---
title: Doubly Charged Scalars in BSM Models
url: https://www.emergentmind.com/topics/doubly-charged-scalars
type: topic
---

# Doubly Charged Scalars in BSM Models

Doubly charged scalars are exotic bosons with electric charge $Q = \pm 2$, predicted in a broad class of Standard Model (SM) extensions addressing the origin of neutrino masses, lepton number violation, and new electroweak sectors. Their defining feature—quantum numbers with $Q = \pm 2$—gives rise to characteristic collider signatures, especially same-sign, high-momentum dilepton pairs. These scalars appear as members of various $SU(2)_L$ multiplets, such as triplets in the type II seesaw mechanism, but also as singlets and higher representations in more general frameworks. A central theoretical and experimental motivation is the direct connection between the couplings and decay modes of doubly charged scalars and the underlying structure of the neutrino mass matrix.

## 1. Theoretical Origin and Model Realizations

Doubly charged scalars ($H^{\pm\pm}$, $\Delta^{\pm\pm}$, $S^{\pm\pm}$, etc.) can arise in a variety of SM extensions:

- **Type II Seesaw Mechanism**: The SM is extended by an $SU(2)_L$ triplet scalar ($\Delta \sim \mathbf{3}, Y=2$), with components
  $$
  \Delta = \begin{pmatrix}
  H^+/\sqrt{2} & H^{++} \\
  H^0 & -H^+/\sqrt{2}
  \end{pmatrix}
  $$
  A small triplet vev $v_T = \langle H^0 \rangle \ll v_{\text{SM}}$ induces neutrino masses: $(m_\nu)_{ij} = \sqrt{2} v_T y_{ij}$, where $y_{ij}$ are Yukawa couplings to lepton doublets [2601.00083, 2508.11336].

- **Left-Right Symmetric Models (LRSMs)**: Both $SU(2)_L$ and $SU(2)_R$ triplets ($\Delta_L$, $\Delta_R$) are present, generating heavy right-handed neutrino masses and accommodating parity restoration at high scales. The masses of doubly charged scalars can be decoupled from the $SU(2)_R$-breaking scale by "hidden" symmetries in the scalar potential [2401.15145, 2307.16111, 1803.11167].

- **Singlet and Multiplet Extensions**: Doubly charged $SU(2)_L$ singlets (e.g., $S^{++}$) can appear in two-loop neutrino mass models (Zee–Babu mechanism) or other frameworks. Isospin $T=0$, $1/2$, $3/2$, $2$ representations can also yield doubly charged states [1305.3904, 1807.10224].

- **Composite Higgs and Little Higgs Models**: $H^{\pm\pm}$ can be present as pseudo-Nambu–Goldstone bosons in composite Higgs sectors or as parts of extended scalar triplets in little Higgs constructions [2304.09195, 1102.3898].

## 2. Gauge Interactions, Couplings, and Decay Patterns

The gauge quantum numbers and couplings of doubly charged scalars are model-dependent:

- **Yukawa Interactions**: In type II seesaw and many related models, the main renormalizable interaction is with left-handed leptons through
  $$
  \mathcal{L}_{Y} \supset y_{ij}\, L_i^{T} C^{-1} i\sigma_2 \Delta L_j + \text{h.c.}
  $$
  yielding $H^{++} \to \ell_i^+ \ell_j^+$ with partial width
  $$
  \Gamma(H^{++} \to \ell_i^+ \ell_j^+) = \frac{k_{ij} |y_{ij}|^2}{16\pi} m_{H^{\pm\pm}},
  $$
  $k_{ij} = 2$ for $i = j$, $k_{ij} = 1$ for $i \neq j$ [2601.00083].

- **Gauge-Boson Decays**: For $v_T \gtrsim 10^{-4}$ GeV, decays $H^{++}\rightarrow W^+W^+$ become relevant. The partial width to $W$ boson pairs scales as $\Gamma \sim g^4 v_T^2 m_{H^{\pm\pm}}^{-1}$ [1305.3904]. This mode is suppressed compared to leptonic decays for small $v_T$ or large $|y_{ij}|$.

- **Cascade and Multi-Scalar Decays**: In models with multiple triplets, e.g., two-triplet type II seesaw, the heavier $H_1^{++}$ may dominantly decay into a lighter singly-charged scalar and a $W^+$, $H_1^{++} \to H_2^{+} W^+$, if kinematically accessible. This can reach branching fractions above 99% [1305.5761].

- **Flavor Structure**: Decay patterns are tightly linked to the origin of neutrino mass. The various $|y_{ij}|$ correspond directly to entries in the neutrino mass matrix, so branching ratio measurements can reconstruct underlying mass and mixing parameters, subject to charged-lepton mass suppressions in singlet scenarios [1005.2817].

## 3. Collider Production and Signature Phenomenology

### 3.1 Production Mechanisms

- **Drell–Yan Pair Production**: The dominant production at hadron colliders is $q\bar{q} \to \gamma^*, Z^* \to H^{++}H^{--}$. The cross section at $\sqrt{s}=13$ TeV is $\sim 10^2$ fb for $m_{H^{\pm\pm}}=300$ GeV, dropping below $0.1$ fb for $m_{H^{\pm\pm}} \approx 1$ TeV [2601.00083].

- **Photon–Photon Fusion**: At higher masses, $\gamma\gamma \to H^{++}H^{--}$ is relevant. While sub-dominant below $\sim 1$ TeV (few-percent effect), the contribution can rise to $20$–$30\%$ at $m_{H^{\pm\pm}}=2$–$3$ TeV, especially as widths grow [2601.00083, 2508.11336].

- **Associated Production**: For non-singlet $SU(2)_L$ (e.g., triplet or doublet), $q'\bar{q} \to W^* \to H^{\pm\pm}H^\mp$ is possible. For further details on cross section scaling with isospin, see [1305.3904].

- **Gluon Fusion Cascades**: In models where a heavy neutral scalar with significant gluon fusion production can decay to a pair of $H^{\pm\pm}$, additional cross section gains are possible. For instance, $gg \to H_2 \to H^{++}H^{--}$ can exceed Drell–Yan in parts of parameter space [1106.3427].

- **Lepton Collider Production**: At $e^+e^-$ or $\mu^+\mu^-$ colliders, pair production proceeds via $s$-channel $\gamma^*/Z^*$, with cross sections scaling as
  $$
  \sigma(e^+e^-\to H^{++}H^{--}) = \frac{\pi \alpha^2}{3s} \beta^3[\cdots]
  $$
  where $\beta = \sqrt{1 - 4 m^2/s}$ [1102.3898, 2307.16111, 2506.00966].

### 3.2 Experimental Signatures

- **Prompt Leptonic Decays**: The canonical signature is two same-sign, same-flavor (or mixed-flavor) isolated leptons with high $p_T$ and narrow invariant-mass peaks at $m_{H^{\pm\pm}}$, resulting in four-lepton final states [2601.00083].
  
- **Long-Lived and Displaced Signatures**: For small Yukawa couplings ($|f_{ij}| \ll 10^{-8}$), $H^{\pm\pm}$ may be long-lived, giving rise to high-$dE/dx$ ionization tracks. Dedicated long-lived particle searches can probe $m_{H^{\pm\pm}} \sim 700$–$900$ GeV depending on the production mechanism [2401.15145].

- **Multi-lepton plus Missing Energy**: Cascade decays in multiple-triplet models or via singly-charged scalars lead to $W$ bosons and further leptons, yielding higher lepton multiplicities, missing energy, and non-standard $p_T$ spectra [1305.5761, 1105.2209].

- **Flavor Violating Channels**: Observing mixed-flavor pairs (e.g., $e^+ \mu^+$ from the same scalar) or lepton-number-violating decays (e.g. $\mu^\pm\tau^\pm$ without associated missing energy) points to new physics in the underlying Yukawa sector, potentially distinguishing between singlet, triplet, or other origins [2508.11336, 1102.3898].

- **High-Mass Reach at Future Colliders**: The reach extends to $m_{H^{\pm\pm}} \sim 7$ TeV at $100$ TeV FCC-hh with $3\,\text{ab}^{-1}$ for favorable branching scenarios [2601.00083]. Muon and $e^+e^-$ colliders can probe masses up to the kinematic limit ($\sqrt{s}/2$) in pair production, and beyond via $t$-channel exchange in off-shell channels [2307.16111, 2506.00966].

## 4. Experimental Constraints and Current Bounds

**LHC Run II (13 TeV, $\sim 139$ fb$^{-1}$):**
- For $BR(\mu\mu)=100\%$, $m_{H^{\pm\pm}} > 1.17$ TeV.
- For $BR(ee)=100\%$, $m_{H^{\pm\pm}} > 0.94$ TeV.
- For $BR(e\mu)=100\%$, $m_{H^{\pm\pm}} > 1.08$ TeV.
- For mixed $(30\%, 40\%, 30\%)$ $(ee, e\mu, \mu\mu)$, $m_{H^{\pm\pm}} > 1.06$ TeV [2601.00083].

**Photon Fusion Limits**: At 14 TeV, forward proton detectors enable bounds up to $m_{\Delta} \sim 1$–$1.3$ TeV, depending on flavor structure [2508.11336].

**Projections at Hadron Colliders:**
- FCC-hh (100 TeV, 3 ab$^{-1}$): up to $m_{H^{\pm\pm}} \sim 7$ TeV [2601.00083].
- HL-LHC (14 TeV, 3 ab$^{-1}$): up to $2.3$ TeV [1909.07429].
- HE-LHC (27 TeV, 3 ab$^{-1}$): up to 3.1 TeV; with 15 ab$^{-1}$, up to 4.3–4.8 TeV depending on flavor [1909.07429].

**Lepton Colliders**: Muon colliders with $\sqrt{s}=3$–$10$ TeV and high integrated luminosity ($\sim 1$–$10$ ab$^{-1}$) probe $H^{\pm\pm}$ masses up to $5$ TeV (discovery reach for $|Y|\sim 0.01$). Off-shell t-channel exchange offers sensitivity to even heavier masses given sufficiently large leptonic couplings [2506.00966, 2307.16111].

**Low-Energy and Precision Constraints**:
- Lepton-flavor violating decays (e.g., $\mu \to 3e$, $\mu \to e\gamma$) constrain products $|f_{ab} f_{cd}|/m^2_{H^{\pm\pm}} \lesssim 10^{-8}$–$10^{-5}$ GeV$^{-2}$ for $m_{H^{\pm\pm}} \sim$ TeV [1512.04225, 1807.10224].
- Parity-violating Møller scattering can probe right-handed doubly charged scalars up to $\sim 3.7$ TeV in the mass–coupling plane [1806.08499].

## 5. Phenomenological Connections: Neutrino Masses and Model Diagnostics

Doubly charged scalar decay branching ratios and coupling measurements offer a diagnostic for the origin and structure of neutrino masses:

- **Direct Mapping to Neutrino Mass Matrix**: In the type II seesaw, $\text{BR}(H^{++}\to \ell^+\ell^+)$ ratios encode the flavor structure of neutrino masses, and, with sufficient collider data, may allow extraction of absolute neutrino masses and Majorana phases [1005.2817]. Closed analytical expressions link observed event rates to PMNS parameters in the tribimaximal limit.

- **Multiplet and Charge Assignments**: Event rates and associated production ($H^{\pm\pm}H^\mp$), the observation of gauge boson modes, and the absence/presence of charge–current production channels can be used to determine the $SU(2)_L$ multiplet assignment of the new state (singlet, doublet, triplet, etc.), using cross section ratios and event-type discriminants [1305.3904].

- **Discrimination from Neutral Scalars and Alternative Explanations**: Angular distributions and polarization asymmetries in lepton-collider final states can distinguish t-channel exchange of doubly charged scalars from that of neutral (e.g., $H^0$) exotics [2506.00966].

- **Complementarity with Low-Energy Observables**: LFV decays and $\mu$–$e$ conversion, together with collider searches, constrain overlapping but not identical regions of the mass–coupling parameter space. In some scenarios (e.g., vanishing off-diagonal couplings), only high-energy colliders can probe the model [1512.04391, 1807.10224].

## 6. Outlook and Future Directions

- **High-Energy Colliders**: Next-generation machines (HL-LHC, FCC-hh, muon/electron colliders) will either exclude or discover doubly charged scalars in the multi-TeV range, decisively testing type II seesaw models and related frameworks [2601.00083, 2307.16111, 2506.00966].

- **Multi-Scalar and Exotic Decays**: More complex triplet-seesaw and extended multiplicity models predict distinctive cascade and multi-lepton signatures, which require tailored search strategies beyond canonical four-lepton analyses [1305.5761, 2304.09195].

- **Long-Lived Particle Searches**: Parameter regimes yielding long-lived $H^{\pm\pm}$ (due to tiny $y_{ij}$ or $f_{ij}$) motivate continued development of high-$dE/dx$, timing, and dedicated LLP detector technologies [2401.15145].

- **Precision Measurements and Parity Violation**: Low-energy experiments (MOLLER, $\mu\to e$ conversion, $0\nu\beta\beta$) serve as essential complementary probes, especially where high-energy production cross sections are suppressed [1806.08499, 1512.04225].

- **Model Discrimination and Coupling Extraction**: Should a doubly charged scalar be observed, flavor-resolved event rates and kinematic distributions will allow distinction between models of different multiplet structure, extraction of leptonic couplings, and ultimately direct interrogation of the neutrino mass-generation mechanism [1005.2817, 1305.3904].

Doubly charged scalars thus provide a uniquely incisive probe of physics beyond the Standard Model, linking high-energy collider, precision low-energy, and flavor-violating phenomena within a common theoretical framework. The next decade of experiments is poised to either discover these states or place stringent limits on the charge structure of possible new scalar sectors.

Source: https://www.emergentmind.com/topics/doubly-charged-scalars