Charged Higgs Boson Phenomenology in the Dark Z mediated Fermionic Dark Matter Model

This paper investigates the phenomenology of a light charged Higgs boson ($110 < m_{H^\pm} < 170$GeV) within a fermionic dark matter model mediated by a light$Z'$ boson, analyzing its production mechanisms at the LHC, current experimental constraints from ATLAS and CMS, and its interplay with dark matter properties.

The Gist

Imagine the Standard Model of physics as a giant, bustling city where every particle has a specific job. For decades, this city has been running smoothly, but scientists suspect there's a "hidden neighborhood" just outside the city limits where dark matter lives. The big mystery is: How does the hidden neighborhood talk to the main city?

This paper proposes a new "diplomatic channel" to solve that mystery, involving a very specific, lightweight messenger particle called a Charged Higgs Boson.

Here is the story of the paper, broken down into simple concepts and analogies:

1. The Setup: A Secret Tunnel and a New Gatekeeper

In this model, the "Dark Matter" is a shy, invisible fermion (a type of particle) living in the hidden sector. It can't talk to our normal particles directly. To bridge the gap, the scientists introduce a new "messenger" field (an extra Higgs doublet).

Think of this messenger like a specialized courier who carries packages between the hidden neighborhood and the main city. But there's a catch: this courier is charged with a new, secret energy called $U(1)_X$. Because of this charge, the courier can't just walk into the city; they need a special gate.

2. The "Dark Z" Gatekeeper

When the universe cooled down after the Big Bang, this secret energy broke, creating a new particle called the Dark Z boson ($Z'$).

• The Analogy: Imagine the standard Z boson is the main security guard at the city gate. The Dark Z is a junior guard who looks almost exactly like the main guard but is much lighter and wears a slightly different uniform.
• Because this junior guard is so light (around 10 GeV, which is tiny in particle physics terms), it creates a lot of noise in the city's security systems. This puts strict rules on how the model can work.

3. The Star of the Show: The Lightweight Charged Higgs

The main character of this paper is the Charged Higgs Boson ($H^\pm$). In many theories, these particles are heavy and hard to find. But in this specific model, the rules of the game force this particle to be surprisingly light (between 110 and 170 GeV).

• The Analogy: Usually, you expect a "Charged Higgs" to be a heavyweight champion boxer. In this model, it's a featherweight boxer. Because it's so light, it doesn't hang around in the heavy machinery of the universe; instead, it gets created easily when heavy particles (like the Top Quark) decay.

4. How We Find It: The "Top Quark" Factory

Since the Charged Higgs is light, the Large Hadron Collider (LHC) doesn't need to smash particles together with maximum force to find it. Instead, it's produced as a byproduct when a Top Quark (the heaviest known particle) falls apart.

• The Scenario: Imagine a Top Quark is a heavy crate. When it breaks open, it usually drops a bottom quark and a W boson. In this model, it sometimes drops a bottom quark and a Charged Higgs instead.

5. The Weird Decay: "Lepton Jets"

Once the Charged Higgs is created, it has to decay (break apart). In most theories, it breaks into heavy fermions. But here, because of the light Dark Z and the light neutral Higgs ($h$), it prefers to break into bosons (force carriers).

• The Decay Chain: The Charged Higgs turns into a W boson and a Dark Z (or a light neutral Higgs).
• The "Lepton Jet": The Dark Z is so light and moves so fast that when it decays into electrons or muons, those particles are squished together so tightly they look like a single jet of light rather than separate particles. It's like a firehose spraying water so fast the droplets merge into a solid stream.
• The "Five-Muon" Signal: The paper suggests a "golden search channel." If the Charged Higgs is produced with a Dark Z, and everything decays into muons, you could see a very rare event with five muons flying out at once. It's like finding a specific, rare hand of cards in a deck of billions.

6. The Dark Matter Connection

The model also explains Dark Matter. The Dark Matter particle interacts with our world only through this Dark Z gatekeeper.

• The Tuning Problem: The paper finds that for the Dark Matter to exist in the right amount (the "relic abundance" we see in the universe), its mass has to be tuned very precisely—either just under half the mass of the Dark Z, or right at the threshold. It's like trying to balance a pencil on its tip; it works, but it requires very specific conditions.

7. The Conclusion: What's Next?

The authors ran the numbers using the latest data from ATLAS and CMS (the two big detectors at the LHC).

• The Good News: The model isn't dead! There is still a "safe zone" where the Charged Higgs is light (110–170 GeV) and the Dark Z is very light (~10 GeV).
• The Challenge: Current searches have mostly looked for heavy Charged Higgses or specific decay patterns. This model suggests we need to look for lighter, stranger signals—like those "lepton jets" or the "five-muon" events.
• The Potential: If the LHC runs its next round of experiments (Run 3) with this specific search in mind, they might find up to 500 of these rare five-muon events. That would be a smoking gun for new physics.

Summary in One Sentence

This paper proposes a new, lightweight "messenger" particle (Charged Higgs) that connects our world to Dark Matter via a tiny "Dark Z" gatekeeper, suggesting that the next big discovery at the LHC might be a rare, multi-muon explosion that looks like a jet of light, rather than the heavy particles we've been hunting for decades.

Technical Summary

Here is a detailed technical summary of the paper "Charged Higgs Boson Phenomenology in the Dark Z mediated Fermionic Dark Matter Model."

1. Problem Statement

The Standard Model (SM) lacks a charged Higgs boson ($H^\pm$) and a viable dark matter (DM) candidate. While Two-Higgs-Doublet Models (2HDMs) introduce $H^\pm$, they often struggle to simultaneously explain DM and satisfy stringent electroweak precision constraints.
This paper investigates a specific extension: a Type-I 2HDM augmented with a hidden sector containing a Dirac fermion DM candidate ($\psi_X$) charged under a new $U(1)_X$ gauge symmetry. The hidden sector communicates with the SM via an additional scalar doublet ($H_1$) acting as a messenger. The spontaneous breaking of $U(1)_X$ at the electroweak scale generates a massive "Dark Z" boson ($Z'$).
The core problem: Determine the allowed parameter space for this model given current experimental constraints (electroweak precision, Higgs data, and DM searches) and evaluate the discovery potential of the resulting light charged Higgs boson at the Large Hadron Collider (LHC).

2. Methodology

The authors employ a comprehensive phenomenological analysis combining theoretical constraints with experimental data:

• Model Framework:

  • Gauge Structure: $SU(3)_c \times SU(2)_L \times U(1)_Y \times U(1)_X$.
  • Fields: SM-like Higgs doublet ($H_2$, neutral under $U(1)_X$) and messenger doublet ($H_1$, charged under $U(1)_X$).
  • Symmetry Breaking: $H_1$ acquires a Vacuum Expectation Value (VEV), breaking $U(1)_X$ and generating the $Z'$ mass. The $Z'$ mixes with the SM $Z$ boson via a mixing angle $\theta_X$.
  • Spectrum: The model predicts a light $Z'$, a light charged Higgs ($H^\pm$), and an additional neutral Higgs ($h$). The CP-odd scalar $A$ is "eaten" by the $Z'$ (longitudinal mode).

• Constraints & Tools:

  • Electroweak Precision: Analyzed via the $\rho$ parameter and atomic parity violation (weak charge of Cesium), which tightly constrain the $Z'$ mass ($m_{Z'}$) and mixing angle ($\sin \theta_X$).
  • Higgs Sector: Used HiggsBounds and HiggsSignals (via HiggsTools) to check exclusion limits from LEP, Tevatron, and LHC (ATLAS/CMS) on scalar production and signal strengths.
  • Theoretical Bounds: Enforced perturbativity ($|\lambda_i| < 4\pi$), vacuum stability, and perturbative unitarity of $WW$ scattering.
  • Dark Matter: Used micrOmegas to calculate the thermal relic abundance via freeze-out and checked consistency with direct detection (XENON, LZ, etc.) and indirect detection limits.

• LHC Phenomenology:

  • Calculated production cross-sections for $pp \to tH^\pm$, $pp \to H^\pm Z'$, and $pp \to H^\pm h$.
  • Computed branching ratios for $H^\pm$ decays into fermions ($cs, \tau\nu$) and bosons ($W^\pm h, W^\pm Z'$).
  • Proposed specific search channels, including trilepton and multi-muon final states involving "lepton jets" from boosted light $Z'$ decays.

3. Key Contributions

• Identification of a Narrow Light $H^\pm$ Window: The study establishes that, due to the interplay between the $U(1)_X$ symmetry breaking and electroweak precision data, the charged Higgs mass is restricted to a narrow, light range: $110 \text{ GeV} < m_{H^\pm} < 170 \text{ GeV}$.
• Dominance of Bosonic Decays: Unlike typical 2HDM scenarios where fermionic decays ($H^\pm \to cs, \tau\nu$) dominate, this model predicts that bosonic decays ($H^\pm \to W^\pm h$ and $H^\pm \to W^\pm Z'$) are the dominant channels when kinematically allowed. This is a direct consequence of the specific coupling structures and the light mass of the $Z'$ and $h$.
• Lepton Jet Signatures: The paper highlights that the light $Z'$ ($m_{Z'} \approx 9.3\text{--}11.3$ GeV) is highly boosted at the LHC, decaying into collimated lepton pairs (e.g., $\mu^+\mu^-$) that mimic jet structures ("lepton jets"). This offers a unique signature for $H^\pm$ production.
• Multi-Muon Discovery Channel: A novel search strategy is proposed for the direct production channel $pp \to H^\pm Z'/h$, leading to a five-muon final state ($\mu\mu\mu\mu\mu$) via $Z' \to \mu\mu$ and $W \to \mu\nu$, with an estimated yield of ~500 events in LHC Run 3.

4. Key Results

• Allowed Parameter Space:
  • $Z'$ Mass: $9.3 \text{ GeV} < m_{Z'} < 11.3 \text{ GeV}$.
  • $H^\pm$ Mass: $110 \text{ GeV} < m_{H^\pm} < 170 \text{ GeV}$.
  • Mixing Angle: The $Z-Z'$ mixing angle is very small ($|\sin \theta_X| \lesssim 0.007$), consistent with atomic parity violation limits.
  • $\tan \beta$: Must be large ($\tan \beta > 2.1$) to satisfy constraints.
• Decay Branching Ratios:
  • For $m_{H^\pm} \approx 120\text{--}160$ GeV, the bosonic modes $H^\pm \to W^\pm Z'$ and $H^\pm \to W^\pm h$ dominate (often $>90\%$).
  • Fermionic modes ($cs, \tau\nu$) are suppressed to $<10\%$ unless the bosonic channels are kinematically closed and $\sin \alpha$ is large.
• Dark Matter Consistency:
  • The model can reproduce the observed DM relic density via thermal freeze-out.
  • Viable DM mass regions are found around **$4.5\text{--}5.5$GeV** (resonance region$2m_X \approx m_{Z'}$) and **$8\text{--}14$GeV** ($Z'$ threshold region).
  • These regions are consistent with current direct detection limits (e.g., XENONnT, LZ) and Bullet Cluster self-interaction constraints.
• Experimental Constraints:
  • Current ATLAS/CMS searches for light $H^\pm$ (primarily in $cs$ and $\tau\nu$ channels) do not exclude the model because the fermionic branching ratios are small in the favored parameter space.
  • However, CMS trilepton searches ($H^\pm \to W^\pm A \to W^\pm \mu\mu$) constrain regions with large $m_h$ and small $\tan \beta$.

5. Significance

• New Physics Discovery Potential: The paper argues that the standard search strategies for charged Higgs bosons (focusing on fermionic decays) are insufficient for this specific model. It provides a roadmap for discovering $H^\pm$ via bosonic decays and lepton jets, which are currently under-explored.
• Unified Framework: It successfully constructs a model that simultaneously explains Dark Matter and predicts a light charged Higgs, linking the DM mass scale to the electroweak scale via the $Z'$ mass.
• Testability: The predictions are highly specific and testable in the near future (LHC Run 3 and High-Luminosity LHC). The "five-muon" signature and displaced vertices (if $h$ is long-lived) offer clean, low-background channels that could definitively confirm or rule out this class of Dark Z-mediated models.
• Theoretical Insight: The work demonstrates how a $U(1)_X$ symmetry can naturally suppress the CP-odd scalar (absorbing it into the $Z'$), leading to a distinct phenomenological profile compared to standard 2HDMs.