Quantum scale-invariant models as effective field theories

We address the question of whether the quantum scale-invariant theories introduced in [1] are renormalizable or play the role of effective field theories that are valid below the Planck scale $M_P$. We show that starting from two-loop level the renormalization procedure requires introduction of counter-terms with structures different from those in the initial Lagrangian, making these theories non-renormalizable and therefore non-predictive above $M_P$. Despite non-renormalizability, the attractive features of these theories, associated with the stability of the Higgs mass agains radiative corrections and the smallness of the cosmological constant, remain intact.