Charged Higgs Bosons (H±)

• Charged Higgs bosons (H±) are massive, electrically charged scalars in extended Higgs sectors that indicate new physics beyond the Standard Model.
• They are produced via multiple collider channels with decay modes—both fermionic and bosonic—sensitive to tanβ and the specific model structure.
• Experimental searches employ advanced strategies like kinematic cuts, b-tagging, and invariant mass reconstruction to isolate H± signals from backgrounds.

A charged Higgs boson (H$^\pm$) is a massive, electrically charged scalar predicted in any extension of the Standard Model Higgs sector containing multiple complex doublets. The charged Higgs occurs universally in Two-Higgs-Doublet Models (2HDMs), supersymmetric frameworks (MSSM, NMSSM, BLSSM), Higgs triplet models (GMHTM), and dark-sector-motivated Z′ models. Observation of H$^\pm$ would constitute a direct indication of physics beyond the Standard Model (BSM) and provide key information about the structure of electroweak symmetry breaking, the pattern of Yukawa couplings, and potentially even the nature of dark matter.

1. Theoretical Foundations: Scalar Sector and Couplings

In the canonical 2HDM, the scalar sector yields five physical states after electroweak symmetry breaking: two CP-even neutral scalars ($h$, $H$), one CP-odd ($A$), and a charged pair ($H^\pm$) (Bao et al., 2011, Arhrib et al., 2022). The scalar potential is typically

$$V(\Phi_1, \Phi_2) = m_{11}^2|\Phi_1|^2 + m_{22}^2|\Phi_2|^2 - (m_{12}^2 \Phi_1^\dagger \Phi_2 + \text{h.c.}) + \text{quartic terms}$$

with parameters traded for physical masses, mixing angles $\alpha$ and $\beta$ ($\tan\beta = v_2/v_1$), and a soft-breaking term $m_{12}^2$. Charged-Higgs mass relations are $m_{H^\pm}^2 = m_A^2 + m_W^2$ in Type-II and MSSM-like models (Arhrib et al., 2018).

The H$^\pm$ couplings to fermions are set by the Yukawa structure. In Type-II (including MSSM), the interaction Lagrangian is

$$\mathcal{L}_Y \supset -\sqrt{2}\; V_{ud}\; \left[\frac{m_u}{v}\cot\beta\, \bar{u}_R H^+ d_L + \frac{m_d}{v} \tan\beta\, \bar{u}_L H^+ d_R\right]$$

where $V_{ud}$ is the CKM matrix element (Bao et al., 2011). In Type-I and X, both up- and down-type couplings scale as $\cot\beta$.

Charged-Higgs–gauge–Higgs couplings arise from doublet covariant derivatives:

• $$g_{H^\pm W^\mp \phi} \propto g\, (m_W/M_\phi)\, \cos(\beta-\alpha)$$ for $\phi=H$, or $\sin(\beta-\alpha)$ for $\phi=A$ (Bao et al., 2011).
• Triplet models introduce $g_{H^\pm W^\mp Z} \propto s_H$, a measure of custodial SU(2) breaking (Collaboration, 2015).

2. Production Mechanisms at Colliders

The dominant production channels depend on $m_{H^\pm}$ and the underlying model:

• Sub-top mass: $pp\to t\bar{t}$ with $t\to b H^+$ (Arhrib et al., 2022, Benbrik et al., 2021, Arhrib et al., 2024). The decay width depends on the model-dependent coupling and phase-space factors.
• Above top threshold: Associated production via $gb\to t H^-$, $gg\to t\bar{b} H^-$ (4FS), or $gg\to H^+ H^-$ (pair production) (Arhrib et al., 2018, Arhrib et al., 2022). In Type-I and X, $pp\to H^\pm W^\mp$ and $pp\to H^\pm bj$ are significant for $m_{H^\pm} < m_t$ (Arhrib et al., 2022, Benbrik et al., 2022).
• Resonant heavy boson: Models with a heavy $Z'$ predict $pp\to Z'\to H^+ H^-$, yielding very energetic final states (Abdallah et al., 2018). BLSSM benchmarks achieve cross sections up to $\mathcal{O}(10^{-2})$ pb at $M_{Z'} = 2.5$–$3.5$ TeV for $M_{H^\pm} = 100$–$150$ GeV.

At lepton colliders (ILC, CLIC), both pair production $e^+e^- \to H^+ H^-$ and associated $e^+e^- \to H^\pm W^\mp S$ ($S=H,A$) are accessible, with the latter often exceeding the former for moderate masses (Hashemi et al., 2023, Ouazghour et al., 2 Jun 2025).

3. Decay Channels and Branching Fractions

Charged Higgs decay patterns are controlled by mass, tan$\beta$, and model:

• Fermionic modes: $H^\pm \to t b$, $H^\pm \to \tau \nu$, $H^\pm \to c s/c b$ (Arhrib et al., 2018, Benbrik et al., 2021, Arhrib et al., 2024). For $m_{H^\pm}<m_t$, $H^\pm\to\tau\nu$ dominates at high tan$\beta$ in II/X, while $cs/cb$ or $\mu\nu$ can prevail in III or with flavor texture.
• Bosonic modes: $H^\pm \to W^\pm \phi$ ($\phi=h,H,A,Z',h_{\rm BSM}$). These dominate whenever kinematically open and at low tan$\beta$ in Type-I and in models with a light neutral scalar or dark $Z'$ (Bao et al., 2011, Arhrib et al., 2022, Bae et al., 2024). For example, BR$(H^\pm\to W^\pm A) > 90\%$ at tan$\beta\sim2$, $m_{H^\pm}\sim100$ GeV (Arhrib et al., 2023).

In Z′-mediated DM models the key signatures are $H^\pm\to W^\pm Z'$, $H^\pm\to W^\pm h$ with distinctive multi-lepton final states. Fermionic decays are typically suppressed below 1% unless $m_{H^\pm}<m_W$ (Bae et al., 2024).

4. Signal Reconstruction and Background Suppression

Collider searches leverage a suite of kinematic cuts and resonance reconstruction techniques:

• Semi-leptonic and fully hadronic topologies: $pp\to W^\pm H^\mp \to \ell\nu\, b\bar{b} jj$, with stepwise cuts on $p_T$, $\eta$, $\Delta R$, missing $E_T$, jet multiplicity, and invariant-mass windows for $H^\pm$, $W$, and $h/A$ (Bao et al., 2011, Arhrib et al., 2022, Benbrik et al., 2022).
• b-tagging and mass windowing: Requiring multiple b-tagged jets and reconstructing $m_{bb}$ or $m_{bjjj}$ significantly suppresses $t\bar{t}$ and $W+$jets backgrounds (Enberg et al., 2014, Enberg et al., 2015).
• Angular distributions: Spin discrimination for H$^\pm$ vs. $W'$ leverages the flat angular distribution of scalar decays vs. $1+\cos^2\theta$ for vectors (Bao et al., 2011).
• Muon-specific final states: In 2HDM-III with large muon Yukawa, $H^\pm\to\mu\nu$ dominates. Transverse mass $m_T(\mu, E_T^{\text{miss}})$ peaks sharply at $m_{H^\pm}$ (Benbrik et al., 2021).
• Complex multi-lepton signatures: For $H^\pm\to W^\pm Z'$, $Z'\to\mu\mu$, trilepton and five-lepton channels with tight isolation and invariant mass cuts are exploited (Bae et al., 2024).

Typical signal-to-background ratios $S/B \sim 0.3$, significances $S/\sqrt{B} \gtrsim 5$ for high-luminosity scenarios and $m_{H^\pm}>400$ GeV (Bao et al., 2011, Enberg et al., 2014).

5. Experimental Constraints, Parameter Space, and Search Strategies

Present bounds derive from both direct and indirect data:

• Direct LHC searches: $H^\pm\to\tau\nu$, $tb$, $cs$, $cb$ in top decays constrain low and high tan$\beta$ regimes differently in 2HDM-II, III, and BLSSM (Arhrib et al., 2024, Abdallah et al., 2018, Arhrib et al., 2022).
• Bosonic modes: Recent analyses place upper limits on $\sigma\times$BR($H^\pm\to HW^\pm$) down to $\sim$0.02 pb at $m_{H^\pm}=700$ GeV for $H$ mass $=200$ GeV (Collaboration, 2022).
• Flavor observables: $B\to X_s\gamma$ excludes $m_{H^\pm}\lesssim 650$–800 GeV in II/Y, but not in I/X for tan$\beta\gtrsim2$ (Arhrib et al., 2022).
• EW precision: T-parameter restrictions typically require near-degenerate H$^\pm$, A, H masses (Bahl et al., 2021).
• Dedicated searches: Many studies emphasize the need for targeted searches in $bbWW$, $Wbj+bb/\tau\tau/\gamma\gamma$, and multi-lepton channels (Arhrib et al., 2022, Benbrik et al., 2022, Arhrib et al., 2023).

Search strategies routinely exploit the dominance of bosonic channels in Type-I/X and the unique final-state kinematics available due to mass relations and mixing angles.

Representative Production and Decay Table (Type-I 2HDM, $m_{H^\pm}<m_t$) (Arhrib et al., 2022)

Channel	$\sigma(pp)$ [fb]	BR $\beta$" title="" rel="nofollow" data-turbo="false" class="assistant-link">\%
$pp \to H^\pm W^\mp$	$100$–$300$	$H^\pm \to W^\pm A$: 80–98
$pp \to H^\pm bj$	$1000$–$3000$	$A \to bb$: 80, $A \to \tau\tau$: 7
$pp \to tH^\pm b$ (subdominant)	$50$–$100$	$H^\pm \to W^\pm h$: 90

6. Beyond Standard 2HDM: Triplet, Dark Sector, and High-Energy Extensions

• Triplet Models (GMHTM): Vector-boson fusion production $pp\to H^\pm jj$ with $H^\pm\to W^\pm Z$ is correlated with custodial $s_H$, with current limits excluding $s_H=1$ for $240\,\text{GeV}<m_{H^\pm}<700\,\text{GeV}$ (Collaboration, 2015).
• Dark Z-mediated DM: Charged Higgs signatures intimately connected with dark matter relic density and direct detection limits; bosonic decays H$^\pm\to W^\pm h$, $W^\pm Z'$ dominate (Bae et al., 2024).
• BLSSM: Heavy $Z'$ can provide essentially background-free $H^\pm$ discovery in both $jj$ and $\tau\nu$ channels at HL-LHC for $m_{H^\pm}<200$ GeV (Abdallah et al., 2018).
• Lepton Colliders: CLIC and ILC studies demonstrate the utility of high-energy, high-luminosity searches in $H^\pm W^\mp S$ modes, with reach exceeding that of hadron colliders for certain regions of tan$\beta$ and $m_{H^\pm}$ (Hashemi et al., 2023, Ouazghour et al., 2 Jun 2025).

7. Phenomenological Implications and Future Prospects

Robust evidence for a charged Higgs would elucidate the structure of EWSB, validate BSM scalar sectors, and inform the flavor and CP properties of fundamental interactions. The observed 3$\sigma$ excess in $H^\pm\to cb$ at $m_{H^\pm}=130$ GeV provides a compelling possibility for near-term experimental resolution (Arhrib et al., 2024). Bosonic decays—long overlooked in favor of fermionic—are now highlighted as leading discovery channels, particularly in Type-I/X and DM-related scenarios.

Designing future searches requires comprehensive analyses targeting mixed bosonic and fermionic decay cascades, leveraging precision jet/lepton identification, optimized mass windowing, and advanced multivariate reconstruction (e.g., BDTs, neutrino weighting) (Hanson et al., 2018, Arhrib et al., 2023). Exploration of extended Higgs sectors remains central to Run 3 and the high-luminosity era, with lepton collider programs offering complementary and sometimes unique sensitivity.

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Key References:

(Bao et al., 2011): H$^\pm$ identification in $W^\pm H^\mp$ associated LHC production (Arhrib et al., 2022, Arhrib et al., 2023, Benbrik et al., 2022): Single charged Higgs production/decay signatures in various 2HDMs (Enberg et al., 2015): $W^\pm h$ channel phenomenology (Arhrib et al., 2024): LHC charged Higgs excess and 2HDM-III fit (Bae et al., 2024): Charged Higgs in dark Z-mediated models (Abdallah et al., 2018): BLSSM and $Z'$-driven signatures (Hanson et al., 2018): MS-2HDM and advanced collider reconstruction (Collaboration, 2015): ATLAS triplet (GMHTM) $W^\pm Z$ search (Hashemi et al., 2023, Ouazghour et al., 2 Jun 2025): Lepton collider discoveries

Charged Higgs bosons, as predicted by extended Higgs sectors, remain one of the most theoretically robust and experimentally approachable portals to BSM physics, with a broad range of discovery and exclusion prospects set to advance rapidly in the coming years.