Quantum scale-invariant models as effective field theories

TL;DR

This paper investigates quantum scale-invariant models, showing they are effective field theories valid below the Planck scale, with non-renormalizability emerging at two-loop level but retaining desirable physical features.

Contribution

It demonstrates that quantum scale-invariant theories are non-renormalizable at two loops, establishing their role as effective field theories rather than fundamental theories.

Findings

Non-renormalizability appears at two-loop level.

Theories remain stable and predictive below the Planck scale.

Attractive features like Higgs mass stability are preserved.

Abstract

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.