Confront a dilaton model with the LHC measurements

The origin of the Higgs boson ($H_{125}$), discovered in 2012, remains a mystery. In the metric affine theory (MAT) framework, we study the scalar potential and investigate a couple of scenarios for the symmetry breaking mechanisms with a dilaton model which is derived from the geometry. The LHC constraints for the couplings of Yukawa couplings, Higgs-weak vector bosons and Higgs self-couplings, in this model are examined, which identify the parameter space where the discovered Higgs boson $m_h=125$ GeV can be dilaton-dominant and the features of Higgs self-couplings are explored. It is found that via the measurements of Higgs pair production, the High Luminosity LHC (HL-LHC) running can either confirm or rule out the dilaton dominance.

💡 Research Summary

The paper investigates a dilaton‑based extension of the Standard Model (SM) within the metric‑affine theory (MAT) framework, where scale (Weyl) symmetry is gauged and incorporated into the geometry. The model contains a real singlet scalar field Φ (the dilaton) and a complex SU(2) doublet ϕ (the usual Higgs doublet). In addition to the usual SM gauge fields, the Lagrangian includes non‑minimal couplings of the scalars to the Ricci scalar, a quadratic curvature term (ˆR²), and a Weyl‑tensor term (ˆC²). The scalar potential reads

V(Φ,ϕ)=ρ Φ⁴+α Φ² ϕ†ϕ+λ (ϕ†ϕ)²+β Φ² ˆR+γ ϕ†ϕ ˆR,

with nine free parameters: ρ, α, λ, β, γ, ξ, η, g_w, g_s.

Scale invariance is broken via a Stueckelberg mechanism: the Weyl gauge boson ω_μ eats the Goldstone boson associated with the local dilation, acquiring a mass. After this breaking the theory can be linearized by introducing a Brans‑Dicke‑type field Θ, defined by Θ²=χ_D′ Φ²+χ_H′ ϕ†ϕ. The vacuum expectation values (VEVs) of Φ (f_D) and ϕ (f_H) generate a combined scale f²=χ_D′ f_D²+χ_H′ f_H².

Two qualitatively different symmetry‑breaking patterns are considered. In the “dilaton‑dominant” case f_D≫f_H, the dilaton drives the breaking of Weyl symmetry; after gauge fixing only the doublet remains, which subsequently breaks electroweak symmetry and leaves a single physical scalar identified with the observed 125 GeV Higgs boson. In the “doublet‑dominant” case f_H≫f_D, the doublet provides the Goldstone mode for the Weyl boson, and the dilaton survives as the light Higgs. The latter scenario would require additional new fermions to generate realistic Yukawa couplings.

The signs of χ_D′ and χ_H′ lead to four mathematical possibilities: two trigonometric scalar scenarios (TSS1, TSS2) and two hyperbolic scalar scenarios (HSS1, HSS2). The authors focus on TSS1 (χ_D′>0, χ_H′>0) because it yields the correct sign for the Einstein‑Hilbert term after symmetry breaking. In this case Θ² can be parametrized as

Θ² = f²