Charged Higgs Boson Production

• Charged Higgs boson production refers to generating electrically charged scalar particles in extended Higgs sectors, offering unique signatures beyond the Standard Model.
• The production methodologies incorporate diverse channels, including top-associated production, vector-boson fusion, and exotic processes, with rigorous NLO and NNLO QCD corrections.
• Observable decay modes like H⁺ → τν and H⁺ → tb connect theoretical predictions with experimental strategies, enabling sensitive probes of scalar sector extensions.

A charged Higgs boson ($H^\pm$) is a hallmark of non-minimal scalar sectors in theories beyond the Standard Model, arising in frameworks such as two-Higgs-doublet models (2HDMs), triplet Higgs models, and certain supersymmetric and extended gauge models. Unlike the neutral Higgs, $H^\pm$ carries electric charge and is absent in the Standard Model. Its production at high-energy colliders provides sensitive probes of the scalar sector's structure, Yukawa interactions, and extended gauge phenomena. The production mechanisms, cross sections, and observable signatures are highly model-dependent, spanning vector-boson fusion, fermionic associate production, loop-induced processes, and exotic signatures in non-minimal Higgs or gauge sectors.

1. Principal Production Mechanisms

Charged Higgs production channels include:

• Top-Associated Production ($gb\to tH^-$, $gg\to tH^- \bar b$): In type-II 2HDM and MSSM, this is the dominant process for $m_{H^\pm}>m_t$. In the five-flavor scheme (5FS), $bg\to tH^-$ is leading; the four-flavor scheme (4FS) uses $gg, q\bar q \to t H^- \bar b$ and treats the $b$ quark as massive (Ubiali, 2017, Degrande et al., 2015). Inclusive cross sections at $\sqrt{s}=13$ TeV and $m_{H^\pm}=200$ GeV are $\mathcal{O}(3~\text{pb})$ at NLO for $\tan\beta=10$, decreasing to ${\sim}0.03~\text{pb}$ for $m_{H^\pm}=1$ TeV.
• Top Decay ($t\to bH^+$) in $pp\to t\bar t$: For $m_{H^\pm}<m_t$, a charged Higgs is produced in top decays. The rate is governed by the branching ratio $\mathrm{BR}(t\to bH^+)$, which depends on model parameters, especially $\tan\beta$ (Guedes et al., 2013, Guedes et al., 2012).
• Single-Top with Charged Higgs ($pp\to tj\to H^+bj$): This provides a complementary probe with distinct kinematics and backgrounds, yielding rates $\sim$30% of $t\bar t$-mediated production for $m_{H^\pm}<m_t$ (Guedes et al., 2013, Guedes et al., 2012).
• Vector-Boson Fusion (VBF): In models with Higgs triplets or extended gauge structures, tree-level $W^\pm H^\mp V$ ($V=Z,\gamma, W^\mp$) vertices allow $pp\to H^\pm jj$ via VBF, with clean experimental signatures of forward jets and a central $H^\pm$ (Zaro et al., 2010, Bandyopadhyay, 2017). NNLO QCD corrections yield $K$-factors $K_{\mathrm{NNLO}}\simeq 1.01$–$1.02$ and theoretical uncertainties as low as $2\%$ (scale) and $3$–$5\%$ (PDF).
• Associated Production with Gauge Bosons ($H^\pm W^\mp,~H^\pm Z^0$): Loop and tree-level processes contribute in various models. E.g., central exclusive $pp\to p+H^+W^-+p$ has cross sections $0.1$–$1$ fb in favorable 2HDM scenarios (Enberg et al., 2011). At $e^+e^-$ or muon colliders, $H^\pm$ may be produced in association with $W^\mp$ or $Z^0$ (1711.02615, Phan et al., 18 Nov 2025, Hashemi, 2012), with cross section enhancements in benchmarks with large $m_A-m_H$ splitting or strong trilinear couplings.
• Fermion-Fusion Channels ($c\bar b\to H^-$): In type-III (and possibly type-III-like) 2HDM, $cb$-fusion with lepton-specific Yukawa textures allows sizable cross sections, up to tens of pb for $m_{H^\pm}\sim 100$ GeV (Hernandez-Sanchez et al., 2020).
• Exotic Channels in Extended Models: In 3-3-1 gauge extensions, enhanced production via $Z'$-pole or non-SM gauge couplings is attainable, distinguishing these models from 2HDMs or MSSM (Alves et al., 2011, Martinez et al., 2012).

2. Calculational Framework and Higher-Order Corrections

• NLO and NNLO QCD Effects: Total and differential rates for $pp\to tH^-$ and $pp\to H^\pm jj$ are known to NLO and NNLO in QCD in both the 4FS/5FS and in the structure-function VBF approach (Zaro et al., 2010, Ubiali, 2017, Degrande et al., 2015, Kovarik, 2014). Predicted $K$-factors are order $1.1$–$1.3$ for $tH^-$ production, with scale uncertainties reduced from $\sim$30% (LO) to $10$–$15\%$ (NLO).
• Parton-Shower Matching and Monte Carlo Tools: Both MC@NLO and POWHEG have implementations for $pp\to tH^-$ and its 4FS/5FS realization. For $m_{H^\pm}\lesssim m_t$, one must include interference with $t\bar t$ production and properly use diagram-removal (DR) or diagram-subtraction (DS) schemes (Kovarik, 2014).
• Treatment of Theoretical Uncertainties: Modern analyses recommend $\mu_R = \mu_F = (m_t + m_{H^\pm})/2$ or $H_T/3$ as central scales. PDF uncertainties and matching scheme ambiguities are included in summary uncertainties for experimental analyses (Degrande et al., 2015, Ubiali, 2017).
• Precision in VBF Channels: The structure-function method for $pp\to H^\pm jj$ via VBF ensures all QCD corrections are included up to $\mathcal{O}(\alpha_s^2)$ (NNLO), with minimal missing contributions (nonfactorizable corrections $<0.5\%$) (Zaro et al., 2010).

3. Kinematic Features, Signatures, and Decay Modes

• Dominant Decays: For $m_{H^\pm}<m_t$, $H^\pm\to\tau^\pm\nu$ is often the cleanest experimental channel, especially at large $\tan\beta$ in type-II and type-X 2HDMs (Guedes et al., 2013, Guedes et al., 2012). For heavier $H^\pm$, $H^\pm\to t\bar b$ becomes dominant, with bosonic decays ($H^\pm\to W^\pm h$, $W^\pm A$) important when kinematically permitted or at low-to-moderate $\tan\beta$ in type-I/X (Arhrib et al., 2022, Benbrik et al., 2022).
• VBF Event Topology: The characteristic VBF topology comprises a centrally produced $H^\pm$ between two forward jets with a large rapidity gap, absence of color flow, and enhanced $m_{jj}$ and $|\Delta\eta_{jj}|$ (Zaro et al., 2010).
• Dedicated Analysis Strategies: Selection cuts involve reconstructing $H^\pm$ mass, $b$-tagging, leptonic decays, missing $E_T$, and vetoes designed to reduce $t\bar t$, single-top, and $W$+jets backgrounds. Differential $p_T$ and $\eta$ distributions for the leading $b$-jet and lepton serve as essential discriminants (Degrande et al., 2015).
• Distinctive Signatures in Exotic Models: In 3-3-1 models, simultaneous observation of multiple charged Higgses ($H_1^\pm, H_2^\pm$) and Drell–Yan-type enhancements via $Z'$ s-channel, or VBF-induced $WZ$-fusion single production in triplet-extended supersymmetric models, provides a distinguishing signal set (Martinez et al., 2012, Bandyopadhyay, 2017). Pair production in association with $Z^0$ or $\gamma$ is especially diagnostic in lepton-collider and muon-collider environments (Phan et al., 18 Nov 2025, 1711.02615, Liu et al., 2010).

4. Cross Section Systematics and Model Dependence

Model/Scenario	Key Production(s)	Cross Section Example	Uncertainties
2HDM-II/MSSM	$gb\to tH^-$, $t\to bH^+$	up to $\mathcal{O}(1$ pb)	NLO: $\pm10$–$20\%$
VBF (Triplet)	$pp\to H^\pm jj$	$0.1$–$1$ pb ($m_H=100$–$400$ GeV)	NNLO: Scales $\pm2\%$, PDFs $\pm3$–$5\%$
2HDM-I, low $\tan\beta$	$pp\to H^\pm W^\mp$, $H^\pm b j$	$200$–$300$ fb (at $m_{H^\pm}\sim150$ GeV)	LO: parameter scan, experimental systematics
Type-III (4-zero texture)	$c\bar b\to H^\pm$	$10$–$70$ pb ($m_{H^\pm}<200$ GeV)	Statistical $>5\sigma$ with few $10$ fb$^{-1}$
3-3-1 model	$pp\to W H_1^\pm$, Drell–Yan	$0.3$–$1.2$ pb ($M_{H_1}=300$ GeV)	Enhancement via $Z'$ resonance
Lepton colliders	$e^+e^-/\mu^+\mu^-\to H^+W^-,~H^+H^-Z$	$0.1$–$0.2$ fb (unpolarized), up to $1$ pb in $\mu^+\mu^-$ with enhanced couplings (Hashemi, 2012, 1711.02615)

The magnitude and precise structure of discovery reach are highly dependent on the parameter space, Yukawa type, and scalar potential realization. For nontrivial alignment or mass hierarchies, cross sections and branching ratios can vary by orders of magnitude.

5. Phenomenological Implications and Experimental Reach

• Discovery Reach: For VBF-production with tree-level $WWH$ couplings, masses up to $m_{H^\pm}\sim$400–500 GeV can be probed at the LHC with $\mathcal{O}(1)$–$10$ fb$^{-1}$ (Zaro et al., 2010, Bandyopadhyay, 2017). In muon collider benchmarks, $H^\pm$ with $m_{H^\pm}\sim$250–400 GeV achieves $S>5\sigma$ at $\sqrt{s}=3$ TeV and $L=1$ ab$^{-1}$, even with two-loop ISR and one-loop EW corrections included (Phan et al., 18 Nov 2025).
• Parameter Sensitivity: Enhanced associated production ($\mu^+\mu^-\to H^+W^-$) in 2HDM-II/III with large $m_A$–$m_H$ splitting can exceed MSSM cross sections by orders of magnitude, due to the derivative $AW^\pm H^\mp$ coupling $~(m_A^2-m_H^2)/m_W$ (Hashemi, 2012).
• Distinguishing Models: Simultaneous observation of multiple charged Higgs bosons, enhanced Drell–Yan pair production, or VBF-induced $WZ$ fusion strongly disfavors minimal doublet models and signals exotic gauge or Higgs content.
• Backgrounds and Systematics: Precise rate predictions, advanced Monte Carlo matching, and proper handling of $b$-initiated contributions and interference with $t\bar t$ or other SM processes are essential for robust signal extraction (Ubiali, 2017, Degrande et al., 2015, Kovarik, 2014).
• Complementarity: $H^\pm b j$ and $H^\pm W^\mp$ channels in type-I/X models with moderate or low $\tan\beta$ provide alternative search pathways when $t\bar t$ and $tj$ signatures are suppressed by mass or coupling structure (Arhrib et al., 2022, Benbrik et al., 2022).

6. Directions in Collider Phenomenology and Model Discrimination

Charged Higgs production remains one of the most incisive probes of scalar sector extensions:

• Precision theory advances—including higher-order corrections and Monte Carlo simulation refinements—are critical for exploiting the full reach of LHC and future colliders.
• Model discrimination relies on identifying anomalies in production rates (e.g., enhancement via new gauge bosons, non-standard VBF, or fermion couplings), pattern of decay channels, and multi-scalar signatures that are difficult to mimic in the minimal 2HDM/MSSM framework.
• Lepton-collider and muon-collider studies access channels suppressed at hadron colliders, especially where beam polarization or clean environments allow for high sensitivity despite lower production cross sections.

7. Summary Table: Representative Production Channels and Their Features

Channel	Dominant Model(s)	Typical Cross Section (LHC/Lepton colliders)	Distinctive Feature/Comments
$gb\to tH^-$, $t\to bH^+$	2HDM-II, MSSM	NLO $\sim$ few pb ($m_{H^\pm}\lesssim 400$ GeV)	Sensitive to $\tan\beta$, NLO precision, heavy region
$pp\to H^\pm jj$ (VBF)	Triplet, GM, TNMSSM	$0.1$–$1$ pb ($m_{H^\pm} \sim 100$–$400$ GeV)	Central $H^\pm$ and forward jets, minimal QCD uncertainty
$pp\to H^\pm W^\mp$	2HDM-I/X, 3-3-1, NMSSM	$200$–$300$ fb (type-I low $\tan\beta$)	Can be loop/s-channel enhanced, EW or QCD background
$pp\to H^\pm b j$	2HDM-I/X, II, GM	up to $2$–$3$ pb ($m_{H^\pm}<m_t$, low $\tan\beta$)	Bosonic decays often dominant; forward jet handles
$c\bar b\to H^-$	2HDM-III, flavor-violating	up to $70$ pb ($m_{H^\pm}\sim120$ GeV)	Enhanced BR($H^\pm\to\tau\nu$); suppressed backgrounds
$e^+e^-,\,\mu^+\mu^-\to H^+W^-,\,H^+H^-Z$	2HDM, GM, LRTH	$0.1$–$1$ fb (lepton colliders), pb in some $\mu^+\mu^-$ scenarios	Enhanced rate with non-decoupling couplings

These results reflect state-of-the-art cross section calculations, including robust higher-order corrections, and quantify the interplay of model parameters, collider environment, and theoretical control.

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References: (Zaro et al., 2010, Ubiali, 2017, Degrande et al., 2015, Kovarik, 2014, Arhrib et al., 2022, Benbrik et al., 2022, Guedes et al., 2013, Phan et al., 18 Nov 2025, Enberg et al., 2011, Hashemi, 2012, Hernandez-Sanchez et al., 2020, Bandyopadhyay, 2017, Alves et al., 2011, Martinez et al., 2012, 1711.02615, Liu et al., 2010).