--- title: Charged Higgs Bosons (H±) url: https://www.emergentmind.com/topics/charged-higgs-bosons-h-pm type: topic --- # Charged Higgs Bosons (H±) 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 ($H^\pm$) [1112.0086][2210.09416]. 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 [1810.09106]. 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 [1112.0086]. 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 $\phi=A$ [1112.0086]. - Triplet models introduce $g_{H^\pm W^\mp Z} \propto s_H$, a measure of custodial SU(2) breaking [1503.04233]. ## 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 $t\to b H^+$ [2210.09416][2112.07502][2402.03195]. 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) [1810.09106][2210.09416]. In Type-I and X, $pp\to H^\pm W^\mp$ and $pp\to H^\pm bj$ are significant for $m_{H^\pm} < m_t$ [2210.09416][2211.02027]. - **Resonant heavy boson:** Models with a heavy $Z'$ predict $pp\to Z'\to H^+ H^-$, yielding very energetic final states [1806.03585]. 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 [2310.06519][2506.01554]. ## 3. Decay Channels and Branching Fractions Charged Higgs decay patterns are controlled by mass, tan$\beta$, and model: - **Fermionic modes:** $H^\pm \to t b$, $H^\pm \to \tau \nu$, $H^\pm \to c s/c b$ [1810.09106][2112.07502][2402.03195]. For $m_{H^\pm} 90\%$ at tan$\beta\sim2$, $m_{H^\pm}\sim100$ GeV [2301.10344]. 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 $m_{H^\pm}400$ GeV [1112.0086][1412.5814]. ## 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 [2402.03195][1806.03585][2210.09416]. - **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 [2207.01046]. - **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$\beta\gtrsim2$ [2210.09416]. - **EW precision:** T-parameter restrictions typically require near-degenerate H$^\pm$, A, H masses [2103.07484]. - **Dedicated searches:** Many studies emphasize the need for targeted searches in $bbWW$, $Wbj+bb/\tau\tau/\gamma\gamma$, and multi-lepton channels [2210.09416][2211.02027][2301.10344]. 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}