Complex sentence: For a QFT to be scale-invariant, its coupling parameters must be independent of the energy-scale of a given process, and this is indicated by the vanishing of the beta-functions of the theory.
Split into simpler sentences: For a QFT to be scale-invariant, these coupling parameters must be independent of the energy-scale of a given process. This scale invariance is indicated by the vanishing of the beta-functions of the theory.