Impact of hidden heavy Higgs channels of VLB-Quarks below 1 TeV in 2HDM

This paper demonstrates that incorporating vector-like bottom quarks into the Type-II Two-Higgs-Doublet Model introduces hidden heavy Higgs decay channels that significantly weaken current LHC mass constraints, lowering the exclusion limit for singlet and doublet configurations from approximately 1.5 TeV to as low as 0.98 TeV.

The Gist

The Great Hiding Game: How New Particles Are Escaping the LHC

Imagine the Large Hadron Collider (LHC) as the world's most powerful particle detective. Its job is to smash protons together to find new, heavy particles that shouldn't exist according to our current rulebook (the Standard Model).

For years, the detectives have been looking for a specific suspect: a heavy, "vector-like" bottom quark (let's call him VLB). They've been very strict, setting up roadblocks to catch him. If VLB exists, they thought he would always break down into three specific, familiar items: a Z boson, a Higgs boson, or a W boson. Because they knew exactly what to look for, they set a rule: "If you don't see VLB breaking down into these three things, he must be heavier than 1.5 TeV (a massive weight)."

The Twist:
This new paper says, "Wait a minute! What if VLB has a secret escape route?"

The authors propose that in a specific universe (called the 2HDM-II, which is like a parallel dimension with two Higgs fields instead of one), VLB doesn't just break down into the familiar items. Instead, he can hide by turning into heavy, hidden Higgs bosons (let's call them H, A, and H-minus).

Think of it like this:

• The Old Search: The police are waiting at the airport exit, looking for VLB wearing a red hat (Z boson), a blue hat (W boson), or a green hat (Higgs). They have a list of people they've already caught.
• The New Reality: VLB is actually wearing a black cloak (the heavy hidden Higgs). Because the police are only looking for red, blue, and green hats, they completely miss him. They think he doesn't exist because they can't find him, but he's actually right there, just invisible to their current search strategy.

The "Magic Door" Analogy

The paper investigates three different "costumes" VLB can wear:

1. The Singlet: A lone wolf.
2. The (T, B) Doublet: A duo partner.
3. The (B, Y) Doublet: Another duo partner.

In the "Singlet" costume, VLB can still open a secret door to the hidden Higgs, but it's a bit harder to hide. The police (LHC) can still catch him if he's lighter than 1.34 TeV.

However, in the "Doublet" costumes, VLB finds a super-secret tunnel. In this scenario, he can turn into the hidden Higgs almost 100% of the time.

• The Result: The police's roadblocks become useless. They can no longer say, "You must be heavier than 1.5 TeV."
• The New Limit: Because VLB is so good at hiding in these doublet costumes, the police can only be sure he doesn't exist if he's lighter than 0.98 TeV.

In simple terms: The paper lowers the "guilt threshold." Before, they thought VLB had to be a giant (1.5 TeV) to hide. Now, they realize he could be a medium-sized guy (under 1 TeV) and still be hiding perfectly well because he's wearing a cloak the detectors aren't looking for.

Why Does This Matter?

1. The "Blind Spot": Current experiments are like a security guard checking for specific types of luggage. If a criminal switches their luggage to something the guard doesn't check for, the criminal walks right past. This paper points out that the LHC might be missing these "VLB criminals" because they are switching their "luggage" to heavy, hidden Higgs bosons.
2. The Numbers:
   • Old Rule: "If we don't see you, you must weigh more than 1.5 tons."
   • New Rule: "If you are wearing a heavy cloak, you could weigh as little as 1 ton and we still wouldn't see you."
3. The Future: The authors are telling the LHC team, "Stop looking only at the red, blue, and green hats! You need to start looking for the black cloaks (heavy Higgses) too."

The Bottom Line

This paper is a wake-up call for particle physicists. It says that the "safe zone" where these heavy particles could be hiding is much larger than we thought. The particles might be lighter and closer to us than the current data suggests, but they are playing a very effective game of hide-and-seek using heavy, undiscovered Higgs bosons as their hiding spots.

If the LHC wants to find them, they need to change their search strategy and look for these new, exotic decay paths, or else these particles will remain invisible forever.

Technical Summary

1. Problem Statement

Current Large Hadron Collider (LHC) searches for Vector-Like Bottom (VLB) quarks rely heavily on the assumption that these particles decay exclusively into Standard Model (SM) final states ($B \to Wt, Zb, hb$). Under this assumption, LHC pair-production searches have established stringent lower mass limits, typically excluding VLB masses up to $\sim 1.5$ TeV (singlet) and $\sim 1.55$ TeV (doublet).

However, in extended scalar sectors like the Type-II Two-Higgs-Doublet Model (2HDM-II), VLBs can decay into non-standard heavy Higgs bosons ($H, A, H^\pm$). The paper addresses the critical gap in current experimental analyses: the potential relaxation of VLB mass constraints when these "hidden" BSM decay channels dominate, effectively rendering standard SM-focused searches insensitive to the VLBs.

2. Methodology

The authors employ a phenomenological approach combining theoretical modeling with the recasting of existing LHC exclusion limits.

• Theoretical Framework:

  • Model: 2HDM-II extended with Vector-Like Bottom (VLB) quarks.
  • Representations: The study covers three VLB configurations:
    1. Singlet: A single $B$ quark.
    2. Doublet $(T, B)$: A doublet containing a top-like and bottom-like quark.
    3. Doublet $(B, Y)$: A doublet containing a bottom-like and $Y$ (charge -4/3) quark.
  • Mixing: The VLB mixes with the SM bottom quark via mixing angles ($\theta_{L,R}$), governed by Yukawa couplings and the bare vector-like mass $M_0$.
  • Decay Channels: The analysis explicitly calculates partial widths for decays into:
    • SM modes: $B \to Wt, Zb, hb$.
    • BSM modes: $B \to Hb, Ab, H^-t$.

• Constraints & Scanning:

  • Theoretical Constraints: Perturbative unitarity, vacuum stability, and perturbativity of the scalar potential.
  • Experimental Constraints: Electroweak Precision Observables (S, T parameters), $b \to s\gamma$ constraints (setting $m_{H^\pm} \gtrsim 600$ GeV), and Higgs signal strength measurements ($\kappa$-framework).
  • Parameter Scan: Extensive scans over $m_B \in [0.8, 2]$ TeV, $\tan\beta \in [0.5, 10]$, mixing angles, and heavy Higgs masses ($m_H, m_A, m_{H^\pm}$).

• Recasting Strategy:

  • The authors use the inclusive branching-ratio rescaling method. They take existing LHC exclusion limits (derived for $\text{BR}_{\text{BSM}} = 0$) and rescale the signal cross-section based on the actual branching ratios in the 2HDM-II scenario.
  • The effective signal cross-section is modified by $\text{BR}_{\text{SM}} = 1 - \text{BR}_{\text{BSM}}$, where $\text{BR}_{\text{BSM}} = \text{BR}(B \to Hb) + \text{BR}(B \to Ab) + \text{BR}(B \to H^-t)$.

3. Key Contributions

• Quantification of "Hidden" Channels: The paper demonstrates that BSM decay modes can reach combined branching ratios of nearly 100%, completely suppressing the SM decay channels that LHC searches target.
• Representation-Dependent Limits: The study reveals that the relaxation of mass limits is highly dependent on the VLB representation (Singlet vs. Doublet) and the specific mixing parameters ($s_R^u, s_R^d$).
• Benchmark Points: The authors provide specific benchmark points (BPs) that satisfy all theoretical and experimental constraints while evading current LHC mass limits, serving as targets for future dedicated searches.

4. Key Results

A. General Trend

As the total BSM branching ratio ($\text{BR}_{\text{BSM}}$) increases, the exclusion limit on the VLB mass ($m_B$) drops significantly.

• When $\text{BR}_{\text{BSM}} \approx 0$, limits are $\sim 1.5$ TeV.
• When $\text{BR}_{\text{BSM}} \approx 0.8 - 0.9$, limits drop to $\sim 0.98$ TeV.
• When $\text{BR}_{\text{BSM}} > 0.9$, standard searches lose sensitivity entirely, leaving the mass unconstrained by current data.

B. Specific Representation Results

1. Singlet (2HDM-II + B):

   • The mass limit relaxes from $\sim 1.5$ TeV to $\sim 1.34$ TeV.
   • The dominant BSM channel is $B \to H^-t$ (up to $\sim 27\%$), while $B \to Hb$ and $B \to Ab$ contribute moderately.
   • The relaxation is less dramatic than in doublets because the singlet retains significant SM branching fractions ($Zb, hb$).

2. Doublet $(T, B)$:

   • Significant Relaxation: Limits drop from $\sim 1.55$ TeV to $\sim 0.98$ TeV.
   • Mechanism: For specific mixing configurations ($s_R^u \ll s_R^d$), the SM decay $B \to Wt$ is suppressed. The BSM channels $B \to Hb$ and $B \to Ab$ dominate, reaching $\sim 88\%$ and $\sim 47\%$ respectively, summing to $\sim 100\%$ total BSM branching.
   • This configuration is driven by the scaling of couplings with $\tan\beta$ and the mixing angles.

3. Doublet $(B, Y)$:

   • Significant Relaxation: Similar to the $(T, B)$ case, limits drop to $\sim 0.98$ TeV.
   • Mechanism: The coupling to the charged Higgs ($B \to H^-t$) vanishes due to the specific structure of the $(B, Y)$ doublet. However, the neutral channels $B \to Hb$ and $B \to Ab$ become dominant (up to $\sim 88\%$ and $\sim 46\%$).
   • The SM channel $B \to Wt$ is kinematically or dynamically suppressed.

C. Parameter Dependence

• $\tan\beta$: High $\tan\beta$ generally enhances BSM decays ($B \to Hb, Ab$) proportional to $\tan^2\beta$, leading to weaker mass limits.
• Mixing Angles: The ratio of right-handed mixing angles ($s_R^u / s_R^d$) is crucial. In the $(T, B)$ doublet, a small $s_R^u$ and large $s_R^d$ maximizes the BSM branching fraction.

5. Significance and Conclusion

• Reinterpretation of LHC Data: The paper proves that current LHC null results for VLBs do not rule out masses below 1.5 TeV if the 2HDM-II framework is correct and BSM decays are active. A VLB with a mass of 0.98 TeV could easily exist and remain undetected by current SM-tuned searches.
• Future Prospects: The authors argue that the High-Luminosity LHC (HL-LHC) is essential for probing this scenario. Dedicated searches targeting cascade decays involving heavy Higgs bosons (e.g., $H/A \to t\bar{t}, b\bar{b}, \tau^+\tau^-$ and $H^\pm \to tb, \tau\nu$) are required to recover sensitivity to VLBs in this mass range.
• Model Viability: The study validates that 2HDM-II extended with VLBs remains a viable BSM scenario with light VLBs ($< 1$ TeV), provided the analysis accounts for non-standard decay topologies.

In summary, this work highlights a critical "blind spot" in current collider phenomenology: the assumption of exclusive SM decays for Vector-Like Quarks. By incorporating heavy Higgs channels, the authors demonstrate that VLBs could be significantly lighter than currently believed, necessitating a shift in search strategies for the next generation of collider experiments.