⚛️ phenomenology

Sensitivity to Single Vector-Like Bottom Quark Production at 3 TeV CLIC

This paper demonstrates that a multivariate analysis at a 3 TeV CLIC can achieve a discovery significance exceeding $5\sigma$ for the single production of vector-like bottom quarks in a type-II Two-Higgs-Doublet Model with masses between 1.3 and 1.5 TeV, even with a 15% background normalization uncertainty, whereas a traditional cut-based approach fails to reach discovery sensitivity.

Original authors: R. Benbrik, M. Berrouj, M. Boukidi, M. Ech-chaouy, K. Kahime, K. Salime

Published 2026-08-18

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CC BY 4.0

Original authors: R. Benbrik, M. Berrouj, M. Boukidi, M. Ech-chaouy, K. Kahime, K. Salime

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The universe as we understand it is built on a foundation of particles and forces, a framework known as the Standard Model. For decades, this model has successfully explained how matter behaves, from the smallest atoms to the vastest stars. Yet, physicists know it is incomplete. It cannot explain why particles have mass, why there is more matter than antimatter, or what makes up the invisible dark matter that holds galaxies together. To fill these gaps, scientists propose that the universe contains hidden layers of reality, populated by new, heavy particles that have not yet been seen. One such proposal involves "vector-like quarks," a type of heavy particle that behaves differently from the ordinary quarks that make up protons and neutrons. Unlike ordinary quarks, which have a specific handedness that dictates how they interact with forces, these new particles would interact symmetrically, allowing them to exist with a mass that does not depend on the mechanism that gives other particles their weight. If these particles exist, they would likely be too heavy to be created by current machines, but they might reveal themselves in the future at a new kind of particle collider.

Researchers are now looking ahead to a machine called the Compact Linear Collider, a proposed facility that would smash electrons and positrons together at energies far beyond what is currently possible. In a recent study, a team of physicists simulated what would happen if this machine, operating at an energy of 3 TeV, were to produce a single vector-like bottom quark. This specific particle is a heavy cousin of the bottom quark, one of the six types of quarks in the Standard Model. The team focused on a scenario where this heavy quark is produced alongside a regular bottom quark and then decays into a bottom quark and a new, heavy Higgs boson. This heavy Higgs boson would then immediately break apart into a pair of top quarks, the heaviest known particles. The final result of this chain reaction would be a complex spray of particles: a charged lepton, missing energy carried away by invisible neutrinos, and several jets of particles, including four that originate from bottom quarks and two from lighter quarks.

To see if this signal could be found, the researchers first applied a set of standard filters, similar to sifting through a pile of sand to find a few specific grains. They looked for events with the right number of particle jets and high energy. However, the background noise from ordinary particle interactions was so overwhelming that this simple method could not distinguish the new signal with enough certainty. Even with the maximum amount of data the collider is expected to collect, the simple filters left the signal buried, falling short of the statistical threshold required to claim a discovery. The researchers then turned to a more sophisticated approach, using machine learning algorithms to analyze the data. They trained two different types of artificial intelligence: one that builds a decision tree by asking a series of questions about the particle data, and another that mimics the way neurons in a brain connect to recognize patterns. These systems were fed millions of simulated events, learning to spot the subtle differences between the rare signal and the common background noise.

The results of this advanced analysis were striking. By using these machine learning tools, the team found that the signal could be separated from the background with much greater clarity. For a range of heavy quark masses between 1.3 and 1.5 TeV, the simulations showed that the signal would stand out clearly, reaching a level of certainty that physicists call a five-sigma discovery. This means that the chance of the result being a random fluke is less than one in a few million. Even when the researchers accounted for a fifteen percent uncertainty in how well they could predict the background noise, the signal remained strong enough to be detected. The study also showed that this method works best for particles with intermediate masses, where the decay patterns are most distinct. The research demonstrates that if these heavy vector-like quarks exist and decay in this specific way, the future Compact Linear Collider would be powerful enough to find them, opening a new window into the extended structure of the universe.

Technical Summary: Sensitivity to Single Vector-Like Bottom Quark Production at 3 TeV CLIC

Problem and Motivation
The discovery of the Higgs boson confirmed the existence of a scalar sector associated with electroweak symmetry breaking, yet it remains unclear whether this sector is minimal or contains additional states. Extended scalar sectors, such as the Two-Higgs-Doublet Model (2HDM), often arise in Beyond the Standard Model (BSM) theories. When such models are extended by Vector-Like Quarks (VLQs), new decay channels emerge that are not accessible in the Standard Model (SM). Specifically, heavy fermions can decay into additional neutral or charged Higgs bosons (e.g., $B \to \phi b$ where $\phi = H, A$ ), which subsequently decay into top-quark pairs.

Current collider searches for VLQs typically assume decays into SM gauge bosons ( $W, Z$ ) and the SM-like Higgs ( $h$ ). However, in the presence of an extended scalar sector, these "exotic" decay modes can compete with or dominate standard channels. This paper investigates the sensitivity of the Compact Linear Collider (CLIC) operating at a center-of-mass energy of $\sqrt{s} = 3$ TeV to the single production of a vector-like bottom quark ( $B$ ) in a Type-II 2HDM extended by a $(T, B)$ doublet. The study focuses on the cascade process $e^+e^- \to B\bar{b} + \bar{B}b$ , followed by $B \to \phi b$ and $\phi \to t\bar{t}$ , probing the interplay between extended quark and Higgs sectors.

Methodology
The authors employ a comprehensive analysis strategy combining theoretical constraints, Monte Carlo simulation, and machine learning techniques:

Theoretical Framework and Constraints: The study utilizes a CP-conserving Type-II 2HDM extended by a $(T, B)$ doublet. The parameter space is constrained by:
- Theoretical requirements: Perturbative unitarity, vacuum stability, and scalar sector perturbativity.
- Electroweak precision observables: Global fits to $S$ and $T$ parameters (with $U=0$ ).
- Higgs sector bounds: Compatibility with the 125 GeV Higgs signal strengths and exclusion limits for heavy scalars ( $H, A, H^\pm$ ) using HiggsTools.
- Flavor and Collider limits: Constraints from $b \to s\gamma$ and LHC searches for VLQs.
  Three benchmark points (BP1, BP2, BP3) are selected with $m_B$ ranging from $\sim 1.0$ to $1.8$ TeV, satisfying all constraints.
Simulation and Event Selection:
- Signal: The process $e^+e^- \to B\bar{b} + \bar{B}b$ with $B \to \phi b$ and $\phi \to t\bar{t}$ is simulated using MadGraph5_aMC@NLO. The focus is on the semileptonic final state: one charged lepton, missing transverse momentum ( $E_T$ ), four $b$ -tagged jets, and two light jets.
- Backgrounds: Dominant SM backgrounds include $t\bar{t}bb$ , $t\bar{t}jj$ , $tWb$, and $WWV$ processes.
- Detector Simulation: Parton showering and hadronization are handled by Pythia 8.30, with detector effects modeled via Delphes 3.5.0 using a dedicated CLIC card. $b$ -tagging efficiency is set to 70%.
Analysis Strategies:
- Cut-Based Analysis: A selection of kinematic cuts is applied based on distributions of observables such as the number of $b$ -jets, total transverse energy ( $E_T$ ), and leading jet momenta.
- Multivariate Analysis (MVA): To improve discrimination, two machine learning classifiers are trained: a Multi-Layer Perceptron (MLP) and an XGBoost (gradient-boosted decision tree). The models utilize 16 input variables, including transverse momenta, angular separations, invariant masses, and jet multiplicities. The datasets are split into training (80%) and testing (20%) sets.

Key Results

Cut-Based Performance: The cut-based analysis fails to reach the $5\sigma$ discovery threshold for any of the three benchmark points at the projected integrated luminosity of $5 \text{ ab}^{-1}$ . The resulting significances are $3.82\sigma$ (BP1), $4.04\sigma$ (BP2), and $1.88\sigma$ (BP3). The primary limitation is the small post-selection signal cross section ( $\sim 10^{-2}$ fb) and insufficient background suppression.
Multivariate Performance: Both the MLP and XGBoost classifiers significantly improve signal-background separation.
- Discrimination Power: Both models achieve high Area Under the Curve (AUC) values ( $\sim 0.95-0.96$ ) on test sets, with XGBoost showing a marginal but consistent advantage over the MLP. Kolmogorov-Smirnov tests confirm negligible overtraining.
- Discovery Sensitivity: With a $15\%$ systematic uncertainty on background normalization, both classifiers maintain a significance above $5\sigma$ for vector-like bottom quark masses ( $m_B$ ) in the range of $1.1 $–$ 1.5$ TeV (MLP) and $1.0 $–$ 1.5$ TeV (XGBoost).
- Extended Reach: For a $10\%$ uncertainty, the XGBoost analysis extends the $5\sigma$ reach to $m_B = 1.6$ TeV.
- Mass Dependence: The highest sensitivity occurs in the intermediate mass region ( $m_B \approx 1.3$ –$1.5$ TeV), where the increasing branching ratio of $B \to \phi b$ and improved kinematic separation compensate for the falling production cross section.

Significance and Claims
The paper concludes that while standard cut-based analyses are insufficient for discovering non-standard VLQ decays at CLIC, multivariate techniques can substantially enhance sensitivity. The study demonstrates that CLIC at 3 TeV has the potential to probe the connection between extended fermion and scalar sectors through the single production of vector-like bottom quarks decaying into heavy neutral Higgs bosons.

The authors modestly claim that their work provides a direct test of parameter regions difficult to access via direct heavy-Higgs production alone. They emphasize that the nonstandard channels lead to final states with multiple heavy-flavor jets and top quarks, which are not fully covered by conventional VLQ searches. The results suggest that heavy-Higgs decays of vector-like quarks constitute a useful and complementary search channel for future high-energy lepton colliders, provided advanced multivariate analysis methods are employed. The paper does not propose new experimental hardware or future collider upgrades beyond the existing CLIC 3 TeV scenario.

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