  There exist renormalisation schemes that explicitly preserve the scale
invariance of a theory at the quantum level. Imposing a scale invariant
renormalisation breaks renormalisability and induces new non-trivial operators
in the theory. In this work, we study the effects of such scale invariant
renormalisation procedures. On the one hand, an explicitly quantum scale
invariant theory can emerge from the scale invariant renormalisation of a scale
invariant Lagrangian. On the other hand, we show how a quantum scale invariant
theory can equally emerge from a Lagrangian visibly breaking scale invariance
renormalised with scale dependent renormalisation (such as the traditional
MS-bar scheme). In this last case, scale invariance is hidden in the theory, in
the sense that it only appears explicitly after renormalisation.
