Effective Theory of a Light Dilaton

TL;DR

This work develops an effective field theory for a dilaton arising from spontaneously broken conformal dynamics that UV-complete electroweak breaking. It shows that a light dilaton is natural only when the conformal-symmetry-breaking operator is near marginal at the breaking scale; otherwise, the dilaton is generically heavy, implying tuning. The authors construct the dilaton EFT, analyze its couplings to SM fields in both technicolor-like and Higgs-as-a-pNGB scenarios, and quantify how conformal-symmetry-violating effects contribute corrections that are typically suppressed by $(m_\sigma/\Lambda)^2$ but can dominate for couplings to marginal operators. The results offer concrete predictions for dilaton interactions with gauge bosons and fermions, and elucidate the observational distinctions between a dilaton and the SM Higgs in LHC phenomenology, within UV-complete conformal frameworks.

Abstract

We consider scenarios where strong conformal dynamics constitutes the ultraviolet completion of the physics that drives electroweak symmetry breaking. We show that in theories where the operator responsible for the breaking of conformal symmetry is close to marginal at the breaking scale, the dilaton mass can naturally lie below the scale of the strong dynamics. However, in general this condition is not satisfied in the scenarios of interest for electroweak symmetry breaking, and so the presence of a light dilaton in these theories is associated with mild tuning. We construct the effective theory of the light dilaton in this framework, and determine the form of its couplings to Standard Model states. We show that corrections to the form of the dilaton interactions arising from conformal symmetry violating effects are suppressed by the square of the ratio of the dilaton mass to the strong coupling scale, and are under good theoretical control. These corrections are generally subleading, except in the case of dilaton couplings to marginal operators, when symmetry violating effects can sometimes dominate. We investigate the phenomenological implications of these results for models of technicolor, and for models of the Higgs as a pseudo-Nambu-Goldstone boson, that involve strong conformal dynamics in the ultraviolet.