2HDMcT Type-III: Scalar Triplet Seesaw Model

• The 2HDMcT Type-III is a model that combines two Higgs doublets with a complex scalar triplet to generate Majorana neutrino masses through a scalar type-II seesaw mechanism.
• It features an enriched scalar spectrum, including doubly charged and singly charged states with significant doublet–triplet mixing that enables novel decay channels and collider signatures.
• The model’s flexible Yukawa sector—especially its Type-III realization—permits enhanced interactions and precision tests, impacting both low-energy observables and high-energy collider phenomenology.

The Two-Higgs-Doublet Type-II Seesaw Model, usually denoted $2HDMcT$, is the extension of a two-Higgs-doublet model by a complex $SU(2)_L$ triplet scalar whose vacuum expectation value generates Majorana neutrino masses through the type-II seesaw mechanism. In this literature, the phrase “Type-II” may refer either to the seesaw mechanism or, in some papers, to the Yukawa assignment of the doublet sector; by contrast, the more recent label “2HDMcT Type-III” refers to a Type-III Yukawa realization of the 2HDM sector inside the scalar-triplet model, not to a fermionic type-III seesaw. This distinction is essential, because papers on 2HDM-III with fermionic singlets or fermion triplets are structurally different models (Chen et al., 2014, Ait-Ouazghour et al., 6 Aug 2025, Gutierrez et al., 2018).

1. Terminology and model identification

The scalar-triplet literature represented here uses “2HDMcT” for a model with two Higgs doublets and one complex scalar triplet implementing a type-II seesaw. In this usage, the neutrino-mass sector is always scalar-triplet-based. What changes across papers is the treatment of the 2HDM Yukawa sector: Type-I, Type-II, aligned, and, in one recent study, Type-III (Ouazghour et al., 2024, Chen et al., 2021, Ait-Ouazghour et al., 2024, Ait-Ouazghour et al., 6 Aug 2025).

Label	Meaning in the cited literature	Representative paper
$2HDMcT$	Two Higgs doublets plus a complex scalar triplet; neutrino masses from type-II seesaw	(Ouazghour et al., 2018)
“2HDMcT Type-III”	$2HDMcT$ with a Type-III Yukawa texture assignment in the 2HDM sector	(Ait-Ouazghour et al., 6 Aug 2025)
2HDM-III with seesaw	Generic 2HDM-III plus fermionic singlets or fermion triplets; not a scalar-triplet $2HDMcT$	(Gutierrez et al., 2018)

A closely related source of confusion is the word “triplet.” In the genuine $2HDMcT$, the triplet is a scalar and the neutrino-mass mechanism is type-II seesaw. In the 2HDM-III paper “See-Saw Mechanism in the 2HDM through the simultaneous introduction of a singlet and triplet of Majorana,” the triplet is an $SU(2)_L$ fermion triplet used for a type-III seesaw, and there is no scalar triplet in the model (Gutierrez et al., 2018). The low-scale type-I-seesaw extension of 2HDM-III with right-handed neutrinos is likewise a different construction (Li et al., 2018).

2. Field content, scalar potential, and neutrino-mass operator

The scalar content consists of two electroweak doublets and one complex electroweak triplet. The literature represented here uses both $Y=1$ and $Y=2$ conventions for the triplet, while the doublets are the usual two Higgs doublets. A common parametrization is

$$\Phi_1 = \begin{pmatrix} \phi_1^+ \ \phi_1^0 \end{pmatrix}, \qquad \Phi_2 = \begin{pmatrix} \phi_2^+ \ \phi_2^0 \end{pmatrix}, \qquad \Delta= \begin{pmatrix} \delta^+/\sqrt{2} & \delta^{++} \ (v_t+\delta^0+i\eta_0)/\sqrt{2} & -\delta^+/\sqrt{2} \end{pmatrix},$$

with

$SU(2)_L$0

and

$SU(2)_L$1

This enlarged scalar sector yields a doubly charged scalar, additional singly charged states, and triplet-doublet mixing, all absent in an ordinary 2HDM (Ouazghour et al., 2024, Ouazghour et al., 2023).

A general renormalizable scalar potential used in modern $SU(2)_L$2 analyses is

$SU(2)_L$3

The dimensionful trilinears $SU(2)_L$4 are the characteristic doublet-triplet couplings. They connect the doublets to the triplet, induce triplet-doublet mixing after electroweak symmetry breaking, and enter the scalar mass matrices (Ouazghour et al., 2024). In several analyses a $SU(2)_L$5 symmetry is imposed to suppress tree-level FCNCs, with $SU(2)_L$6, softly broken by $SU(2)_L$7 (Ouazghour et al., 2024, Ait-Ouazghour et al., 2024).

The neutrino-mass operator is the triplet Yukawa interaction

$SU(2)_L$8

or equivalently

$SU(2)_L$9

which yields Majorana neutrino masses once the triplet acquires a vev. The cited papers write this either as

$2HDMcT$0

or

$2HDMcT$1

with the difference reflecting convention choices (Nomura, 2015, Chen et al., 2014).

3. Electroweak symmetry breaking and scalar spectrum

After electroweak symmetry breaking, the $2HDMcT$2 contains 11 physical Higgs states: $2HDMcT$3 This spectrum is one of the main structural differences from an ordinary 2HDM (Ouazghour et al., 2024, Ouazghour et al., 2023).

The triplet vev is small. In the notation $2HDMcT$4, a widely used approximate expression is

$2HDMcT$5

and one convenient relation adopted in early analyses is

$2HDMcT$6

which preserves $2HDMcT$7 by cancellation (Chen et al., 2014, Nomura, 2015). A more explicit tadpole formulation in the notation of (Ouazghour et al., 2018) is

$2HDMcT$8

The CP-even neutral mass matrix is $2HDMcT$9. One commonly used form is

$2HDMcT$0

with, for example,

$2HDMcT$1

$2HDMcT$2

and off-diagonal entries

$2HDMcT$3

$2HDMcT$4

Diagonalization is performed by an orthogonal matrix $2HDMcT$5,

$2HDMcT$6

parameterized by $2HDMcT$7 (Ouazghour et al., 2024, Ait-Ouazghour et al., 2024).

The singly charged sector is the most distinctive structural novelty. In the reduced $2HDMcT$8 basis, the physical states are

$2HDMcT$9

with

$2HDMcT$0

$2HDMcT$1

The crucial point is that $2HDMcT$2 is proportional to the cubic $2HDMcT$3-parameters and can therefore be large, producing a sizable $2HDMcT$4 (Nomura, 2015, Chen et al., 2014).

The doubly charged scalar originates directly from the triplet. One explicit formula used in the $2HDMcT$5 convention is

$2HDMcT$6

while older analyses often worked with approximate hierarchies such as $2HDMcT$7 in collider benchmarks (Ouazghour et al., 2024, Nomura, 2015).

4. Theoretical consistency and constrained parameter space

A detailed theory analysis of the $2HDMcT$8 established a complete set of tree-level unitarity constraints on the coupling parameters of the potential and exact tree-level boundedness-from-below constraints for all directions (Ouazghour et al., 2018). The core quartic positivity conditions include

$2HDMcT$9

$2HDMcT$0

$2HDMcT$1

together with triplet-sector requirements such as

$2HDMcT$2

plus additional mixed doublet-triplet conditions denoted $2HDMcT$3 (Ouazghour et al., 2018). Tree-level unitarity is imposed through scalar-scattering eigenvalues $2HDMcT$4 with

$2HDMcT$5

Electroweak precision is central because the triplet vev breaks custodial symmetry. One early tree-level result is

$2HDMcT$6

so that

$2HDMcT$7

Using $2HDMcT$8, one paper inferred

$2HDMcT$9

at $SU(2)_L$0, while later scans typically restricted $SU(2)_L$1 to the $SU(2)_L$2–$SU(2)_L$3 GeV or $SU(2)_L$4–$SU(2)_L$5 GeV range (Chen et al., 2014, Ouazghour et al., 2023, Ait-Ouazghour et al., 6 Aug 2025).

The $SU(2)_L$6 parameter space has also been revisited under modified Veltman conditions and $SU(2)_L$7. In one detailed study, the one-loop quadratic-divergence combinations were written as

$SU(2)_L$8

$SU(2)_L$9

$Y=1$0

and the surviving sample was significant around $Y=1$1 GeV (Ouazghour et al., 2023).

That same analysis concluded that naturalness affects drastically the masses of heavy Higgs $Y=1$2, $Y=1$3, $Y=1$4 and $Y=1$5. For $Y=1$6 GeV it found

$Y=1$7

and, once $Y=1$8 is included, the lower mass limits of nonstandard Higgs bosons are pushed up to higher values located between $Y=1$9 and $Y=2$0 GeV. It also reported that the $Y=2$1 experimental limits can only be accommodated if two conditions are fulfilled: $Y=2$2 The $Y=2$3 interval used there was

$Y=2$4

at $Y=2$5 C.L. (Ouazghour et al., 2023).

5. Charged-scalar mixing and doubly charged Higgs phenomenology

The phenomenological signature most often emphasized in the $Y=2$6 is the large mixing between the singly charged scalar from the doublet sector and the singly charged scalar from the triplet. This changes the usual doubly charged Higgs phenomenology of the minimal type-II seesaw. Early analyses stressed that the new interactions in the scalar potential cause the sizable mixture of charged Higgses in triplet and doublet, opening the new channels

$Y=2$7

with $Y=2$8 the lightest charged Higgs (Chen et al., 2014).

This has two immediate consequences. First, the triplet charged Higgs inherits quark couplings through its doublet admixture, so the triplet charged Higgs could couple to quarks in the model (Chen et al., 2014). Second, the doubly charged state no longer decays predominantly through the classic minimal-type-II channels

$Y=2$9

because the cascade channels can dominate even when the triplet vev is at GeV level (Chen et al., 2014, Nomura, 2015).

A typical cascade emphasized in the literature is

$$\Phi_1 = \begin{pmatrix} \phi_1^+ \ \phi_1^0 \end{pmatrix}, \qquad \Phi_2 = \begin{pmatrix} \phi_2^+ \ \phi_2^0 \end{pmatrix}, \qquad \Delta= \begin{pmatrix} \delta^+/\sqrt{2} & \delta^{++} \ (v_t+\delta^0+i\eta_0)/\sqrt{2} & -\delta^+/\sqrt{2} \end{pmatrix},$$0

and the corresponding QCD-assisted production channels are

$$\Phi_1 = \begin{pmatrix} \phi_1^+ \ \phi_1^0 \end{pmatrix}, \qquad \Phi_2 = \begin{pmatrix} \phi_2^+ \ \phi_2^0 \end{pmatrix}, \qquad \Delta= \begin{pmatrix} \delta^+/\sqrt{2} & \delta^{++} \ (v_t+\delta^0+i\eta_0)/\sqrt{2} & -\delta^+/\sqrt{2} \end{pmatrix},$$1

$$\Phi_1 = \begin{pmatrix} \phi_1^+ \ \phi_1^0 \end{pmatrix}, \qquad \Phi_2 = \begin{pmatrix} \phi_2^+ \ \phi_2^0 \end{pmatrix}, \qquad \Delta= \begin{pmatrix} \delta^+/\sqrt{2} & \delta^{++} \ (v_t+\delta^0+i\eta_0)/\sqrt{2} & -\delta^+/\sqrt{2} \end{pmatrix},$$2

These channels are absent or negligible in the minimal type-II seesaw because there the triplet states do not couple significantly to quarks (Nomura, 2015).

A focused LHC study of this regime used MADGRAPH/MADEVENT 5, PYTHIA 6, PGS 4, and CalcHEP 3.6.15 with CTEQ6L PDFs, and defined the significance as

$$\Phi_1 = \begin{pmatrix} \phi_1^+ \ \phi_1^0 \end{pmatrix}, \qquad \Phi_2 = \begin{pmatrix} \phi_2^+ \ \phi_2^0 \end{pmatrix}, \qquad \Delta= \begin{pmatrix} \delta^+/\sqrt{2} & \delta^{++} \ (v_t+\delta^0+i\eta_0)/\sqrt{2} & -\delta^+/\sqrt{2} \end{pmatrix},$$3

At $$\Phi_1 = \begin{pmatrix} \phi_1^+ \ \phi_1^0 \end{pmatrix}, \qquad \Phi_2 = \begin{pmatrix} \phi_2^+ \ \phi_2^0 \end{pmatrix}, \qquad \Delta= \begin{pmatrix} \delta^+/\sqrt{2} & \delta^{++} \ (v_t+\delta^0+i\eta_0)/\sqrt{2} & -\delta^+/\sqrt{2} \end{pmatrix},$$4 TeV it found that with integrated luminosity $$\Phi_1 = \begin{pmatrix} \phi_1^+ \ \phi_1^0 \end{pmatrix}, \qquad \Phi_2 = \begin{pmatrix} \phi_2^+ \ \phi_2^0 \end{pmatrix}, \qquad \Delta= \begin{pmatrix} \delta^+/\sqrt{2} & \delta^{++} \ (v_t+\delta^0+i\eta_0)/\sqrt{2} & -\delta^+/\sqrt{2} \end{pmatrix},$$5,

$$\Phi_1 = \begin{pmatrix} \phi_1^+ \ \phi_1^0 \end{pmatrix}, \qquad \Phi_2 = \begin{pmatrix} \phi_2^+ \ \phi_2^0 \end{pmatrix}, \qquad \Delta= \begin{pmatrix} \delta^+/\sqrt{2} & \delta^{++} \ (v_t+\delta^0+i\eta_0)/\sqrt{2} & -\delta^+/\sqrt{2} \end{pmatrix},$$6

could be discovered at the $$\Phi_1 = \begin{pmatrix} \phi_1^+ \ \phi_1^0 \end{pmatrix}, \qquad \Phi_2 = \begin{pmatrix} \phi_2^+ \ \phi_2^0 \end{pmatrix}, \qquad \Delta= \begin{pmatrix} \delta^+/\sqrt{2} & \delta^{++} \ (v_t+\delta^0+i\eta_0)/\sqrt{2} & -\delta^+/\sqrt{2} \end{pmatrix},$$7 level, while for $$\Phi_1 = \begin{pmatrix} \phi_1^+ \ \phi_1^0 \end{pmatrix}, \qquad \Phi_2 = \begin{pmatrix} \phi_2^+ \ \phi_2^0 \end{pmatrix}, \qquad \Delta= \begin{pmatrix} \delta^+/\sqrt{2} & \delta^{++} \ (v_t+\delta^0+i\eta_0)/\sqrt{2} & -\delta^+/\sqrt{2} \end{pmatrix},$$8,

$$\Phi_1 = \begin{pmatrix} \phi_1^+ \ \phi_1^0 \end{pmatrix}, \qquad \Phi_2 = \begin{pmatrix} \phi_2^+ \ \phi_2^0 \end{pmatrix}, \qquad \Delta= \begin{pmatrix} \delta^+/\sqrt{2} & \delta^{++} \ (v_t+\delta^0+i\eta_0)/\sqrt{2} & -\delta^+/\sqrt{2} \end{pmatrix},$$9

could be discovered at the $SU(2)_L$00 level (Nomura, 2015).

The triplet also reshapes loop phenomenology. In a study of muon $SU(2)_L$01 in a two-Higgs-doublet model with a type-II seesaw mechanism, the dominant effect came from two-loop Barr-Zee diagrams mediated by the Higgs triplet fields, especially the doubly charged scalar. The paper stressed that, unlike the usual two-Higgs-doublet models that require exotic Higgs bosons light in mass, the masses of the corresponding particles in the model are of $SU(2)_L$02 GeV, and that the doubly-charged Higgs boson presents a different decay pattern from the usual Higgs triplet model, motivating multi-$SU(2)_L$03 searches at the LHC (Chen et al., 2021).

6. Yukawa realizations, loop probes, and the “Type-III” scenario

The scalar-triplet sector does not fix the Yukawa realization of the two-doublet part. The literature represented here includes a Type-II Yukawa assignment, an aligned scheme, a Type-I texture for the $SU(2)_L$04 GeV excess problem, and a recent Type-III texture at a muon collider (Ouazghour et al., 2024, Chen et al., 2021, Ait-Ouazghour et al., 2024, Ait-Ouazghour et al., 6 Aug 2025).

In the Type-II Yukawa assignment used in one $SU(2)_L$05 study,

$SU(2)_L$06

and the loop-induced process

$SU(2)_L$07

was found to be strongly dependent on $SU(2)_L$08, $SU(2)_L$09, $SU(2)_L$10, and the trilinear Higgs couplings. After imposing theoretical constraints and experimental data, including the $SU(2)_L$11 limit at $SU(2)_L$12 C.L., the paper found

$SU(2)_L$13

can be enhanced up to

$SU(2)_L$14

and that $SU(2)_L$15 is entirely correlated with both the $SU(2)_L$16 and $SU(2)_L$17 signal strengths (Ouazghour et al., 2024).

A distinct phenomenological use of the $SU(2)_L$18 appeared in a study of the $SU(2)_L$19 GeV excesses. There the analysis was performed using the Type-I Yukawa texture, and the paper explicitly stated that the other Yukawa textures—Types II, III, and IV—do not explain the excesses within the allowed parameter space. In that framework, a light CP-even Higgs boson $SU(2)_L$20 around $SU(2)_L$21 GeV could simultaneously account for the $SU(2)_L$22 and $SU(2)_L$23 excesses, while the combination of a nearly degenerate $SU(2)_L$24 and $SU(2)_L$25 gave the best three-channel fit with

$SU(2)_L$26

corresponding to

$SU(2)_L$27

in the paper’s convention (Ait-Ouazghour et al., 2024).

The label “$SU(2)_L$28 Type-III” appears explicitly in a later charged-Higgs study at future $SU(2)_L$29 colliders. In that paper, “Type-III” refers to the Type-III Yukawa texture assignment of the 2HDM sector embedded in the $SU(2)_L$30, not to a fermionic type-III seesaw (Ait-Ouazghour et al., 6 Aug 2025). Its central point is that, in Type-II and Type-III, the neutral-Higgs couplings to muons are approximately proportional to

$SU(2)_L$31

at large $SU(2)_L$32, but the Type-III realization permits much larger $SU(2)_L$33 values than the Type-II realization under the imposed bounds (Ait-Ouazghour et al., 6 Aug 2025).

For a $SU(2)_L$34 TeV muon collider, that study found

$SU(2)_L$35

$SU(2)_L$36

with enhancement up to

$SU(2)_L$37

if electroweak precision observables constraints are relaxed, and

$SU(2)_L$38

The paper emphasized that the $SU(2)_L$39 cross section is significantly enhanced due to the large $SU(2)_L$40 amplification characteristic of the Type-III scenario, and it presented discovery $SU(2)_L$41 regions at a $SU(2)_L$42 TeV muon collider for $SU(2)_L$43, $SU(2)_L$44, and $SU(2)_L$45 (Ait-Ouazghour et al., 6 Aug 2025).

Taken together, these studies show that the $SU(2)_L$46 is best understood as a scalar type-II-seesaw extension of the 2HDM whose phenomenology is highly sensitive to the Yukawa realization chosen for the doublet sector. A plausible implication is that the phrase “2HDMcT Type-III” should be read with care: in the current literature it designates a Yukawa texture inside a scalar-triplet type-II-seesaw model, not a fermionic type-III seesaw.