scale-invariant regularization and quantum effective operators

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 \μ of the dimensional regularization is generated after spontaneous scale symmetry breaking, from a subtraction function of the fields, \μ(\φ,\σ). This function is then uniquely determined from general principles showing that it depends on the dilaton only, with \μ(\σ)\~ \σ. The result is a scale invariant one-loop potential U for a higgs field \φ and dilaton \σ that contains an additional {\ finite} quantum correction \Δ U(\φ,\σ), beyond the Coleman Weinberg term. \Δ U contains new, non-polynomial effective operators like \φ⁶/\σ² 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 \φ remains small without tuning (of its self-coupling, etc) beyond the initial, classical tuning (of the dilaton coupling) that enforces a hierarchy \\σ\\ \\φ\. The approach is useful to models that investigate scale symmetry at the quantum level.