⚛️ phenomenology

Exploring the $t\bar{t}$ threshold at an electron-positron collider

This paper presents a prospect study demonstrating that a future Circular Electron-Positron Collider (CEPC) can achieve a top-quark mass measurement precision of a few MeV—nearly two orders of magnitude better than HL-LHC projections—by scanning the $t\bar{t}$ threshold, though this potential is currently limited by theoretical uncertainties in cross-section calculations.

Original authors: Leyan Li, Yuming Lin, Xiaohu Sun, Yajun Mao, Zhan Li, Kaili Zhang, Shudong Wang, Gang Li, Hongbo Liao, Yaquan Fang

Published 2026-03-19

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CC BY 4.0

Original authors: Leyan Li, Yuming Lin, Xiaohu Sun, Yajun Mao, Zhan Li, Kaili Zhang, Shudong Wang, Gang Li, Hongbo Liao, Yaquan Fang

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

Imagine you are trying to weigh a ghost.

That's essentially what particle physicists are doing with the top quark. It's the heaviest known elementary particle in our universe, but it's so unstable that it vanishes in a trillionth of a trillionth of a second. Because it disappears so fast, we can't just put it on a scale. Instead, we have to infer its weight by watching how it behaves when it's created.

For decades, we've been trying to weigh this ghost using giant proton smashers (like the Large Hadron Collider, or LHC). But proton smashers are like trying to find a specific needle in a haystack by throwing two haystacks together at high speed. You get a lot of needles, but the "hay" (the messy debris from the protons) makes it very hard to get a precise measurement. The best we've done so far is accurate to about 330 million electron-volts (a unit of mass). That's like weighing a human and being off by the weight of a small dog.

The New Approach: The "Slow-Motion" Collision

This paper proposes a different strategy using a future machine called the CEPC (Circular Electron-Positron Collider).

Think of the LHC as a chaotic mosh pit where everything is flying everywhere. The CEPC, however, is like a precision ballet. It smashes electrons and their antimatter twins (positrons) together. Because these particles are clean and fundamental, the collision is much cleaner.

But the real magic happens at the threshold.

Imagine you are trying to start a car. If you press the gas pedal just a tiny bit, nothing happens. If you press it a little harder, the engine sputters. But right at the exact moment the engine catches, a tiny change in how hard you press the pedal makes a huge difference in how fast the car goes.

The top quark behaves similarly. There is a very specific energy level (the "threshold") where top quarks start to appear. Right at this tipping point, the physics is incredibly sensitive. If you change the top quark's mass by a tiny amount, the number of top quarks produced changes dramatically.

The "Five-Point Scan" Strategy

The authors of this paper suggest a clever way to measure this. Instead of guessing the energy, they propose a five-step dance:

They will set the collider to five specific energy levels, hovering just around the point where top quarks are born (342 to 344 GeV).
At each step, they count how many top quarks appear.
By looking at the shape of this "curve" (how the number of particles rises and falls), they can reverse-engineer the exact mass of the top quark.

It's like tuning a radio. You turn the dial slightly left, then right, then left again. By listening to how the static changes, you can pinpoint the exact frequency of the station with incredible precision.

What They Found

Using a detailed computer simulation of the CEPC's new detector design, the team calculated what would happen if they ran this experiment.

The Result: They could measure the top quark's mass with a precision of about 7 MeV (million electron-volts).
The Comparison: This is two orders of magnitude (100 times) better than what the future High-Luminosity LHC can achieve.
The Analogy: If the LHC measurement is like weighing a person and being off by a dog, the CEPC measurement would be like weighing that same person and being off by a grain of sand.

Why Does This Matter?

Why do we care about weighing a grain of sand? Because the top quark is the "anchor" of our universe's stability.

The Vacuum Stability: The universe is like a ball sitting in a valley. We think we are in a stable valley, but the heavy weight of the top quark is pulling on the landscape. If the top quark is even slightly heavier or lighter than we think, it might mean our universe is actually in a "metastable" state—like a ball balanced on a hilltop, waiting to roll down into a deeper valley. If that happens, the laws of physics as we know them would change instantly.
The "God Particle" Connection: The top quark gets its mass from the Higgs field (the "God Particle"). Measuring the top quark's mass precisely tells us how strongly it talks to the Higgs. This helps us understand if the Standard Model (our current rulebook of physics) is complete or if there are hidden rules we haven't discovered yet.

The One Catch: Theory vs. Reality

The paper concludes with a "but."

While the machine (the CEPC) and the math (the statistical analysis) are ready to give us this grain-of-sand precision, our current theoretical calculations aren't quite there yet.

Think of it like this: You have a super-precise ruler (the CEPC) that can measure to the micrometer. But the blueprint you are using to interpret the measurement has a smudge on it. The smudge represents the "theoretical uncertainty" in how we calculate the top quark's behavior.

Currently, this smudge is bigger than the precision of the ruler. The authors show that if we can clean up the smudge (improve the theoretical math to higher orders), the CEPC could revolutionize our understanding of the universe.

Summary

This paper is a roadmap for the future. It says: "We have built a blueprint for a machine that can weigh the heaviest particle in the universe with unprecedented precision. We know exactly how to do it, and we know it will tell us if our universe is stable. The only thing holding us back is that our math needs a little polishing."

It's a promise that in the near future, we might finally know the true weight of the universe's heaviest building block.

1. Problem Statement

The top quark mass ( $m_t$ ) is a fundamental parameter of the Standard Model (SM), critical for determining the stability of the electroweak vacuum. Currently, $m_t$ is measured exclusively at hadron colliders (Tevatron and LHC) via direct reconstruction of decay products.

Limitations of Hadron Colliders: These measurements yield a "Monte Carlo mass" ( $m_t^{MC}$ ), which is not a rigorously defined field-theoretic parameter. They are limited by non-perturbative QCD effects at the scale $\Lambda_{QCD} \sim 200$ MeV, resulting in total uncertainties of $\sim 330$ MeV (LHC) and a projected $\sim 200$ MeV for the High-Luminosity LHC (HL-LHC). This precision is insufficient to definitively determine the stability of the electroweak vacuum.
Theoretical Gap: Extracting a well-defined mass scheme (e.g., pole mass $m_t^{Pole}$ or $\overline{MS}$ mass) from hadron collider data is difficult and currently limited to GeV-level precision.
Opportunity: Electron-positron ( $e^+e^-$ ) colliders offer a unique environment where the $t\bar{t}$ production cross-section near the kinematic threshold is highly sensitive to $m_t$ , allowing for measurements in a well-defined renormalization scheme with $\mathcal{O}(10)$ MeV precision, free from $\Lambda_{QCD}$ ambiguities.

2. Methodology

The authors present the first prospect study for a simultaneous determination of $m_t$ , the top-quark width ( $\Gamma_t$ ), the strong coupling constant ( $\alpha_S$ ), and the top-Yukawa coupling modifier ( $y_t$ ) using the Circular Electron-Positron Collider (CEPC).

Detector and Simulation:
- Utilized the latest CEPC reference detector design (TDR 2025).
- Generated Monte Carlo samples using MG5_aMC@NLO for signal ( $t\bar{t}$ ) and backgrounds (single top, $WW$, $ZZ$, etc.).
- Processed events through PYTHIA 8.3 (showering/hadronization) and DELPHES (parametric detector simulation) using the specific CEPC card.
Theoretical Framework:
- Calculated the $t\bar{t}$ cross-section near threshold at N $^3$ LO QCD (using resummed non-relativistic perturbation theory via QQbar_threshold) and NNLO Electroweak.
- Adopted the Potential-Subtracted (PS) mass scheme to avoid renormalon ambiguities inherent in the pole mass.
- Included Initial State Radiation (ISR) and Luminosity Spectrum (LS) effects (beam energy spread).
Experimental Strategy:
- Scan Points: A five-point energy scan at $\sqrt{s} = \{342.0, 342.5, 343.0, 343.5, 344.0\}$ GeV to capture sensitivity peaks for all parameters.
- Luminosity Scenarios:
  - BASE: 280 fb $^{-1}$ (2 interaction points, 1 year).
  - EXT: 420 fb $^{-1}$ (50% luminosity upgrade).
- Channels: Analyzed two decay channels with high branching ratios:
  1. Full-hadronic: $t\bar{t} \to b\bar{b} q\bar{q}' q\bar{q}''$ (BR $\approx 44.2\%$ ).
  2. Semi-leptonic: $t\bar{t} \to b\bar{b} q\bar{q}' \ell\nu$ (BR $\approx 29.9\%$ ).
- Event Selection: Optimized kinematic cuts based on jet clustering ( $k_T$ algorithm), particle-flow object (PFO) multiplicities, event shape variables (Sphericity, Thrust), and $b$ -tagging.
- Kinematic Fit: Applied a $\chi^2$ fit with constraints on energy/momentum conservation and $W/t$ masses to resolve jet-parton pairing and suppress backgrounds.
- Statistical Analysis: Used a profiled likelihood scan to extract parameters. Systematic uncertainties (luminosity, beam energy, $b$ -tagging, $\alpha_S$ , $y_t$ ) were profiled, while the theoretical cross-section uncertainty was evaluated separately.

3. Key Contributions

First CEPC Reference Detector Study: This is the first analysis to incorporate the latest CEPC reference detector design (TDR 2025) for $t\bar{t}$ threshold physics, providing a realistic assessment of detector performance.
Simultaneous Parameter Extraction: Demonstrated the feasibility of simultaneously measuring $m_t$ , $\Gamma_t$ , $\alpha_S$ , and $y_t$ in a single scan, optimizing the use of the threshold region's sensitivity.
Optimized Kinematic Selections: Developed new, dedicated kinematic selections and multi-dimensional optimizations specifically for the CEPC threshold environment, significantly improving signal-to-background ratios.
Comprehensive Uncertainty Budget: Provided a detailed breakdown of statistical and systematic uncertainties, identifying the theoretical cross-section calculation as the current bottleneck.

4. Key Results

The study quantifies the precision achievable in the BASE and EXT scenarios (excluding theoretical cross-section uncertainty):

Top Quark Mass ( $m_t$ ):
- Precision: 7.5 MeV (BASE) and 6.8 MeV (EXT).
- This is nearly two orders of magnitude better than HL-LHC projections (200 MeV).
- If theoretical uncertainties are reduced to match statistical levels, precision could reach a few MeV ( $\sim 10^{-5}$ relative precision).
Top Quark Width ( $\Gamma_t$ ):
- Precision: 19.4 MeV (BASE) and 16.2 MeV (EXT).
- Represents an order-of-magnitude improvement over current capabilities.
Strong Coupling ( $\alpha_S$ ) and Yukawa Coupling ( $y_t$ ):
- $\delta \alpha_S \approx 0.0014$ (BASE) / $0.0012$ (EXT).
- $\delta y_t \approx 0.20$ (BASE) / $0.16$ (EXT).
- These measurements are complementary to those from the Z-pole and above-threshold regions.
Dominant Uncertainties:
- Statistical: Currently the largest contributor (e.g., 5.6 MeV for $m_t$ in BASE).
- Systematic: The top Yukawa coupling ( $y_t$ ) and $\alpha_S$ uncertainties are the leading systematic sources.
- Theoretical: The N $^3$ LO cross-section calculation uncertainty is the limiting factor. Varying the renormalization scale results in asymmetric shifts: $+1.3/-32.9$ MeV for $m_t$ and $<+0.1/-79.9$ MeV for $\Gamma_t$ .

5. Significance

Precision Standard Model Tests: Achieving $m_t$ precision at the few-MeV level would allow for a definitive test of the electroweak vacuum stability, a question currently unanswerable with hadron collider data.
Theoretical Motivation: The results highlight a critical need for higher-order QCD calculations (beyond N $^3$ LO) to reduce theoretical uncertainties and fully exploit the potential of future lepton colliders.
Collider Physics Benchmark: This study establishes the CEPC (and by extension FCC-ee) as a premier facility for precision top-quark physics, capable of measuring fundamental parameters with unprecedented accuracy, surpassing the HL-LHC by a significant margin.