Non-standard decays of vector-like top partners in a $2$-Higgs doublet model at the HL-LHC

This paper investigates the discovery potential at the High-Luminosity LHC for non-standard decays of vector-like top partners into charged Higgs bosons and subsequent tau leptons within a 2-Higgs doublet model, demonstrating that the resulting $2\tau + 2b + E_T^{\text{miss}}$ final state can probe vector-like top partner masses up to approximately 1.9 TeV.

The Gist

Imagine the Large Hadron Collider (LHC) as a giant, high-speed particle accelerator that smashes protons together to see what tiny pieces fly out. Scientists usually look for specific "standard" pieces that fit their current rulebook (the Standard Model). However, this paper suggests that if we look for a different, more exotic set of pieces, we might find a whole new world of physics hiding in plain sight.

Here is a simple breakdown of what the authors are proposing:

1. The Missing Puzzle Pieces: "Vector-Like Top Partners"

Think of the "Top Quark" as the heaviest, most famous brick in the Standard Model's wall. Theorists suspect there might be a "twin" or a "partner" to this brick, called a Vector-Like Top Partner (T).

• The Problem: Current experiments are looking for this partner by seeing how it breaks apart into standard pieces (like a W boson and a bottom quark). They have found nothing up to about 1.3–1.5 TeV (a unit of mass).
• The Twist: This paper asks: What if the partner doesn't break into standard pieces? What if, instead, it breaks into something exotic that the current searches are ignoring?

2. The Exotic Decay: The "Ghostly" Path

The authors propose a specific scenario using a theory called the 2-Higgs Doublet Model. Imagine the Higgs boson (the particle that gives things mass) isn't just one particle, but part of a family with extra siblings, including a Charged Higgs (H±).

In this scenario, the heavy Top Partner (T) doesn't decay the usual way. Instead, it takes a "secret route":

1. The Top Partner (T) splits into a Charged Higgs (H±) and a bottom quark (b).
2. The Charged Higgs is unstable and immediately splits into a Tau lepton (τ) and a neutrino (ν).
   • Analogy: Imagine a heavy suitcase (T) that doesn't just open to reveal clothes (standard particles). Instead, it opens to reveal a glowing, unstable balloon (Charged Higgs) that instantly pops into a heavy, mysterious package (Tau) and a ghost (neutrino) that vanishes without a trace.

3. The Detective Work: Hunting at the HL-LHC

The authors are looking ahead to the High-Luminosity LHC (HL-LHC), which will run with much more data (3 ab⁻¹) than it does now. They want to know: Can we catch this specific "ghostly" decay?

The Final Clue (The Signature):
When two of these Top Partners are created and decay this way, the final scene looks like this:

• 2 Tau leptons: Heavy, unstable particles that leave a specific track.
• 2 Bottom jets: Clumps of particles from the bottom quarks.
• Missing Energy: The neutrinos (ghosts) escape the detector, leaving a "hole" in the energy balance.

The authors call this the 2τ + 2b + Missing Energy channel. It's like finding a crime scene with two specific footprints, two specific tire tracks, and a missing person.

4. How They Filter the Noise

The universe is messy. The most common background noise is the production of Top-Antitop pairs (t-tbar), which can accidentally look like the signal.

• The Strategy: The authors built a "filter" using math and physics rules. They look at the speed and energy of the particles. Because the Top Partner is very heavy (up to 1.9 TeV), the particles it creates fly much faster and harder than the particles from the common background noise.
• The Result: By setting strict rules on how much energy and momentum the particles must have, they can filter out 99% of the background noise and keep the potential signal.

5. The "Spin" Trick: Reading the Tau's Mood

There is a clever secondary trick mentioned in the paper.

• The Signal: The Tau particles from the Charged Higgs are "right-handed" (they spin in a specific direction).
• The Background: The Tau particles from the common Top-Antitop background are "left-handed" (they spin the opposite way).
• The Analogy: Imagine trying to tell the difference between two identical-looking cars. One drives with the steering wheel on the left, the other on the right. By looking closely at how the "wheels" (the decay products of the Tau) turn, scientists can tell which car is which. This adds an extra layer of certainty to their search.

6. The Bottom Line

The paper concludes that with the upcoming High-Luminosity LHC:

• If these exotic Top Partners exist and weigh up to 1.9 TeV, this specific search method has a very good chance of discovering them (a 5-sigma certainty, which is the gold standard for a discovery).
• Even if they don't find them, they can confidently rule out (exclude) their existence up to about 2.1 TeV.

Why this matters:
Current searches are like looking for a lost key in a specific drawer. This paper suggests the key might be in a completely different drawer (the exotic decay channel) that no one has been checking thoroughly. If the Top Partner exists but decays this way, the current searches would miss it entirely. This paper provides a new map to find it.

Technical Summary

Technical Summary: Non-standard decays of vector-like top partners in a 2-Higgs doublet model at the HL-LHC

Problem Statement
Vector-like quarks (VLQs) are a theoretically well-motivated extension of the Standard Model (SM), appearing in frameworks such as composite Higgs and extra-dimensional models. While current Large Hadron Collider (LHC) searches constrain the mass of the top-quark partner ($T$) up to approximately 1.3–1.5 TeV, these limits rely on the assumption that $T$ decays exclusively into SM-like final states ($Wb$, $Zt$, $ht$). In scenarios where VLQs couple to an extended Higgs sector, such as the 2-Higgs Doublet Model (2HDM), non-standard decay channels (e.g., $T \to H^\pm b$) can become dominant. These exotic modes render existing exclusion limits inapplicable, creating a significant gap in the search for top partners. This paper investigates the discovery potential of the specific cascade decay $T \to H^\pm b \to \tau \nu b$ at the High-Luminosity LHC (HL-LHC).

Methodology
The authors perform a model-independent collider analysis within a Type-II 2HDM augmented by a singlet up-type VLQ. The signal topology involves the pair production of top partners followed by the cascade decay:
$$pp \to T\bar{T} \to (H^+ b)(H^- \bar{b}) \to (\tau^+ \nu_\tau b)(\tau^- \bar{\nu}_\tau \bar{b})$$
This results in a final state of two hadronic tau leptons ($\tau_h$), two $b$-jets, and missing transverse energy ($\not{E}_T$).

• Simulation and Backgrounds: Signal and background events are generated using MadGraph5_aMC@NLO (LO accuracy) interfaced with Pythia 8 and Delphes 3 (ATLAS detector card). The dominant backgrounds include $t\bar{t} + \text{jets}$ (where both tops decay to $W \to \tau \nu$), $t\bar{t}V$ ($V=W,Z,H$), and single-top production. Higher-order K-factors are applied to normalize backgrounds.
• Event Selection: A sequential cut-based analysis is employed. Baseline requirements include exactly two $\tau_h$ candidates ($p_T > 30$ GeV, $|\eta| < 2.5$) and at least two $b$-tagged jets. Lepton vetoes suppress dileptonic $t\bar{t}$.
• Kinematic Observables: To handle the unmeasured longitudinal neutrino momentum, an effective four-vector for $\not{E}_T$ is constructed. Discriminants include global variables ($\not{E}_T$, scalar sum $S_T$) and multi-body effective invariant masses ($IM(\not{E}_T, \tau, \tau)$, $IM(\not{E}_T, \tau, b)$). Cuts are optimized to maximize Asimov significance for a benchmark point ($M_T = 1500$ GeV, $M_{H^\pm} = 500$ GeV).
• Tau Polarization: As a complementary probe, the authors examine polarization-sensitive observables ($R_1, R_2$) derived from hadronic $\tau$ decay products. Since the signal $\tau$s originate from a scalar $H^\pm$ (right-handed helicity) while background $\tau$s from $W$ bosons are left-handed, these variables offer orthogonal discrimination power.
• Statistical Analysis: Discovery ($5\sigma$) and exclusion ($2\sigma$) sensitivities are evaluated using the Asimov significance formalism with a conservative 10% systematic uncertainty on background normalization.

Key Contributions and Results
The study presents the first dedicated analysis of the $2\tau + 2b + \not{E}_T$ channel for non-standard VLQ decays at the HL-LHC ($\mathcal{L} = 3 \text{ ab}^{-1}$, $\sqrt{s} = 14$ TeV).

1. Discovery Reach: For an optimistic scenario where the cascade branching ratio product $B \equiv \text{BR}(T \to H^\pm b) \times \text{BR}(H^\pm \to \tau \nu) = 1$, the analysis achieves $5\sigma$ discovery sensitivity for $T$ masses up to approximately 1.9 TeV. The $2\sigma$ exclusion reach extends to approximately 2.05–2.18 TeV, depending on the charged Higgs mass ($M_{H^\pm}$).
2. Model Independence: Results are presented as contours in the $(M_T, B)$ and $(M_{H^\pm}, M_T)$ planes, allowing reinterpretation in any BSM scenario involving a heavy colored fermion decaying via a charged Higgs.
3. Background Suppression: The sequential cuts effectively suppress the dominant $t\bar{t}$ background by several orders of magnitude while maintaining signal efficiency. The residual background is dominated by $t\bar{t}$, with $Z(\to \tau\tau) + \text{jets}$ becoming relevant at lower $S_T$.
4. Polarization Utility: The analysis demonstrates that the signal and background populate distinct regions in the $(R_1, R_2)$ plane. While not included in the baseline cut-based selection, the authors note that incorporating these variables into multivariate or machine-learning analyses could further improve sensitivity, particularly for high $M_T$ where kinematic separation alone may be insufficient.

Significance
The paper claims that the $2\tau + 2b + \not{E}_T$ channel provides a "promising and largely orthogonal avenue" to search for non-standard VLQ decays. It addresses a critical blind spot in current experimental programs, which focus on SM-like decay modes. By establishing sensitivity to $T$ masses up to ~1.9 TeV, this work motivates dedicated experimental searches for top partners in extended Higgs sectors. The authors emphasize that ignoring these non-standard decay modes could lead to missed discoveries, even if the mass of the VLQ falls within the reach of current SM-focused searches. The results are framed as a necessary complement to existing VLQ search strategies, highlighting the importance of considering extended Higgs sector signatures in future HL-LHC analyses.