Probing a long-lived pseudoscalar in type-I 2HDM with displaced vertices and jets at the LHC

This paper investigates the discovery potential of a long-lived pseudoscalar $A$ in the type-I two-Higgs-doublet model at the LHC, demonstrating that while Run-2 data has already excluded a significant portion of the parameter space for $m_A > 10$ GeV via displaced-vertex signatures, the high-luminosity LHC will be capable of probing broader regions.

The Gist

Imagine the Large Hadron Collider (LHC) as the world's most powerful particle accelerator, a giant circular racetrack where protons zoom around at near-light speed and crash into each other. For years, scientists have been looking for "new physics"—particles that don't fit into our current rulebook, the Standard Model.

This paper is about hunting for a specific, elusive ghost-like particle called a pseudoscalar (A) within a theory called the Type-I Two-Higgs-Doublet Model.

Here is the story of the hunt, explained simply:

1. The "Ghost" Particle (The Long-Lived Particle)

In our standard understanding, when heavy particles are created in a crash, they usually die instantly, splitting into other particles right where they were born. It's like a firecracker that explodes the moment you light the fuse.

However, this paper suggests that under certain conditions (specifically when a parameter called $\tan \beta$ is very large), our "Ghost Particle" (A) behaves differently. Instead of exploding immediately, it acts like a slow-motion firecracker. It travels a noticeable distance—maybe a few centimeters or even meters—before it finally decays.

In physics terms, this is called a Long-Lived Particle (LLP). Because it travels a macroscopic distance, it leaves behind a "displaced vertex" (DV). Imagine a firecracker that flies across the room and then explodes. That explosion point, far from where it started, is the "displaced vertex."

2. The Hunting Ground: The "Inner Detector"

The ATLAS and CMS experiments at the LHC have a high-tech camera system called the Inner Detector. It's like a very sensitive security camera system inside the collision room.

• Normal particles: Explode right at the center (the "collision point").
• Our Ghost Particle: Travels a bit, then explodes inside the camera's view, creating a "displaced vertex."

The paper focuses on a mass range for this particle between 10 and 100 GeV. In this range, the particle loves to decay into bottom quarks, which look like "jets" of particles in the detector. So, the scientists are looking for a specific signature: Jets of particles appearing out of nowhere, away from the center of the collision.

3. How They Make the Ghost

The paper explains that these particles aren't just popping out of thin air. They are produced in pairs through a specific chain reaction:

1. Two protons collide.
2. They create a heavy "parent" particle (either a charged Higgs $H^\pm$ or a neutral Higgs $H$).
3. This parent particle quickly splits into a Z or W boson (standard force carriers) and our Ghost Particle (A).
4. The Z or W boson turns into jets of particles.
5. The Ghost Particle (A) flies away, travels a bit, and then turns into two jets of bottom quarks.

The Analogy: Imagine a parent (the heavy Higgs) throwing a child (the Ghost A) and a ball (the Z/W boson). The ball lands right next to the parent. The child runs a few steps away before tripping and dropping a backpack (the jets). The scientists are looking for that backpack landing far away from the parent.

4. The Detective Work: Two Strategies

The authors didn't just guess; they ran massive computer simulations (Monte Carlo) to see if the LHC could actually catch this ghost. They tested two different "search strategies" (analyses):

• The "Original" Analysis: This is the strict, high-security search used by ATLAS recently. It looks for very energetic jets and very specific patterns. It's like a guard who only looks for backpacks that are heavy and thrown with great force.
• The "Modified" Analysis: This is a more flexible approach, inspired by older searches. It lowers the energy threshold, looking for lighter or slower jets. It's like a guard who says, "I'll look for any backpack, even if it's light or thrown gently."

5. The Results: What Did They Find?

The team simulated millions of collisions to see how many "ghosts" they could catch.

• The Bad News: A large chunk of the "safe zone" where this particle could hide has already been ruled out by data from the LHC's second run (Run-2). If the particle exists in that specific mass range, the "Original" analysis likely would have seen it by now.
• The Good News: There is still plenty of territory left to explore!
  • The Future: The High-Luminosity LHC (HL-LHC), which will run in the future with much more data (3000 times more collisions), will be able to probe much deeper.
  • The "Modified" Strategy: The flexible "Modified" analysis is actually better at finding these ghosts in certain scenarios, especially when the particle is very long-lived or the parent particles are heavy. It can see things the strict "Original" search might miss.

6. The Bottom Line

This paper is a roadmap for the future. It tells us:

1. Don't give up: Even though some areas are closed, the "Ghost Particle" is still hiding in the shadows of the parameter space.
2. Look further: The next generation of the LHC (HL-LHC) is our best bet to find it.
3. Change tactics: Using the "Modified" search strategy (looking for lower-energy signals) might be the key to catching this elusive particle.

In short, the authors are saying: "We know the rules of the game, we know where the ghost might be, and we have a new, better flashlight to find it in the next few years."

Technical Summary

1. Problem Statement

The paper investigates the discovery potential of a long-lived pseudoscalar ($A$) within the Type-I Two-Higgs-Doublet Model (2HDM).

• Theoretical Context: In the Type-I 2HDM, the coupling of the pseudoscalar $A$ to Standard Model (SM) fermions is suppressed by a factor of $1/\tan\beta$. For sufficiently large values of $\tan\beta$, the decay width of $A$ becomes extremely narrow, resulting in a macroscopic decay length. This makes $A$ a candidate for a Long-Lived Particle (LLP).
• Mass Range: The study focuses on the mass range $10 \text{ GeV} \lesssim m_A \lesssim 100 \text{ GeV}$. In this range, $A$ predominantly decays into a pair of bottom quarks ($b\bar{b}$).
• Production Mechanism: At the LHC, $A$ is primarily produced in pairs via electroweak processes:
  • $pp \to W^*/Z^* \to H^\pm A$
  • $pp \to W^*/Z^* \to H A$
  • Followed by the decays $H^\pm \to W^\pm A$ and $H \to Z A$.
• Experimental Challenge: Traditional prompt-search strategies at ATLAS and CMS often miss LLPs because they decay outside the primary interaction vertex. The paper aims to probe this specific parameter space using Displaced Vertex (DV) signatures accompanied by jets.

2. Methodology

Theoretical Framework and Constraints

• Model Setup: The authors utilize the Type-I 2HDM with two scalar doublets. They impose the alignment limit ($\cos(\beta-\alpha) \to 0$) to ensure the observed 125 GeV Higgs boson ($h$) behaves like the SM Higgs.
• Constraints Applied:
  • Theoretical: Vacuum stability, perturbativity (quartic couplings $< 4\pi$), and perturbative unitarity.
  • Experimental:
    • Higgs signal strength measurements ($\mu_{\gamma\gamma}$).
    • Limits on the branching ratio $Br(h \to AA) < 0.1\%$ (for $m_A < 62.5$ GeV).
    • Electroweak oblique parameters ($S, T, U$).
    • Exclusion limits from direct searches for neutral and charged Higgs bosons.
• Parameter Scan: A random scan is performed over $\cos(\beta-\alpha)$, $\tan\beta$, $m_H$, $m_{H^\pm}$, and $m_A$. The study focuses on large $\tan\beta$ ($10^3$ to $10^6$, extended to $10^8$ in sensitivity plots) and $m_A$ between 10 and 100 GeV.

Simulation and Analysis Strategy

• Event Generation:
  • Signal events are generated using MadGraph5_aMC@NLO at leading order (LO) with a K-factor of 1.2 to approximate NLO QCD corrections.
  • Parton showering and hadronization are handled by Pythia8.
  • A custom "toy-detector" module in Pythia8 is used to reconstruct truth-level jets.
• Experimental Recasting: The authors evaluate the signal against two specific analysis strategies at ATLAS (and applicable to CMS):
  1. "Original Analysis": Based on a recent ATLAS Run-2 search (139 fb$^{-1}$) for long-lived electroweakinos. It employs high jet-$p_T$ thresholds (e.g., $\ge 137$ GeV) and specific DV reconstruction criteria (fiducial volume, impact parameter, invariant mass).
  2. "Modified Analysis": Inspired by a past 8-TeV ATLAS search. It lowers the jet-$p_T$ thresholds (e.g., $\ge 90$ GeV) to improve acceptance for softer jets, while maintaining the same DV reconstruction criteria.
• Signal Definition: The final state consists of multiple jets (from $W/Z \to jj$) and displaced vertices (from $A \to b\bar{b}$).
• Background Assumption: Both analyses assume negligible background (0 events) after selection cuts, setting the exclusion limit at 3 signal events for 95% Confidence Level (C.L.).

3. Key Contributions

• Comprehensive Recasting: The paper provides a rigorous recasting of ATLAS DV searches specifically tailored for the Type-I 2HDM scenario, including a novel "modified" analysis that lowers kinematic thresholds to enhance sensitivity.
• Fine-Tuning Analysis: The authors quantify the degree of fine-tuning required in the Higgs potential parameters ($m_{12}^2$ vs. $m_H^2 s_\beta c_\beta$) to satisfy theoretical constraints at very large $\tan\beta$. They show that as $\tan\beta$ increases, the required fine-tuning becomes severe ($R_f \sim 10^{-12}$), necessitating high numerical precision.
• Dual-Analysis Comparison: By comparing the "original" and "modified" analyses, the paper demonstrates the significant gain in sensitivity achievable by relaxing jet-$p_T$ cuts for LLP searches.

4. Numerical Results

• Exclusion of Parameter Space:
  • A substantial portion of the parameter space with $m_A > 10$ GeV and large $\tan\beta$ has already been excluded by LHC Run-2 data (139 fb$^{-1}$).
  • The exclusion is driven by the requirement that $A$ must decay within the inner detector ($4 \text{ mm} < R_{xy} < 300 \text{ mm}$) to be detected. If $\tan\beta$ is too low, $A$ decays promptly; if too high, it decays outside the detector.
• Sensitivity of the Modified Analysis:
  • The modified analysis (lower $p_T$ thresholds) consistently outperforms the original analysis, probing both larger and smaller values of $\tan\beta$.
  • For $m_H = 200$ GeV and $3000$ fb$^{-1}$ (HL-LHC), the modified analysis can probe $\tan\beta \lesssim 10^8$ for $m_A \lesssim 100$ GeV.
• Dependence on Masses:
  • $m_A$: Sensitivity cuts off sharply at $m_A \approx 10$ GeV due to the $m_{DV} > 10$ GeV requirement.
  • $m_H$: Heavier $H$ ($m_H = 600$ GeV) leads to harder jets (higher efficiency) but significantly lower production cross-sections. The net result is a reduction in the number of signal events ($N_S$) compared to lighter $H$.
• Decay Length: For the most sensitive points (large $\tan\beta$, $m_A \sim 100$ GeV), the decay length $c\tau_A$ can reach $\sim 650$ meters, meaning many events would escape detection unless $\tan\beta$ is tuned to keep the decay within the inner detector.

5. Significance

• Validation of LLP Searches: The study confirms that displaced vertex searches are a powerful tool for probing light pseudoscalars in Type-I 2HDM, a region often overlooked by prompt searches.
• Optimization of Future Searches: The "modified analysis" results suggest that lowering jet-$p_T$ thresholds in future LLP searches could significantly extend the discovery reach, particularly for scenarios with softer kinematics.
• HL-LHC Prospects: The paper provides concrete projections for the High-Luminosity LHC, indicating that the HL-LHC will be able to probe broader regions of the Type-I 2HDM parameter space, potentially covering $\tan\beta$ values up to $10^8$ for $m_A < 100$ GeV.
• Theoretical Consistency: It highlights the tension between large $\tan\beta$ (required for long lifetimes) and theoretical constraints (vacuum stability/unitarity), emphasizing the need for precise numerical handling of fine-tuning in such models.

In conclusion, the paper establishes that the Type-I 2HDM with a light, long-lived pseudoscalar is highly constrained by current LHC data but remains a viable target for future high-luminosity runs, provided experimental strategies are optimized to detect displaced vertices with lower momentum thresholds.