Doubly charged Higgs production within the Higgs triplet model at future electron-positron colliders

This paper investigates the discovery potential of doubly charged Higgs bosons at the Compact Linear Collider (CLIC) within the Higgs triplet model across various collision modes and benchmark scenarios, demonstrating that CLIC offers superior sensitivity compared to the High-Luminosity LHC, particularly for masses up to 1.2 TeV.

The Gist

Imagine the universe as a giant, bustling construction site. For decades, physicists have been trying to understand the blueprints of this site, specifically how the tiny particles that make up everything get their "weight" (mass). The current blueprint, called the Standard Model, works great for most things, but it has a glaring hole: it can't explain why neutrinos (ghostly, tiny particles) have mass.

To fix this hole, scientists proposed a new addition to the blueprint called the Higgs Triplet Model. Think of the Standard Model's Higgs field as a single, lonely worker. The new model suggests there's actually a whole construction crew (a triplet) working there. One of the most exciting members of this crew is a new, hypothetical particle called the Doubly Charged Higgs ($H^{\pm\pm}$). It's like a "super-charged" version of the famous Higgs boson, carrying double the electric charge.

This paper is a detective story. The authors are asking: "Where and how can we catch this elusive super-charged particle?" They compare two major "hunting grounds": the HL-LHC (a massive proton-smashing ring in Europe) and the CLIC (a proposed, ultra-clean electron collider).

Here is the breakdown of their investigation, using simple analogies:

1. The Two Hunting Grounds: The Sledgehammer vs. The Scalpel

• The HL-LHC (The Sledgehammer): This machine smashes protons together at incredible speeds. It's like trying to find a specific, rare coin in a pile of gravel by smashing the whole pile with a sledgehammer. You get a lot of debris (background noise), and it's hard to see the coin clearly.
• The CLIC (The Scalpel): This machine collides electrons and positrons (matter and anti-matter). It's like using a scalpel to carefully dissect a specific layer of the pile. The environment is much "cleaner," meaning there is less junk noise, making it easier to spot the rare coin if it's there.

2. The Two Clues: The "Yukawa" and "Gauge" Regions

The paper looks at two different scenarios for how this super-charged particle behaves, depending on how it interacts with other particles:

• Scenario A: The "Yukawa-like" Region (The Social Butterfly)

  • The Behavior: In this mode, the particle loves to hang out with other light particles (leptons like electrons). It's very chatty.
  • The Hunt: The best way to find it at CLIC is to use electron-electron ($e^-e^-$) or electron-photon ($e^-\gamma$) collisions.
  • The Result: Because the particle is so chatty, it produces a very loud signal: a pair of same-sign leptons (like two electrons with the same charge). The authors found that CLIC is incredibly good at spotting this. It's like hearing a specific whistle in a quiet library. They can find this particle even if it's quite heavy (up to 2.5 TeV), provided it interacts enough.

• Scenario B: The "Gauge-like" Region (The Heavy Lifter)

  • The Behavior: Here, the particle prefers to interact with heavy force-carriers (W bosons). It's less chatty with light particles and more focused on heavy interactions.
  • The Hunt: The best way to find it is to smash particles together to create pairs of these super-charged Higgs bosons. This works best with photon-photon ($\gamma\gamma$) or electron-positron ($e^+e^-$) collisions.
  • The Result: The particle decays into pairs of W bosons, which then turn into jets of particles and leptons. It's a bit messier to spot, but CLIC can still find it up to a mass of about 1.2 TeV.

3. The Showdown: CLIC vs. HL-LHC

The authors ran simulations to see who wins the hunt.

• The HL-LHC (The Sledgehammer): It struggles here. Because the "super-charged" particle is so rare in proton collisions, and the background noise is so loud, the LHC can only see it if it's relatively light and only barely reaches the threshold of discovery. It's like trying to find a needle in a haystack while the haystack is on fire.
• The CLIC (The Scalpel): It dominates. Because the collisions are cleaner and the production rates are higher for these specific particles, CLIC can spot the particle much more easily and at much higher masses.
  • Analogy: If the HL-LHC is trying to find a rare bird in a noisy jungle, CLIC is finding that same bird in a silent, controlled aviary.

4. The Verdict

The paper concludes that the Compact Linear Collider (CLIC) is the superior tool for finding this specific "Doubly Charged Higgs" particle.

• In the "Social" (Yukawa) scenario: CLIC can find it easily, whereas the LHC might miss it entirely.
• In the "Heavy" (Gauge) scenario: CLIC can find it up to 1.2 TeV, while the LHC struggles to even get a clear signal.

The Takeaway:
If nature has built this "super-charged" particle as part of the solution to the neutrino mass mystery, the best place to look isn't the biggest, loudest machine we have (the LHC), but the cleanest, most precise one we are planning to build (CLIC). The authors are essentially saying, "Don't just smash harder; smash smarter."

Technical Summary

1. Problem Statement

The Standard Model (SM) cannot naturally explain the non-zero masses of neutrinos. The Type-II Seesaw mechanism, realized via the Higgs Triplet Model (HTM), introduces a complex $SU(2)_L$ scalar triplet to generate neutrino masses. A key prediction of this model is the existence of a doubly charged Higgs boson ($H^{\pm\pm}$).

While the Large Hadron Collider (LHC) has set lower mass limits on $H^{\pm\pm}$ (up to $\sim 1.08$ TeV for leptonic decays), the discovery potential is limited by:

• High background rates in hadron collisions.
• The dependence of production cross-sections on specific model parameters (Yukawa couplings vs. gauge couplings).
• The need to probe higher mass ranges and different coupling regimes (Yukawa-like vs. Gauge-like) to fully test the HTM.

The paper investigates whether the Compact Linear Collider (CLIC), operating at $\sqrt{s} = 1.5$ TeV and $3.0$ TeV, offers superior discovery potential compared to the High-Luminosity LHC (HL-LHC) for $H^{\pm\pm}$ across different collision modes ($e^-e^-$, $e^-\gamma$, $\gamma\gamma$, and $e^+e^-$).

2. Methodology

Model Framework

The study is based on the HTM with a scalar triplet $\Delta$ and a doublet $\Phi$. The model is constrained by:

• Theoretical constraints: Perturbativity, vacuum stability, and perturbative unitarity of the scalar potential.
• Experimental constraints: Electroweak precision data (specifically the $\rho$ parameter, limiting the triplet VEV $v_\Delta < 4.9$ GeV), neutrino mass limits (KATRIN, Planck), and LHC Run 2 exclusion limits.

Benchmark Points

The authors analyze two extreme regions of the parameter space defined by the triplet VEV ($v_\Delta$) and the Yukawa coupling ($Y_{ee}$):

1. Yukawa-like Region (BP1): $v_\Delta = 2 \times 10^{-10}$ GeV, $Y_{ee} = 0.35$.
   • Decay: $H^{\pm\pm} \to \ell^\pm \ell^\pm$ (dominantly $e^\pm e^\pm$) with $\approx 100\%$ branching ratio.
   • Mass Range: $m_{H^{\pm\pm}} \ge 1100$ GeV.
2. Gauge-like Region (BP2): $v_\Delta = 4.5$ GeV, $Y_{ee} = 1.5 \times 10^{-11}$.
   • Decay: $H^{\pm\pm} \to W^\pm W^\pm$ with $\approx 100\%$ branching ratio.
   • Mass Range: $m_{H^{\pm\pm}} \ge 400$ GeV.

Simulation and Analysis

• Event Generation: Used FeynRules to derive Feynman rules and MadGraph5_aMC@NLO to generate signal and background events.
• Simulation: Pythia8 for parton showering/hadronization; Delphes with a CLIC-specific detector card for detector simulation (tracking, energy resolution).
• Collision Modes: Analyzed four modes at CLIC:
  • $e^-e^-$ (single production via $e^-e^- \to H^{--}\gamma$).
  • $e^-\gamma$ (single production via $e^-\gamma \to H^{--}e^+$).
  • $\gamma\gamma$ (pair production via $\gamma\gamma \to H^{++}H^{--}$).
  • $e^+e^-$ (pair production via $e^+e^- \to H^{++}H^{--}$).
• Comparison: Parallel analysis performed for the HL-LHC ($\sqrt{s}=14$ TeV, $3 \text{ ab}^{-1}$) focusing on Drell-Yan pair production.
• Selection: Applied baseline kinematic cuts ($p_T$, $\eta$) and optimized kinematic cuts (invariant masses, $H_T$, $\Delta R$, missing $p_T$) to maximize signal significance ($S = N_S / \sqrt{N_S + N_B}$).

3. Key Contributions

1. Comprehensive Multi-Mode Analysis: Unlike previous studies focusing on a single collider mode, this work systematically compares $e^-e^-$, $e^-\gamma$, $\gamma\gamma$, and $e^+e^-$ collisions within the same HTM framework.
2. Identification of Dominant Channels:
   • Yukawa-like: Identified single production ($e^-e^- \to H^{--}\gamma$ and $e^-\gamma \to H^{--}e^+$) as the dominant mechanism, which is largely independent of $v_\Delta$ but scales with $Y_{ee}$.
   • Gauge-like: Identified pair production ($\gamma\gamma \to H^{++}H^{--}$ and $e^+e^- \to H^{++}H^{--}$) as dominant, driven by gauge couplings.
3. Optimization of Search Strategies: Developed specific kinematic cut strategies for the complex $4W$ final state (in the gauge-like region) to suppress backgrounds from $t\bar{t}$, $WWZ$, and multiboson processes.
4. Direct HL-LHC vs. CLIC Comparison: Provided a rigorous side-by-side comparison of discovery reach, demonstrating that CLIC's cleaner environment and higher effective cross-sections in specific modes outperform the HL-LHC for this specific BSM scenario.

4. Results

A. Yukawa-like Region (BP1)

• Dominant Process: Single production $e^-e^- \to H^{--}\gamma$ and $e^-\gamma \to H^{--}e^+$.
• Discovery Potential:
  • CLIC can achieve $>5\sigma$ significance for $H^{\pm\pm}$ masses between 1100 GeV and 2500 GeV.
  • The required Yukawa coupling $Y_{ee}$ to reach $5\sigma$ is in the range 0.05 – 0.15, well below the current experimental limit ($Y_{ee} < 0.35$).
  • The signal is characterized by same-sign dileptons ($e^\pm e^\pm$) and a photon or positron, with very low SM background.
• HL-LHC Performance: The HL-LHC reaches only $\sim 4\sigma$ for a 1.1 TeV mass due to the much smaller production cross-section ($\sim 10^{-4}$ times that of CLIC) and higher backgrounds.

B. Gauge-like Region (BP2)

• Dominant Process: Pair production via $\gamma\gamma$ and $e^+e^-$.
• Discovery Potential:
  • $\gamma\gamma$ mode: Can discover $H^{\pm\pm}$ up to $\sim 800$ GeV with $5\sigma$ significance (using $50 \text{ fb}^{-1}$). The signal is $\ell^\pm \ell^\pm + \ge 3j$ (from $4W$ decay).
  • $e^+e^-$ mode: Despite a lower cross-section than $\gamma\gamma$, the high integrated luminosity ($5 \text{ ab}^{-1}$) allows discovery up to $\sim 1200$ GeV with $>10\sigma$ significance.
  • Kinematic cuts on $H_T$, $M_{jjj}$, and $\Delta \phi$ effectively separate signal from $t\bar{t}$ and multiboson backgrounds.
• HL-LHC Performance: The HL-LHC struggles in this region. For $m_{H^{\pm\pm}} > 400$ GeV, the significance drops rapidly (below $3\sigma$ for masses $>600$ GeV) due to the steep fall-off in cross-section and overwhelming QCD backgrounds.

C. Comparative Summary

• CLIC Advantage: CLIC offers a discovery reach up to 1.2 TeV in the gauge-like region and up to 2.5 TeV in the Yukawa-like region.
• HL-LHC Limitation: The HL-LHC is limited to a narrow mass window just above current exclusion limits and fails to probe the high-mass or low-coupling regions effectively.
• Cross-Section: In the Yukawa-like region, CLIC production cross-sections are generally one order of magnitude higher than at the LHC.

5. Significance

This paper establishes that future lepton colliders (specifically CLIC) are indispensable for the discovery of the doubly charged Higgs boson in the Higgs Triplet Model.

• Complementarity: While the LHC is excellent for heavy resonances with large couplings, CLIC's ability to utilize single production mechanisms and its clean experimental environment allows it to probe parameter spaces (high mass, specific coupling regimes) inaccessible to hadron colliders.
• Physics Reach: The study demonstrates that CLIC can cover the entire kinematically allowed mass range for $H^{\pm\pm}$ in the gauge-like region and extend significantly into the TeV scale for the Yukawa-like region, providing a definitive test of the Type-II Seesaw mechanism.
• Strategic Guidance: The results provide a roadmap for experimental searches at CLIC, identifying specific final states ($e^-e^-\gamma$, $\ell^\pm \ell^\pm + \text{jets}$) and kinematic variables that maximize discovery potential.

In conclusion, the authors argue that without the high-energy, high-luminosity lepton collisions offered by CLIC, the discovery of the doubly charged Higgs boson in the HTM, particularly in the gauge-like regime or at high masses, would likely remain elusive even at the HL-LHC.