Anatomy of the Real Higgs Triplet Model

In this article, we examine the Standard Model extended by a $Y=0$ real Higgs triplet, the $Δ$SM. It contains a $CP$-even neutral Higgs ($Δ^0$) and two charged Higgs bosons ($Δ^\pm$), which are quasi-degenerate in mass. We first study the theoretical constraints from vacuum stability and perturbative unitarity and then calculate the Higgs decays, including the loop-induced modes such as di-photons ($γγ$) and $Zγ$. In the limit of a small mixing between the SM Higgs and $Δ^0$, the latter decays dominantly to $WW$ and can have a sizable branching ratio to di-photon. The model predicts a positive definite shift in the $W$ mass, which agrees with the current global electroweak fit. At the Large Hadron Collider, it leads to a $(i)$ stau-like signature from $pp\to Δ^+Δ^-\to τ^+τ^-ν\barν$, $(ii)$ multi-lepton final states from $pp\to γ^\to Δ^+Δ^-\to W^+W^-ZZ$ and $pp\to W^{} \to Δ^\pmΔ^0\to W^\pm Z W^+W^-$ as well as $(iii)$ associated di-photon production from $pp\to W^{*} \to Δ^\pm(Δ^0\toγγ)$. Concerning $(i)$, the reinterpretation of the recent supersymmetric tau partner search by ATLAS and CMS excludes $m_{Δ^\pm}<110$ GeV at 95% CL. From $(ii)$, some of the signal regions of multi-lepton searches lead to bounds close to the predicted cross-section, but electroweak scale masses are still allowed. For $(iii)$, the recast of the associated di-photon searches by ATLAS and a combined log-likelihood fit of signal and background to data find that out of the 25 signal regions, 10 provide relevant limits on Br$(Δ^0\toγγ)$ at the per cent level. Interestingly, 6 signal regions show excesses at around 152 GeV, leading to a preference for a non-zero di-photon branching ratio of about 0.7% with the corresponding significance amounting to about $4σ$.

💡 Research Summary

The paper presents a comprehensive study of the Standard Model extended by a real SU(2)ₗ triplet with hypercharge Y = 0, dubbed the ΔSM. The field content consists of the usual SM Higgs doublet Φ and a real triplet Δ, which after electroweak symmetry breaking yields a CP‑even neutral scalar Δ⁰ and a pair of charged scalars Δ⁺, Δ⁻ that are quasi‑degenerate. The authors first write down the most general renormalizable scalar potential, featuring quartic couplings λ_Φ, λ_Δ, λ_ΦΔ and a soft‑breaking trilinear term A Φ†ΔΦ. Minimisation conditions relate the mass parameters to the vacuum expectation values v_Φ≈246 GeV and the triplet VEV v_Δ. Diagonalisation of the CP‑even and charged mass matrices introduces a neutral mixing angle α and a charged mixing angle β (β≈−2v_Δ/v_Φ). In the phenomenologically relevant limit of small α and v_Δ, the triplet states are almost degenerate, with a loop‑induced mass splitting of order 160 MeV.

Theoretical consistency is examined through vacuum‑stability and perturbative‑unitarity constraints. By demanding that the quartic part of the potential be bounded from below, the authors derive copositivity conditions: λ_Φ>0, λ_Δ>0 and √2 λ_ΦΔ + min(λ_Φ,λ_Δ)>0. Unitarity of 2→2 scalar scattering imposes |λ_i|≲8π, which together with electroweak precision limits on the ρ‑parameter forces v_Δ to be at most a few GeV and A to be modest. These bounds also restrict the possible mass hierarchy, leading to m_Δ⁰ > m_Δ± > m_h for the typical parameter choices.

The decay phenomenology is then computed. Because the triplet does not couple directly to fermions, Δ⁰ decays predominantly into W⁺W⁻ when the mixing α is small. Loop‑induced channels Δ⁰→γγ and Δ⁰→Zγ acquire non‑negligible branching ratios (up to ~10⁻³) due to the residual mixing and the λ_ΦΔ coupling. Charged scalars decay mainly via Δ⁺→W⁺Z, Δ⁺→W⁺h or, for very small v_Δ, via Δ⁺→τ⁺ν, mimicking a stau signature.

Production at the LHC proceeds mainly through Drell‑Yan processes: pp→γ*/Z*→Δ⁺Δ⁻ and pp→W*→Δ±Δ⁰. Three characteristic signatures are identified:

(i) A “stau‑like” final state pp→Δ⁺Δ⁻→τ⁺τ⁻ + missing energy. Recasting the latest ATLAS and CMS searches for supersymmetric τ‑partners excludes charged‑triplet masses below 110 GeV at 95 % CL.

(ii) Multi‑lepton final states arising from Δ⁺Δ⁻→W⁺W⁻ZZ and from Δ±Δ⁰→W±Z WW. Existing multi‑lepton analyses constrain parts of the parameter space, but electroweak‑scale masses remain viable.

(iii) Associated diphoton production pp→W*→Δ±(Δ⁰→γγ). The authors recast 25 ATLAS/CMS signal regions; 10 provide per‑cent‑level limits on Br(Δ⁰→γγ). Remarkably, six regions exhibit excesses around a mass of 152 GeV, corresponding to a preferred diphoton branching ratio of ≈0.7 % with an overall significance of about 4σ. This suggests that Drell‑Yan production of a ~152 GeV triplet scalar could account for the observed narrow diphoton excesses.

The model also predicts a positive shift in the W‑boson mass through the tree‑level contribution of the triplet VEV to the ρ‑parameter, bringing the theoretical prediction into agreement with the recent global electroweak fit (including the CDF measurement). The paper concludes that the minimal real triplet extension simultaneously addresses the W‑mass anomaly, the multi‑lepton anomalies, and the diphoton excess, while remaining consistent with theoretical bounds and existing LHC searches. Future high‑luminosity LHC data, refined W‑mass measurements, and dedicated searches for the charged triplet will be crucial to confirm or refute this scenario.