⚛️ phenomenology

Searching for vectorlike $T$ quarks in the $T\to tZ$ channel at a future muon-proton collider

This paper investigates the discovery potential of singly produced vector-like top quarks ( $T$ ) decaying via $T\to tZ$ at future muon-proton colliders, demonstrating through full detector simulations that this channel offers complementary sensitivity and unique advantages for probing high-mass VLQs compared to other decay modes and collider facilities.

Original authors: Yin-Hao Gao, Yao-Bei Liu

Published 2026-08-31

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CC BY 4.0

Original authors: Yin-Hao Gao, Yao-Bei Liu

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

Deep within the subatomic world, physicists have long suspected that the known particles are only a fraction of the full story. The Standard Model, our best current map of matter, works beautifully but leaves gaps, such as why the universe has mass or why certain forces behave the way they do. To fill these gaps, theorists propose the existence of "vector-like quarks," heavy cousins of the familiar top quark that might exist at energy levels far beyond what we can currently reach. Unlike the particles we know, these heavy partners would not be constrained by the same rules of symmetry, allowing them to be much heavier and potentially stable enough to be found. Finding one would be a monumental shift, confirming that the universe is built on a more complex foundation than we currently understand. The challenge is that these particles are so massive that they require collisions of immense energy to create, and even then, they decay instantly into other particles, leaving behind only a fleeting, messy signature that must be distinguished from a sea of ordinary background noise.

A team of researchers has turned its attention to a specific type of future machine, a muon-proton collider, to see if it could spot these elusive heavy particles. In this proposed facility, a beam of muons, which are heavy versions of electrons, would smash into a beam of protons. The researchers focused their search on a specific scenario: a single heavy top-like quark being created and then immediately decaying into a standard top quark and a Z boson, a neutral particle that carries the weak force. The top quark would then break apart into a lighter quark and a W boson, which decays into a charged lepton and a neutrino, while the Z boson splits into two quarks that fly so close together they merge into a single, large spray of particles. This specific combination of decay products creates a unique fingerprint that the researchers hoped to isolate from the overwhelming background of ordinary particle collisions.

To test this idea, the team ran detailed computer simulations of what would happen if such a machine existed, modeling three different energy levels: 5.29, 6.48, and 9.16 TeV. They simulated millions of collision events, tracking how the signal particles would behave and how they would be detected by a hypothetical instrument. They also simulated the vast number of background events that occur naturally, such as standard top quarks being produced or Z bosons appearing without the heavy partner. By applying a series of strict filters to their data, they looked for events that matched the specific pattern of a heavy particle decaying: a high-energy lepton, a heavy jet of particles with a mass matching the Z boson, and missing energy caused by the invisible neutrino. The simulations showed that while the background noise was significant, the unique signature of the heavy particle could be separated out with high precision, especially at the highest energy levels.

The results of these simulations were promising. The researchers found that with enough data, the machine could not only rule out the existence of these heavy particles up to certain masses but could also discover them if they exist within a specific range of weights and interaction strengths. At the highest energy setting of 9.16 TeV, the team calculated that they could potentially discover a heavy top-like quark with a mass up to 3.1 TeV, provided the particle interacts with ordinary matter with a certain strength. Even if the particle is slightly heavier, the machine could still set strict limits, proving that such a particle does not exist below a mass of 3.7 TeV. These capabilities represent a significant leap forward compared to current experiments at the Large Hadron Collider, which have so far only been able to exclude these particles up to about 1.5 TeV. The muon-proton collider offers a cleaner environment with less background noise, allowing it to peer deeper into the high-mass frontier.

The study also compared this specific search method against other ways of looking for these particles, such as searching for a different decay path where the heavy particle turns into a W boson and a bottom quark. The researchers found that while the decay into a Z boson happens less frequently, it offers a distinct advantage. The way the particles fly apart in this specific decay creates a kinematic signature that is easier to distinguish from the background noise than other methods. This means that searching for this specific decay mode is not just a backup plan, but a powerful, complementary strategy that could confirm a discovery with greater certainty. The team concluded that if these heavy particles exist within the mass ranges they studied, a future muon-proton collider would be an ideal tool to find them, offering a clear path to uncovering new physics beyond our current understanding.

Technical Summary: Searching for Vectorlike T Quarks in the $T \to tZ$ Channel at a Future Muon-Proton Collider

Problem and Motivation
Vector-like quarks (VLQs) are predicted by various Beyond the Standard Model (BSM) extensions, such as little Higgs and composite Higgs models. The singlet VLQ-T state, carrying an electric charge of $+2e/3$ , can decay via $T \to bW$ , $tZ$ , or $th$. While current Large Hadron Collider (LHC) searches have established mass limits around 1.3–1.46 TeV for singlet VLQ-Ts, the complementary decay channel $T \to tZ$ remains unexplored in the context of future muon-proton ( $\mu p$ ) colliders. Although the branching ratio for $T \to tZ$ is approximately half that of the dominant $T \to Wb$ mode in the high-mass limit, the unique final-state topology—featuring a semileptonically decaying top quark and a hadronically decaying $Z$ boson reconstructed as a fat jet—offers distinct kinematic handles for background suppression. This study investigates the discovery potential of singly produced VLQ-Ts in the $T \to tZ$ channel at a future $\mu p$ collider, leveraging the reduced QCD backgrounds characteristic of this machine compared to the LHC.

Methodology
The authors employ a simplified effective model for a singlet VLQ-T, defined by two parameters: the mass $m_T$ and the effective coupling $g^*$ . The analysis focuses on the single production process $\mu p \to \nu_\mu T \bar{b}$ via $Wb$ fusion, followed by the decay chain $T \to tZ \to (b\ell\nu)(q\bar{q})$ . The final state consists of an isolated lepton, a $b$ -tagged jet, a large-radius "fat" jet ( $J$ ) reconstructing the $Z$ boson, and missing transverse momentum ( $E_T^{\text{miss}}$ ) from the neutrino.

The study utilizes full detector-level Monte Carlo simulations for three benchmark center-of-mass (c.m.) energies: $\sqrt{s} = 5.29$ , $6.48$, and $9.16$ TeV, with a fixed proton beam energy of 7 TeV and varying muon beam energies. Signal and dominant irreducible Standard Model (SM) backgrounds ( $\mu p \to \nu_\mu t j$ , $\nu_\mu t Z j$ , and $\nu_\mu W Z j$ ) are generated using MadGraph5-aMC@NLO with NNPDF23L01 parton distribution functions. Parton showering and hadronization are handled by Pythia 8.3, while detector effects are simulated using Delphes 3.4.2 with an LHeC detector card.

Kinematic selection cuts are optimized based on the signal's harder transverse momentum spectra and the distinct $Z$ -boson mass peak in the fat jet invariant mass ( $M_J$ ). Key cuts include:

A fat jet with $p_T^J > 400$ GeV and $|M_J - m_Z| < 10$ GeV.
At least one isolated lepton and one $b$ -tagged jet, with the leading $b$ -jet satisfying $p_T^b > 150$ GeV and $\Delta R_{b,\ell} < 1.0$ .
A reconstructed invariant mass of the lepton- $b$ -jet-fat jet system $M_{b\ell J} > 800$ GeV.

Significance calculations for discovery ( $5\sigma$ ) and exclusion (95% CL) are performed using the Asimov formula, assuming an integrated luminosity of $1000 \text{ fb}^{-1}$ and a conservative systematic uncertainty of $\delta_{\text{sys}} = 20\%$ .

Key Results
The analysis demonstrates that the $\mu p$ collider offers significant sensitivity to the $T \to tZ$ channel, particularly in the high-mass region:

Discovery Reach ( $5\sigma$ ): With $1000 \text{ fb}^{-1}$ $1000 fb^{- 1}$ and $\delta_{\text{sys}} = 20\%$ $δ_{sys} = 20%$ , the collider can discover VLQ-Ts with masses up to:
- $2.2$ TeV at $\sqrt{s} = 5.29$ TeV (for $g^* \in [0.16, 0.5]$ ).
- $2.5$ TeV at $\sqrt{s} = 6.48$ TeV (for $g^* \in [0.12, 0.5]$ ).
- $3.1$ TeV at $\sqrt{s} = 9.16$ TeV (for $g^* \in [0.09, 0.5]$ ).
Exclusion Limits (95% CL): The projected exclusion limits extend to masses of $2.5$, $3.0$, and $3.7$ TeV for the respective energies, probing coupling values as low as $g^* \approx 0.06$ –$0.08$ at $m_T \sim 1.5$ TeV.
Comparison with Other Facilities: The study compares these results with current LHC bounds and projected High-Luminosity LHC (HL-LHC) sensitivities. The $\mu p$ collider results show a significant improvement in sensitivity, capable of probing much smaller coupling values ( $g^*$ ) at the same mass scale compared to current LHC limits.
Comparison with $T \to Wb$ : While the $T \to Wb$ channel at the same $\mu p$ collider (analyzed in a separate study with $100 \text{ fb}^{-1}$ ) reaches slightly higher masses for $g^*=0.5$ , the $T \to tZ$ channel provides complementary sensitivity. The distinct topologies (fat jet from $Z$ vs. $W$ ) offer different systematic uncertainties and background rejection capabilities, suggesting that a combined analysis would strengthen discovery potential.

Significance and Claims
The paper claims that the $T \to tZ$ decay mode provides a complementary and unique avenue for probing high-mass vector-like T quarks at a future $\mu p$ collider. The primary significance lies in the machine's ability to significantly reduce QCD backgrounds compared to the LHC, allowing for the reconstruction of the boosted $Z$ -jet topology with high efficiency. The authors assert that the $\mu p$ collider offers "significantly enhanced and complementary sensitivity" for singlet VLQ-T searches, particularly in the high-mass region where LHC capabilities are limited.

The study also addresses the validity of the narrow-width approximation (NWA), noting that for $\Gamma_T/m_T \leq 10\%$ , the results remain robust. The authors acknowledge that their calculations are performed at leading order (LO) and do not include next-to-leading order (NLO) corrections or full off-shell interference effects, but argue that these higher-order effects are unlikely to qualitatively alter the main conclusions regarding the discovery potential. Finally, the paper notes that alternative decay topologies (e.g., invisible $Z$ decays or fully hadronic top decays) were not fully analyzed due to lower signal cross-sections and overwhelming SM backgrounds, reinforcing the choice of the semileptonic top/hadronic $Z$ channel as the optimal search strategy.

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