Vacuum Structure of an Extended Standard Model with $U(1)_D$ Symmetry

In this research, we investigate the vacuum structure of an extended standard model with a $U(1)_D$ global symmetry. The scalar sector consists of two $SU(2)$ doublets as well as one complex singlet and one real singlet, resulting in a more complicated vacuum structure compared to that of the Standard Model. We analyze various theoretical constraints, including the conditions for being bounded from below, the existence of a global minimum, and perturbativity up to the Planck scale. Additionally, we consider experimental constraints from the Higgs invisible decay. Through a detailed statistical analysis using numerical methods, we show that the extended scalar potential can accommodate a stable vacuum while satisfying both theoretical and experimental constraints for a small region of the parameter space.

💡 Research Summary

In this work the authors study the vacuum structure of an extended Standard Model that incorporates a global U(1)₍D₎ symmetry. The scalar sector is enlarged by two SU(2) doublets (the Standard‑Model‑like Higgs doublet H and an inert doublet η), a complex singlet Φ′ and a real singlet Φ. The inert doublet is protected by a Z₂ parity and therefore has zero vacuum expectation value (VEV), while Φ′ and Φ acquire VEVs v₁ and v₃ respectively, breaking the U(1)₍D₎ symmetry. The hierarchy v₁ > v₂ ≫ v₃ (with v₂ the SM Higgs VEV) is assumed throughout the analysis.

The scalar potential contains the usual quadratic and cubic terms together with a set of twelve dimensionless quartic couplings λ₁ … λ₁₂. The authors add three new quartic interactions (λ₁₀, λ₁₁, λ₁₂) that are absent in the original model of Ref.