Higgs mass naturalness and scale invariance in the UV

TL;DR

This paper explores how the Higgs mass naturalness could be explained by a transition to conformal field theory at the TeV scale, emphasizing the importance of an interacting UV fixed point for protecting the Higgs mass.

Contribution

It demonstrates the sensitivity of the Higgs mass to the scale where Standard Model couplings turn over to conformal behavior, highlighting the necessity of an interacting UV fixed point.

Findings

Higgs mass is sensitive to the UV turn-over scale.

Scale invariance protection requires an interacting UV fixed point.

Transition to CFT must occur near the TeV scale.

Abstract

It has been suggested that electroweak symmetry breaking in the Standard Model may be natural if the Standard Model merges into a conformal field theory (CFT) at short distances. In such a scenario the Higgs mass would be protected from quantum corrections by the scale invariance of the CFT. In order for the Standard Model to merge into a CFT at least one new ultraviolet (UV) scale is required at which the couplings turn over from their usual Standard Model running to the fixed point behavior. We argue that the Higgs mass is sensitive to such a turn-over scale even if there are no associated massive particles and the scale arises purely from dimensional transmutation. We demonstrate this sensitivity to the turnover scale explicitly in toy models. Thus if scale invariance is responsible for Higgs mass naturalness, then the transition to CFT dynamics must occur near the TeV scale with observable consequences at colliders. In addition, the UV fixed point theory in such a scenario must be interacting because logarithmic running near a free fixed point constitutes hard breaking of scale invariance and spoils the Higgs mass protection.