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Status of the Higgs Singlet Extension of the Standard Model after LHC Run 1

Tania Robens, Tim Stefaniak

TL;DR

This work analyzes the real Higgs singlet extension of the Standard Model by scanning the second Higgs mass from $1~\mathrm{GeV}$ to $1~\mathrm{TeV}$ and evaluating three scenarios relative to the SM-like Higgs at $\sim125~\mathrm{GeV}$. It integrates theoretical constraints (perturbative unitarity, perturbativity, vacuum stability) with RG evolution up to $\mu_{\rm run}\sim4\times10^{10}~\mathrm{GeV}$ and experimental inputs from HiggsBounds and HiggsSignals to delineate viable regions in the parameter space characterized by $(m,\alpha,\tan\beta)$ and the potential for $H\to hh$ decays. The results reveal that in the high-mass region $m_H\gtrsim200$–$300$ GeV, the $W$-mass corrections from the singlet extension and RG constraints strongly limit the mixing angle $|\sin\alpha|$, while in the low-mass region LEP limits and Higgs-signal rates dominate, with $\text{BR}(H\to hh)$ potentially up to about 26–40% in certain zones. The study also highlights that the heavy Higgs typically has a narrow total width, and that near-degenerate scenarios near $125$ GeV pose experimental challenges but may be probed by future colliders. Overall, the paper maps the viable parameter space and provides concrete predictions for heavy-Higgs production, branching ratios, and widths to guide LHC searches and future facilities.

Abstract

We discuss the current status of theoretical and experimental constraints on the real Higgs singlet extension of the Standard Model. For the second neutral (non-standard) Higgs boson we consider the full mass range from 1 GeV to 1 TeV accessible at past and current collider experiments. We separately discuss three scenarios, namely, the case where the second Higgs boson is lighter than, approximately equal to, or heavier than the discovered Higgs state at around 125 GeV. We investigate the impact of constraints from perturbative unitarity, electroweak precision data with a special focus on higher order contributions to the W boson mass, perturbativity of the couplings as well as vacuum stability. The latter two are tested up to a scale of 4 x 10^10 GeV using renormalization group equations. Direct collider constraints from Higgs signal rate measurements at the LHC and 95% C.L. exclusion limits from Higgs searches at LEP, Tevatron and LHC are included via the public codes HiggsSignals and HiggsBounds, respectively. We identify the strongest constraints in the different regions of parameter space. We comment on the collider phenomenology of the remaining viable parameter space and the prospects for a future discovery or exclusion at the LHC.

Status of the Higgs Singlet Extension of the Standard Model after LHC Run 1

TL;DR

This work analyzes the real Higgs singlet extension of the Standard Model by scanning the second Higgs mass from to and evaluating three scenarios relative to the SM-like Higgs at . It integrates theoretical constraints (perturbative unitarity, perturbativity, vacuum stability) with RG evolution up to and experimental inputs from HiggsBounds and HiggsSignals to delineate viable regions in the parameter space characterized by and the potential for decays. The results reveal that in the high-mass region – GeV, the -mass corrections from the singlet extension and RG constraints strongly limit the mixing angle , while in the low-mass region LEP limits and Higgs-signal rates dominate, with potentially up to about 26–40% in certain zones. The study also highlights that the heavy Higgs typically has a narrow total width, and that near-degenerate scenarios near GeV pose experimental challenges but may be probed by future colliders. Overall, the paper maps the viable parameter space and provides concrete predictions for heavy-Higgs production, branching ratios, and widths to guide LHC searches and future facilities.

Abstract

We discuss the current status of theoretical and experimental constraints on the real Higgs singlet extension of the Standard Model. For the second neutral (non-standard) Higgs boson we consider the full mass range from 1 GeV to 1 TeV accessible at past and current collider experiments. We separately discuss three scenarios, namely, the case where the second Higgs boson is lighter than, approximately equal to, or heavier than the discovered Higgs state at around 125 GeV. We investigate the impact of constraints from perturbative unitarity, electroweak precision data with a special focus on higher order contributions to the W boson mass, perturbativity of the couplings as well as vacuum stability. The latter two are tested up to a scale of 4 x 10^10 GeV using renormalization group equations. Direct collider constraints from Higgs signal rate measurements at the LHC and 95% C.L. exclusion limits from Higgs searches at LEP, Tevatron and LHC are included via the public codes HiggsSignals and HiggsBounds, respectively. We identify the strongest constraints in the different regions of parameter space. We comment on the collider phenomenology of the remaining viable parameter space and the prospects for a future discovery or exclusion at the LHC.

Paper Structure

This paper contains 18 sections, 43 equations, 18 figures, 6 tables.

Table of Contents

  1. Introduction
  2. The model
  3. Potential and couplings
  4. Model parameters
  5. Theoretical and experimental constraints
  6. Perturbative unitarity
  7. Perturbativity of the couplings
  8. Renormalization group equation evolution of the couplings
  9. The $W$ boson mass and electroweak oblique parameters $S$, $T$, $U$
  10. Exclusion limits from Higgs searches at LEP and LHC
  11. Higgs boson signal rates measured at the LHC
  12. Results of the Full Parameter Scan
  13. High mass region
  14. Low mass region
  15. Intermediate mass region
  16. ...and 3 more sections

Figures (18)

  • Figure 1: Maximally allowed values for $\tan\beta$ in the low mass range, $m \in [20, 120]~{\rm GeV}$, for various values of $\sin\alpha = 1.0, 0.9, 0.5, 0.0$, from considering only perturbative unitarity.
  • Figure 2: Limits in the ($\sin\alpha, \tan\beta$) plane for $m_H=600~{\rm GeV}$ from requiring perturbativity and vacuum stability at a scale $\mu_\text{run}\,=\,2.7\,\times\,10^{10}\,{\rm GeV}$ using RGE evolution. Taken from Ref. Pruna:2013bma.
  • Figure 3: Maximal allowed values for $| \sin\alpha |$ in the high mass region, $m_H\in [130, 1000]\,{\rm GeV}$, from NLO calculations of the $W$ boson mass (red, solid) Lopez-Val:2014jva, electroweak precision observables (EWPOs) tested via the oblique parameters $S$, $T$ and $U$ (orange, dashed), as well as from the perturbativity requirement of the RG-evolved coupling $\lambda_1$ (blue, dotted), evaluated at $\tan\beta\,=\,0.1$. For Higgs masses $m_H\lesssim 800\,{\rm GeV}$ the NLO corrections to the $W$ boson mass yield the strongest constraint.
  • Figure 4: $95\%$ C.L. excluded values of $| \sin\alpha |$ from LEP and LHC Higgs searches, evaluated with HiggsBounds-4.2.0 in the mass regions $m~{\in}~[1,100{]}~{\rm GeV}$ (a) and $m~{\in}~[100,1000{]}~{\rm GeV}$ (b). We assume a vanishing decay width for the Higgs-to-Higgs decay mode, $\Gamma_{H \rightarrow hh}\,=\,0$, hence the displayed results in the high mass region correspond to the most stringent upper limit on $| \sin\alpha |$ that can be obtained from current LHC Higgs searches. The other Higgs boson mass is set to $125.14~{\rm GeV}$ and is indicated by the dashed, magenta line in Fig. \ref{['fig:sinaexp_b']}.
  • Figure 5: Branching ratio $\mathrm{BR}(H\to hh)$ in the ($\sin\alpha$, $\tan\beta$) plane for fixed Higgs masses $m_h = 50\,{\rm GeV}$ and $m_H = 125.14\,{\rm GeV}$. It becomes minimal for either $\sin\alpha\,=\,0$, $\cos\alpha\,=\,0$ or $\tan\beta=-\cos\alpha/\sin\alpha$.
  • ...and 13 more figures